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Unit 1 Fundamental Concepts Chemistry 020, R. R. Martin 1 Introduction Q: What is chemistry? A: The study of matter and its properties at the atomic and molecular levels. Matter is anything that has mass and occupies space. It exists in three phases (= states): solid: rigid shape and fixed volume liquid: fixed volume but not rigid in shape gas: neither fixed volume nor rigid shape 2 Properties of Substances Physical properties: Can be observed without changing the chemical identity of a substance (i.e. without making or breaking covalent bonds) Examples: Melting point and boiling point. A substance that melts at 0°C and boils at 100°C is most likely water. Solubility - table salt (NaCl) is easily dissolved in water, copper (Cu) is not. 1 Color: Substances are colored if they selectively absorb certain wavelength regions of the visible spectrum. Chemical properties are observed when a substance takes part in a chemical reaction. Mercury II oxide decomposes to mercury (Hg) and oxygen when heated to 600°C. Physical and chemical properties can be used to identify a substance. We indicate the physical state of matter by following its formula with one of these symbols: (s) solid (l) liquid (g) gaseous H2O(l): liquid water H2O(s): ice H2O(g): water vapor Element: A type of matter that cannot be broken down into two or more pure substances. Alternatively: A substance in which all atoms have the same atomic number. Every element is identified by its symbol, e.g. C (carbon), Cu (copper), He (Helium), Hg (mercury) 2 3 Atoms Atom: a neutral species consisting of • Protons (particles carrying one positive charge (+1), and a mass of ~1 amu [atomic mass units]) • Neutrons (neutral particles, mass ~1 amu) Protons and neutrons form the atomic nucleus • Electrons (e-, particles carrying one negative charge (-1), their mass is small, ~1/2000 amu). If you want, you can imagine that the electrons “orbit” around the nucleus, like the planets around the sun. Example - Helium atom: 2 protons, 2 electrons, 2 neutrons, mass ~ 4 amu In an atom, the number of electrons is equal to the number of protons, so that the overall charge is zero. Positive and negative charges attract each other, that is why electrons are “bound” to the nucleus. (The nucleus is extremely small, most of the atom is “empty”. The diameter of an atom is 10,000 times that of its nucleus). The chemical properties of an atom are determined by its electrons. BUT the number of electrons is determined by the number of protons in the nucleus. We can define the atomic number Z: 3 Z = number of protons Remember the definition of element: “A substance in which all atoms have the same atomic number” Symbol H He Li Be B C N O F Ne Element name Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Z 1 2 3 4 5 6 7 8 9 10 Example: all carbon atoms have six protons and six electrons The mass number A of an atom is obtained by adding up the number of protons and neutrons in the nucleus. A = number of protons + number of neutrons 4 We can thus describe the composition of the nucleus by a nuclear symbol; it is written in the following way: Mass Number A Z Atomic Number X Element symbol The number of neutrons is therefore given by A – Z. Examples: 12 Carbon: 6 C 235 Uranium: 92 often called C-12 U often called U-235 However, not all atoms of one element have the same mass. They can differ in their number of neutrons. Atoms that contain the same number of protons, but a different number of neutrons are called isotopes. 5 Example: There are three isotopes of hydrogen 1 1 H ”protium” – zero neutrons usually what we mean when we say hydrogen (of course it is most commonly found as the molecule H2) (This is the most common isotope of hydrogen) 2 1 H ”deuterium” – one neutron (Sometimes the symbol “D” is used instead) 3 1 H ”tritium” – two neutrons (Sometimes the symbol “T” is used instead) For the most part, isotopes of the same element have very similar chemical properties because they have the same number of electrons. Note: Some atoms are radioactive and decay to form different elements (transmutation) 14 6C → 7N14 + e- 6 The mass of atoms (and molecules) can be measured by mass spectrometry. It shows that chlorine consists of two isotopes: 35 17 Cl mass 34.97 amu, with 75.53% abundance 37 17 Cl 36.97 amu, with 24.47% abundance (Note: these are atom %'s, not mass %'s) The mass of an element is usually represented as the weighted average of all its isotopes (i.e. in the periodic table, see below) For Cl: 34.97 amu × 0.7553 + 36.97 amu × 0.2447 = 35.46 amu Some elements have only one stable isotope, e.g. for sodium 23 11 Na is the only isotope. 7 For carbon there are two: 12 6 C 13 ~ 99% abundance, 6 C ~ 1% abundance 12 6 We define the mass of one C atom as exactly 12 amu (i.e. 12.0000000000000000000000000000 … amu) 8 EXAM QUESTION: Nov. 2004, Q1 Naturally-occurring magnesium consists of three isotopes. Of the three, 24Mg, atomic mass 23.985 amu, is 79.0% abundant, and 26Mg, atomic mass 25.983 amu, is 11.0% abundant. The number of neutrons in the nucleus of the third isotope is A) 10 B) 12 C) 13 D) 15 E) 16 The periodic table gives an average atomic mass for Mg of 24.31 amu and atomic # = 12 Let the third isotope = xMg. Its abundance must be 1 - .79 -0.11 = 0.1 Now: Average mass Mg = Fraction24Mg(mass 24Mg ) + Fraction26Mg(mass 26Mg ) + FractionxMg(mass xMg ) OR: 24.31 = .79 x 23.985 + 0.11 x 25.983 + 0.10(mass xMg ) mass xMg = 25.04 or 25Mg 25 = #of Protons + #of Neutrons = 12 + #of Neutrons #of Neutrons = 13 9 4 Brief Introduction to the Periodic Table The “official” Chem 020/023 periodic table is shown on the next page. It will be provided to you for exams. Learn how to use it !!! The horizontal rows in the table are called periods. As we go through these periods, there is a certain periodicity that is similar for most rows of the table. First period: Second period: H Li Be B C N O F He Ne The vertical columns are called groups (or “families”) Elements in the groups 1,2,13,14,15,16,17,18 are called main group elements. This is a new nomenclature; 13 used to be 3, 14 used to be 4, etc. Elements in group 1 are called alkali metals. Elements in group 2 are called alkaline earth metals. (owing to their tendency to form basic (=alkaline) hydroxides, i.e. Ca(OH)2) Elements in groups 3 - 12 are called transition metals. Elements in group 17 are called halogens. All halogens form stable molecules consisting of 2 atoms (F2, Cl2) Elements in group 18 are called noble gases. “Noble” indicates that they are very unreactive. They do not form stable molecules consisting of two atoms. He does exist, He2 does not exist. Ar does exist, Ar2 does not exist. Elements 58-71 are called lanthanides, 90-103 are called actinides. 10 Periodic Table of the Elements 1 18 1 H 1.008 2 13 14 15 16 17 2 He 4.003 3 Li 6.941 4 Be 9.012 5 B 10.81 6 C 12.01 7 N 14.01 8 O 16.00 9 F 19.00 10 Ne 20.18 11 Na 22.99 12 Mg 24.31 3 4 5 6 7 12 13 Al 26.98 14 Si 28.09 15 P 30.97 16 S 32.07 17 Cl 35.45 18 Ar 39.95 19 K 39.10 20 Ca 40.08 21 Sc 44.96 22 Ti 47.88 23 V 50.94 24 Cr 52.00 25 Mn 54.94 26 Fe 55.85 27 Co 58.93 28 Ni 58.69 29 Cu 63.55 30 Zn 65.39 31 Ga 69.72 32 Ge 72.61 33 As 74.92 34 Se 78.96 35 Br 79.90 36 Kr 83.80 37 Rb 85.47 38 Sr 87.62 39 Y 88.91 40 Zr 91.22 41 Nb 92.91 42 Mo 95.94 43 Tc (98) 44 Ru 101.1 45 Rh 102.9 46 Pd 106.4 47 Ag 107.9 48 Cd 112.4 49 In 114.8 50 Sn 118.7 51 Sb 121.8 52 Te 127.6 53 I 126.9 54 Xe 131.3 55 Cs 132.9 56 Ba 137.3 57 La 138.9 72 Hf 178.5 73 Ta 180.9 74 W 183.9 75 Re 186.2 76 Os 190.2 77 Ir 192.2 78 Pt 195.1 79 Au 197.0 80 Hg 200.6 81 Tl 204.4 82 Pb 207.2 83 Bi 209.0 84 Po (209) 85 At (210) 86 Rn (222) 87 Fr (223) 88 Ra (226) 89 Ac (227) 104 Rf (261) 105 Db (262) 106 Sg (266) 107 Bh (262) 108 Hs (265) 109 Mt (266) 110 111 112 (269) (272) (277) 58 Ce 140.1 59 Pr 140.9 60 Nd 144.2 61 Pm (145) 62 Sm 150.4 63 Eu 152.0 64 Gd 157.3 65 Tb 158.9 66 Dy 162.5 67 Ho 164.9 68 Er 167.3 69 Tm 168.9 70 Yb 173.0 71 Lu 175.0 90 Th 232.0 91 Pa (231) 92 U 238.0 93 Np (237) 94 Pu (242) 95 Am (243) 96 Cm (247) 97 Bk (247) 98 Cf (251) 99 Es (252) 100 Fm (257) 101 Md (258) 102 No (259) 103 Lr (260) 8 9 10 11 11 Elements in the same group tend to show very similar chemical properties, e.g. “Noble Gases” (group 18): He, Ne and Ar do not react with any other substances. Li, Na, K all react violently with water according to 2 Na + 2 H2O Æ 2 NaOH + H2 + HEAT Metals and Nonmetals The diagonal line starting at B and ending at Po separates the metals from the nonmetals. Metals are on the left; nonmetals are on the right. Metals are “shiny“ solids that conduct electric current (very low resistance); they also conduct heat very well. Nonmetallic solids tend not to conduct electric current (exception: carbon as graphite). Many nonmetals are gases (of course gases do not conduct electric current). The elements very close to the diagonal line are difficult to classify B Si Ge As Sb Te Boron silicon germanium arsenic antimony tellurium They have electric conductivities between those of metals and nonmetals and are often called metalloids. Especially Si, Ge and As are used as semiconductors. 12 5 Molecules It is rare to find isolated atoms in nature, only the noble gases He, Ne, Ar, …. consist of individual, nonreactive molecules. Most atoms tend to combine with one another in various ways. Molecules are neutral particles, consisting of two or more atoms. The atoms are held together by strong forces called covalent bonds. In a covalent bond, two atoms share a pair of electrons, details later. Molecules can be very small, such as H2 (2 amu); or they can be huge, like proteins (> 10,000 amu) The protein cytochrome c consists of thousands of atoms, all linked by covalent bonds. Its mass is 12,360 amu 13 Molecular substances are often represented as molecular formulas. Examples: H2O water, NH3 ammonia, CH4 methane Structural formulas are more informative, because they show the bonding pattern within the molecule. Examples: Lines in these structures represent covalent bonds. 14 Simplest (= “empirical”) formula gives the simplest whole-number ratio of the atoms in a compound The compounds with the molecular formula: which gives the actual number of atoms in a molecule of the substance, the molecular formulae: C2H4 and C3H6 both have the same simplest formula: CH2 C6H12O6 (glucose) simplifies to: CH2O For water and many other small molecules, the molecular formula and the simplest formula are identical. 15 6 Ions When an atom loses or gains electrons it becomes an ion. Generally, metals tend to lose electrons. Examples: Sodium (Na) and calcium (Ca) are metals Na Æ Na+ + eCa Æ Ca2+ + 2e- Positively charged ions are called cations. Nonmetals tend to gain electrons Cl + e- Æ ClNegatively charged ions are called anions. The ions dealt with so far are monoatomic (or “simple”) ions. In contrast, polyatomic (or “complex”) ions are like a molecule, several atoms joined by covalent bonds, but there is an overall charge. Examples: OH-, NH4+ 16 When ions are formed, the number of protons in the nuclei does not change. Some common polyatomic ions Note that: • NH4+ is the only common polyatomic cation, most others are derived from individual metal atoms: Na+, Ca2+, … • Most polyatomic anions contain oxygen “oxoanions” -1 Hydroxide, OHNitrate, NO3Chlorate, ClO3Perchlorate, ClO4Cyanide, CNAcetate, C2H3O2Permanganate, MnO4Hydrogen carbonate HCO3Dihydrogen phosphate H2PO4- -2 Carbonate, CO32Sulfate, SO42Chromate, CrO42Dichromate, Cr2O72Hydrogen phosphate HPO42- -3 Phosphate, PO43- 17 Ions that are equally charged repel each other due to electrostatic interactions. Oppositely charged ions attract each other, this is referred to as ionic bond. A bulk sample of matter is electrically neutral, ionic compounds always contain anions and cations, so that the overall charge is zero. Table salt has the overall composition NaCl, it consists of Na+ and Cl- ions that forms a continuous network (crystal lattice). There are no individual “Na-Cl molecules”. 18 7 Units Chemistry deals with qualitative questions • How do we prepare X? • What happens when X reacts with Y? • How can we convert X into Z? • How can we separate X and W? … and with quantitative questions. • What is the bond length in the molecule X-Y? • How much X reacts with 1 g of Y? • How fast does X react with Y? • How much energy is released in the reaction? Quantitative measurements need units. Chemistry (and other Sciences) uses almost exclusively S.I. units (Systeme International, a.k.a. metric, “mks-system”, for meter, kilogram, second): All of the units of a particular quantity are related to one another by factors of 10. It is often advantageous to convert all quantities to SI units, before starting a calculation. SI units meter cubic meter kilogram Kelvin second mole (m) (m3) (kg) (K) (s) (mol) for length for volume for mass for temperature = oC + 273.14 for time for amount of substance 19 Metric Prefixes Factor 103 10-1 10-2 10-3 10-6 10-9 10-12 Prefix kilo deci centi milli micro nano pico Abbreviation K D C M μ N P Mass (symbol: m) kg kilogram (defined) 1 kg is roughly the mass of 1 L of water g gram 10-3 kg 1 g is roughly the mass of 1 mL of water mg milligram 10-3 g = 10-6 kg µg microgram 10-6 g = 10-9 kg Length (symbol: l) m meter (defined) km kilometer 103 m cm centimeter 10-2 m mm millimeter 10-3 m µm micrometer 10-6 m nm nanometer 10-9 m pm picometer 10-12 m The wavelength of light is measured in nm. Blue light ~ 400 nm, red light ~ 700 nm. Another unit that is sometimes used is the Ångstrom (Å) 1 Å = 10-10 m. The length of a chemical bond is on the order of 1 Å. 20 Time (symbol: t) s second (same prefixes as above...) Volume (symbol: V) L liter 1 L = 10-3 m3 = 103 mL mL milliliter 1 mL = 1 cm3 = 10-3 dm3 = 10-3 L = 10-6 m3 It is helpful to visualize these volumes as little cubes. Remember that liters are NOT an S.I. unit. Many important units have more than one dimension, that is, they involve the product or ratio of two or more fundamental units. Example: Density d Density = mass / volume. Always watch the units used! 60 ml of benzene, C6H6(l), weigh 52.71g. density of benzene in g/ml? What is the Density = mass / volume = 52.71g/60ml = 0.8785g/ml 21 The metal rhenium has a density of 20.53 g/ml at room temperature. What is the weight (mass) of 1.5 liters of rhenium? Note 1.5 l = 1500 ml Density = Mass/Volume = 20.53g/ml = mass/1500ml Mass = 307950 g = 307.950 kg 22 Conversion of units: Example: convert a volume of 543 cm3 to liters XL 1L ~ ~ 543 cm3 1000 cm3 (you can read “~” as “corresponds to”) Therefore: x L 543 cm 3 = 1 L 1000 cm 3 543 cm3 cross-multiply: x L = 1000 cm3 × 1 L = 0.543 L The Mole The mole is just a number. It is just one word we use to represent a certain number of things. We use it because it is handy. It is easier than actually saying the number itself. One dozen eggs (12 eggs) One mole of atoms (6.02 ×1023 atoms) One mole of pennies (6.02 ×1023 pennies) = 6.02 ×1021 $ Total cash in the world = approx 2 x1017 $ 23 One mole contains 6.02 ×1023 items. 6.02 ×1023 is called “Avogadro’s Number” (NA) (three significant figures) NA has the unit mol-1 We abbreviate one mole as “1 mol” How many moles of atoms are in one mole of He? 6.02 ×1023 How many moles of atoms are on one mole of CH4 ? One mole contains CH4 6.02 ×1023 molecules But one mole CH4 contains 5 moles of atoms # 0f atoms = 5 x 6.02 ×1023 = 3.01 x 1024 24 Q. Why do we use this strange number, 6.02 x 1023 ? Essentially because individual atoms are not very heavy… we need a large number of atoms to achieve weights we can handle easily. Individual atom weights are expressed in amu. Let’s try expressing 1 amu in grams: We know 6.02 x 1023 atoms of the most abundant isotope of carbon weigh 12.0g Therefore 1 C-12 atom weighs 12.0g/6.02 x 1023atoms = 1.99 x 10-23 g/atom but 1 C-12 atom weighs 12 amu or 1 amu = 1.99 x 10-23 gatom-1/12amuatom-1 = 1.66 x 10-24g/amu 25 The molar mass (MM) is the mass of one mole of substance. MM has units of g/mol C-12 has a molar mass of 12 g/mol The atomic mass of He is 4.003 amu. 1 mol of He atoms (6.02 ×1023 atoms) weighs 4.003 g The molar mass of He is 4.003 g/mol The atomic mass of S is 32.07 amu. 1 mol of S atoms (6.02 ×1023 atoms) weighs 32.07 g The molar mass of S is 32.07 g/mol This also works for compounds: Water: The atomic mass of hydrogen is 1.01 amu The atomic mass of oxygen is 16.00 amu One molecule of water has two hydrogen atoms and one oxygen atom, the mass of one water molecule is therefore 2 x 1.01 + 16.00 = 18.02 amu 1 mol of water molecules weighs The molar mass of water is 18.02 g 18.02 g/mol 26 Mole – Gram Conversions Use the equation m = MM × n m: MM: n: mass [g] molar mass [g/mol] number of moles [mol] Example: What is the mass of 0.0753 mol of CO2 ? mass = 44g/mol × 0.0753 mol = 3.31g Always include units in your calculations !!! It’s easier to check your result (and memorize equations) when you know what the units are. 27 EXAM QUESTION: Nov. 2004, Q2 How many atoms of Os (atomic number 76) are there in 1.0 × 10-3 g of OsO4 ? A) B) C) D) E) 6.0 × 1023 2.4 × 1024 2.4 × 1018 9.5 × 1018 3.0 × 1024 Molar Mass OsO4 = 190.2g + (4 x 16g) = 254.2g # of moles OsO4 = Mass/molar mass = (1.0 x 10-3 g)/(254.2g/mol) = 3.93 x 10-6 g/mol # of atoms Os = 6.03 x 1023 atoms/mol x 3.93 x 10-6 g/mol = 2.4 x 1018 28 8 Mass Relations in Chemical Formulas The composition of a compound is often specified by citing the mass percents of the elements present. Let’s take a 100 g sample of water. What is the mass in grams of each element? Let’s first figure out how many moles of water we are dealing with: m = MM × n 100g = 18.02 g/mol x n n= # of moles water = 5.55 Therefore there are 2 x 5.55 moles of H atoms and 5.55 moles of O atoms in 100 g of H2O. 2 x 5.55 moles of H atoms weigh 2 x 5.55 x 1.01 = 11.21 g 5.55 moles of O atoms weigh 5.55 x 16 = 88.80g Therefore the mass composition of water is H = (11.21/100) x 100 = 11.21 % O = (88.80/100) x 100 = 88.80 % NOTE: These are mass % !!! 29 The composition of H2O in mole % is Mole % H = (Moles H)/(total moles) = [Moles H/(Moles H + Moles O)] x 100 Mole % H = ( 2 x 5.55)/(2 x 5.55 + 5.55)] x 100 =66.7 Mole % 0 = ( 5.55)/(2 x 5.55 + 5.55)] x 100 = 33.3 30 The percent composition of a compound is often obtained as the result of a chemical analysis. This can be used to obtain the simplest ( empirical ) formula of the compound. EXAM QUESTION: Nov. 2004, Q4 A compound containing manganese, chlorine and oxygen contains 39.7% by mass of Mn and 25.6% by mass of Cl. The empirical formula of this compound is A) B) C) D) E) MnOCl MnOCl2 MnO2Cl MnO3Cl MnO3Cl2 We want the simplest ratio of the moles of each element in the compound. If we assume 100 g of compound then the weight of Mn = 39.7g , the weight of Cl = 25.6 and the weight of O = 100 - 39.7 – 25.6 = 34.7g Then: Moles Mn = 39.7g/(54.94g/mol) = 0.72 Moles Cl = 25.6g/(35.45g/mol) = 0.72 Moles O = 34.7g/(16g/mol) = 2.17 Dividing by the lowest # of moles yields the ratio: Mn 1 Cl 1 O 3 The empirical formula is: MnClO3 31 9 Mass Relations in Reactions Chemical reactions are of the form Reactants Æ Products There are several distinct types of reaction, these include: 1. Acid/base reactions (will be studied in detail later). 2. Precipitation reactions (when a solid is produced by reaction of two or more components in solution). 3. Oxidation/reduction reactions (will also be studied later in detail). 4. Combustion reactions in which a compound reacts with oxygen to produce the most stable oxidation products. (the exception is in nitrogen containing compounds where N2 is produced). It would be better to write “Reactants → ← Products” to emphasize that chemical reactions always represent an equilibrium, but for now we don’t have to worry about that. Often you will have to perform calculations involving chemical equations. Always use a balanced equation! H2 + O2 Æ H2O is not balanced 2 H2 + O2 Æ 2 H2O is balanced (atom and charge balance!) 32 Use the symbols g, l, s to designate the physical state of reactants and products. “aq” is used for species dissolved in water (= aqueous solution), especially ions. You also have to “know” what happens during the reaction, e.g. when you burn hydrogen, a lot of heat is generated, and thus the water is “g”, not “l”. 2 H2(g) + O2(g) Æ 2 H2O(g) Table salt is dissolved in water: NaCl(s) Æ Na+(aq) + Cl-(aq) 33 The “rocket fuel” used by NASA is a mixture of two liquids: Hydrazine (N2H4) and dinitrogen tetraoxide (N2O4) The products of the reaction are gaseous nitrogen and water vapor. A lot of thermal energy is generated during the reaction. The gas molecules are expelled from the rocket engine with an extremely high velocity; that is what makes the rocket “fly”. How do we balance a chemical equation like this? 1. Write down the “skeleton” equation: N2H4 + N2O4 ÆN2 + H2O 2. Indicate the physical states of reactants and products N2H4(l) + N2O4(l) ÆN2(g) + H2O(g) 3. Balance the reaction by finding the right coefficients (Essentially by trial and error, more systematic methods for balancing oxidation/reduction equations) 2 N2H4(l) + N2O4(l) Æ3 N2(g) + 4 H2O(g) The coefficients in this equation represent the number of molecules (also the number of moles!) that react with each other. Other possible solutions are: 34 4 N2H4(l) + 2 N2O4(l) Æ6 N2(g) + 8 H2O(g) or N2H4(l) + ½ N2O4(l) Æ3/2 N2(g) + 2 H2O(g) Usually we go for the smallest whole-number coefficients. The relationships between amounts of reactants and products (in moles and grams) are called stoichiometry. 35 The following is a “combustion question” Stoich-1, Q#7 (similar to many exam questions !!!). “Combustion” means “burning in excess oxygen”. All C is turned into CO2, all H is turned into H2O. A compound contains C, H, and O only. When a sample of mass 0.246 g is burned in excess oxygen, 0.600 g of CO2 and 0.080 g of water are produced. a) Calculate the empirical formula b) Given that the molar mass is about 160 g/mol, what is the molecular formula? The reaction is: CxHyOx + AO2 → xCO2 + (y/2) H2O Notice: The moles CO2 produced = moles C in the reactant = (mass CO2 produced)/molar mass CO2 = 0.6/44 = 0.036 Or mass C in the reactant = moles x molar mass = 12 x 0.036 = .1636 g And 2 x Moles H2O produced = Moles H in the reactant Moles H2O produced = mass/molar mass = 0.08/18 = 0.0044 Moles H in reactant = 2 x 0.004 = 0.0088 Mass H in reactant = moles H x molar mass = 0.0088 x 1.01= 0.009 36 And now % C in the reactant = (mass C/mass reactant) x 100 = (0.1636/0.246) x 100 = 66.5 % H = (mass H/mass reactant) x 100 = (0.009/0.246) x 100 = 3.66 % O = 100 -%C -%H = 100 -66.5 – 3.66 = 29.84 Now we can proceed by assuming 100g of reactant: Then Mass C = 66.5, moles C = 66.4/12 = 5.53 Mass H = 3.66, moles H = 3.66/1.01 = 3.66 Mass O = 29.84, moles O = 29.84/16 = 1.865 Dividing by the lowest yields: C = 2.96 , H = 1.96 , O = 1 OR C = 3 H =2 O = 1 The empirical formula then is C3H2O The molar mass of the empirical formula is 3 X 12 + 2 x 1.01 + 1 x 16 = 54 Estimated molar mass is 160 The molecular formula must contain 160/54 = 2.96 = 3 empirical formulae The molecular formula is: C9H6O3 37 10 Solute Concentrations, Molarity Most chemical reactions that you will encounter occur in solution. The concentration of a solution is expressed in terms of its concentration, another term for this is molarity. molarity = moles of solute / liters of solution The molarity (=concentration) has units of moles per liter (unit M). 1 M = 1 mol L-1 A 6 M solution of NaOH has 6 moles of NaOH per liter of liquid. [ ]s are often used in this context. [NaOH] means “the concentration of NaOH” In this example, [NaOH] = 6 M. We say “the solution is 6 molar”. Solutions can be concentrated (high conc.), e.g. 6 M 38 NaOH, or dilute (low conc.), e.g. 10-3M NaOH = 3 mM NaOH. Here is how you prepare a 0.1 M solution: Calculating with concentrations You have a bottle labeled “concentrated HCl”. It has [HCl] = 12.0 M. How many moles are there in 25.0 mL? Molarity = Moles/Volume (in liters) Moles = Molarity x volume (in liters) = 12moles/liter X 0.025 liters = 0.3 What volume of the 12 M solution must be taken to contain 1.00 mol HCl? Molarity = Moles/Volume (in liters) Moles = Molarity x volume (in liters) 1.00 = 12 moles/liter x Volume Volume = .083 liters = 83 ml 39 Any substance which is IONIC in solid is IONIC in aqueous solution (i.e. positive and negative ions separate from one another). e.g. KCl (s) Æ K+(aq) + Cl-(aq) A crystal of KCl contains K+ cations and Cl- anions. Some covalent substances give ions in solution: (e.g. acids, see chapter 3) e.g. HCl (g) Æ H+(aq) + Cl-(aq) Water is generally the best solvent for ionic substances, i.e. ionic substances are most soluble in water. Give the concentration, in mol/L, of each ion in 0.080 M K2SO4 K2SO4(s) + H2O(l) → 2K+(aq) + SO42-(aq) [K+(aq) ] = 2 x 0.080 = 0.160, [SO42-(aq)] = 0.080 Substances that exist completely as anions/cations in solution are called strong electrolytes. Solutions of these substances conduct electric current. 40 Weak electrolytes are only partially ionized, e.g. acetic acid CH3COOH Æ CH3COO-(aq) + H+(aq) ~99% ~1% Charges of some “transition metal cations” commonly found in aqueous solution: 11 Limiting Reactant and Yield of a Reaction A cheese sandwich consists of 1 bun and 1 slice of cheese. You have 100 buns, and 32 slices of cheese. How many cheese sandwiches can you make??? Cheese is the limiting reactant, buns are the excess reactant. 1 mol of oxygen is mixed with 1 mol of hydrogen, ignition of this mixture leads to the formation of water. What is the limiting reactant? What is the excess reactant? 2H2 + O2 → 2H2O Clearly one mole of oxygen requires two moles of hydrogen for complete reaction. Hydrogen is the limiting reagent, oxygen is in excess. After reaction ½ mole of oxygen will be left open. 41 Reactants are not always mixed exactly in their stoichiometric proportions. Often you will have to decide which is the limiting reactant. The final amount of limiting reactant is always ZERO. 42 EXAM QUESTION: Nov. 2004, Q7 Insoluble Ag2CrO4 is formed from AgNO3(aq) and Na2CrO4(aq) according to the equation 2 AgNO3 + Na2CrO4 Æ Ag2CrO4(s) + 2 NaNO3 When 50.0 mL of 0.100 M AgNO3(aq) are mixed with 100.0 mL of 0.0200 M Na2CrO4(aq), the maximum mass, in grams, of Ag2CrO4(s) that can be produced is A) B) C) D) E) 0.567 1.66 0.448 0.332 0.664 Moles AgNO3 = MV = 0.1 x .050 = 0.005 Moles Na2CrO4 = MV = 0.02 x 0.1 = .002 Now if we have 0.002 moles of Na2CrO4, 0.004 moles of AgNO3 will be required for complete reaction. We have 0.005 moles AgNO3 , therefore Na2CrO4 is the limiting reagent and 0.002 moles of Ag2CrO4 will be produced. Mass Ag2CrO4 produced = moles x MM = 0.002 x (2 x 107.9 + 52 + 4 x 16) = 0.664g 43 12 Yield Suppose you carry out a chemical reaction. Based on the reactant amounts used, and on the equation of the reaction you expect 10 g of product. However, due to experimental imperfections only 9 g are obtained. (Some material was “lost” during handling …) This means you only obtained 9/10 = 0.9 (= 90%) of the expected product. We say that the yield of the reaction is 0.9 (or 90%). In general: mass obtained Yield = maximum mass expected which is the same as Yield = moles obtained maximum number of moles expected (usually expressed in %) Example: 4 mol of H2 and 2 mol of O2 are mixed and ignited. 1.3 mol H2O are found as reaction product. What is the yield? 44 2H2 + O2 → 2H2O 2 moles O2 would react with 4 moles H2 to yield 4 moles H2O (note the stoichiometry is exact in this case). We get only 1.3 moles H2O Yield = actual / expected = 1.3/4 = .325 or 32.5% 45 Percentage Purity Calculations Sometimes a chemical substance is not pure (e.g. gold in a rock sample). For an impure compound, we define the Percent Purity = mass of pure compound present × 100% mass of total compound present This may also be expressed on a molar basis (but that’s uncommon). Example A sample of concentrated nitric acid contains 70.0% HNO3 by mass (the remainder being water). The density of this solution is 1.41 g cm-1. What volume of solution will contain 2.50 mol of nitric acid? % HNO3 = [ (Mass HNO3 )/ (Mass Solution) ] x 100 = 70 0.7 x Mass solution = mass HNO3 2.5 moles HNO3 weight 1 + 14 + 3 x 16 = 63g = mass HNO3 0.7 x Mass solution = 63g Mass solution = 90 g Now we want the volume of the solution and: Density = Mass solution/volume = 1.41 g cm-1 = 90g/volume volume = 90g/1.41 g cm-1 = 63.83 cm-1 46 Some Solubility Rules You should Know Solubility of Ionic Solids in Water Soluble Compounds Exceptions Nitrates (NO3-) None Li+ , Na+ , K+ , NH4+ None Halides (Cl-, Br-, I-) Ag+, (Hg2)2+, Pb2+ Sulfates (SO42-) Ca2+, Sr2+, Ba2+, Pb2+ Insoluble Compounds Exceptions Sulfides (S2-) Groups 1 and 2 and NH4+ Carbonates (CO32-) Group 1 and NH4+ Phosphates (PO43-) Group 1 and NH4+ Hydroxides (OH-) Group 1, Ba2+ and NH4+ 47 13 Uncertainties in Measurements, Significant Figures Chemistry is based on experiments, experiments are based on measurements, the result of a measurement carries a certain degree of uncertainty. Although there are some exact numbers in chemistry (e.g. there are exactly two hydrogen atoms in a H2 molecule), most experimental results contain some amount of error or uncertainty. This is unavoidable in most cases. Difference between accuracy and precision: Accuracy - how closely does the measured value agree with the "true" value? Precision - how well do repeated measurements of the same thing agree with each other? 48 The uncertainty of a measurement has to reported, together with the actual result. Example: “5 mL” of liquid are removed from a beaker by three different methods that have a different accurracy. The actual results are: - 5 mL ± 1 mL - 5 mL ± 0.1 mL - 5 mL ± 0.01 mL We will drop the ± sign and simply write 5 mL, 5.0mL, 5.00 mL In doing this, it is understood that there is an uncertainty of no more than one unit in the last digit (i.e. 1 mL, 0.1 mL, 0.01 mL, respectively). There is one significant figure in 5 mL, two in 5.0 mL, and three in 5.00 mL. Example: Three persons weigh the same object. They report: (a) 15.02 g (b) 15.0 g (c) 0.001502 kg There are 4 significant figures in (a) 3 (b) 4 (c) 49 Zeros are not significant when used to fix the position of the decimal point (leading zeros”, as in [c]). BUT trailing zeros are significant (as in [b]). The last digit to be shown should be the first “doubtful digit”. When we say “1.005 g”, it is implied that the real value is probably between 1.004 and 1.006 g. The number of a piece of rock is given as “500 g”. This statement can be ambiguous. Is it 500 g ± 1 g (three significant figures) ??? 500 g ± 10 g (two significant figures) ??? (anything is possible) Usually it is better to use exponential notation to make clear what is meant: 5.00 × 102 g (three significant figures) 5.0 × 102 g (two significant figures) 5 × 102 g (one significant figure) Note that for exact numbers the concept of significant figures is not required (there is no uncertainty). 50 Number of significant figures in combined expressions Carrying significant figures through calculations is discussed in the Lab Manual (pages 17-19), but this is a more sophisticated treatment than we need to use. Instead we will use the method given MH5, (pages 17-21). When measured quantities are multiplied or divided, the number of significant figures in the result is the same as that in the quantity with the smallest number of significant figures. Example: a plane travels about 5.6 × 103 km in 8.50 hours. What is the average velocity ? By using your calculator, you will find that velocity = distance / time = 658.82353 km/h Are all these figures meaningful? There are 2 significant figures in the numerator, and 3 in the denominator. The result has 2 significant figures. It should be reported as speed = 6.6 × 102 km/h. When you discard insignificant figures, the result has to be rounded off or rounded up. In a calculation, do not do any rounding until you obtain the final result. Note: Your calculator will give as many figures as it has room to display, but usually they are not all significant. Another problem with calculators is that they usually omit trailing zeros to the right of the decimal place, which, as we discussed, are significant. Never copy numbers from your calculator without thinking about them !!!! 51 When measured quantities are added or subtracted, the number of significant decimal places of the result is the same as that in the quantity with the smallest number of decimal places i.e. in this case you should pay attention to the position of the decimal place Example: Let’s find the total mass of a solution containing 10.21 g of instant coffee 0.2 g of sugar 256 g of water Your calculator reports 266.41 g, but this should be reported as 266 g. Because “256” has zero significant decimal places, the result also has zero significant decimal places (but three significant figures in total). Exact numbers don't count when determining the number of significant figures in the result of a calculation. Examples: One standardized paper weight has mass of 25.0 g. What would be the mass of two of these paper weights? An inch is defined as 2.54 cm. How many inches are there in 1.2345 cm? 52 Combined Calculations Combined operations are carried out step by step carry extra digits till the end: (41.23 x 4.184 x 18.3) + (28 x 18.3) = 3.156 x 103 + 5.18 x 102 = 3.156 x 103 + 0.518 x 103 = 3.67 x 103 53