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Chemistry 068, Chapter 6 Moles and Chemical Formulas • This section deals with the relationships between elements and compounds. – Specifically, that compounds have a definite composition in terms of the number and type of atoms which make them up. • It also introduces the idea of the mole, which is a unit of amount in chemistry. Compounds and the Law of Definite Proportions • Pure substances are either elements or compounds. • Elements cannot be decomposed into simpler substances. • Compounds are substances composed of two or more elements. – Compounds have different properties from either element alone. – They have a constant elemental composition. Compounds and the Law of Definite Proportions (Cont’d) • The law of definite proportions states that in a pure compound, the elements present are always in the same proportion by mass. – All samples of the same compound will have the same elemental proportion by mass. • The simplest illustrations of this are decomposition reactions. • It is also useful to look at the law in terms of individual atoms. Law of Definite Proportions in Terms of Atoms • Consider three compounds AB, AB2, and AB3. – A is blue and B is red. – Each is made up of A and B atoms, but in different ratios. Law of Definite Proportions in Terms of Atoms (Cont’d) • The different ratios between the atoms will correspond to a different mass ratio and mass % for each of the three compounds. – Even if A and B had exactly the same mass, the ratio would still be different. • This difference will also lead to a different mass per molecule. The Mole • A mole, sometimes written as mol, is like a dozen, except that a mole is 6.0221415x1023. – Usually, it is sufficient to use 6.022x1023. • The number 6.0221367x1023 is called Avogadro’s number. • Like a dozen you can have a mole of anything – atoms, DVDs, pennies. • Chemists have set up the periodic table such that the masses on the periodic table correspond to the mass of one mole of atoms in grams. Calculations Using Avogadro's Number • You can use Avogadro’s number to go back and forth between moles of something and single objects by treating it as a unit conversion. • Conversion like this sometimes also require you to keep track of chemical formulas. Calculations Using Avogadro's Number Problems • How many molecules of CH4 are there in 0.010 moles of CH4? • How many moles of NaCl are there if there are 1.50*1027 molecules? Molar Mass • Is the mass for one mole of molecules of a substance. • Calculated in exactly the same way as a molecular or formula mass. • Units are usually g/mol. • Will have the same numerical value as the molecular or formula mass, but the units will be different. – Grams instead of amu. Calculations Using Molar Mass • Molar mass is calculated in exactly the same way as formula mass. – The only thing that is different is the mass units used. – Molar mass will be in g/mole, whereas formula mass will be in amu. • It is possible to freely switch between moles and mass by using the molar mass as a unit conversion. Relationship Between Amu and Gram Masses • Amu and gram masses are related by: 1.000g = 6.022*1023 amu Or: 1.000 amu = 1.661*10-24g • You can thus relate amu and gram masses using unit conversion calculations. Significant Figures and Calculations Using Avogadro’s Number • Avogadro’s number is an experimentally determined value. • As such, it is not an exact number. • Normally, it is sufficient to use 6.022x1023. • If more significant figures are needed, the value 6.0221415x1023 can be used. Molar Mass Problems • Calculate each of the following: – Number of moles in 150.0g of He. – Mass of 9.6 moles of C. – Number of atoms in 100.0g of Fe. Molar Mass Problems (Cont’d) • Calculate the following molar masses: – MgCl2 – H 2O – H2SO4 Molar Mass Problems (Cont’d) • Calculate each of the following: – Number of molecules in 100.0g of MgCl2. – Number of moles in 50.0g of H2O. – Mass of 3.2moles of H2SO4. Moles and Chemical Formulas • At the single atoms level, chemical formulas represent ratios within a given formula unit. • At the macroscopic level, chemical formulas represent the mole ratio of the elements in a compound. • These two representations are not exclusive – they represent the same thing just at two different scales. Moles and Chemical Formulas (Cont’d) • Again, let’s consider three compounds AB, AB2, and AB3. – A is blue and B is red. • At the single atom level the ratio represents individual atoms. • At the macroscopic level, the ratio is a mole ratio. Moles and Chemical Formulas Problems • How many moles of oxygen atoms are in 6.10*1025 molecules of CO2? How many moles of carbon? • How many atoms of carbon are in 2.6 moles of C2H6? How many moles of hydrogen? Chemical Calculations Using Moles • With this knowledge in mind, there are several types of calculation which can be performed. • It is important to remember that you can go back and forth between moles, number of particles, and masses. Chemical Calculations Using Moles (Cont’d) • You can convert between moles and number of particles using Avogadro's number. • Mass and number of moles are related using molar mass. • The chemical formula of a compound can be used to get a mole or number of particles relationship within a compound. – This is NOT true for mass. – Mass relationships are more complicated because different elements have different masses. Calculations Using Moles Problems • How many molecules are there in a 32.00g sample of CH4? • How many atoms of carbon are in that same sample? • How many atoms of hydrogen? Calculations Using Moles Problems (Cont’d) • What mass of oxygen is there in a 9.00g sample of H2O? • What mass of hydrogen? Calculations Using Moles Problems (Cont’d) • How much does 3.00*1020 molecules of NH3 weigh? Calculations Using Moles Problems (Cont’d) • What is the mass, in grams, of a single molecule of CO2? Mass % and Mass Ratio • % composition by mass, or mass % is a way to represent the elemental breakdown of a compound. Mass % = 100*(mass element) / (total mass compound) • Another way to represent elemental composition is mass ratio. Mass ratio A to B = (mass element A/mass element B) Using a Formula to Determine Mass % • A formula mass can be used to determine mass %. • First the formula mass is determined. • Second, the masses of each of the elements is taken as a % of the total. Using a Formula to Determine Mass % Problems • Determine the mass %, of each element in C2H3Cl. Using Synthesis Data to Determine Mass % • Synthesis data can also be used to determine mass %. • The mass of each element can be taken as a % of the whole to find its mass %. Using Synthesis Data to Determine Mass % Problems • A 27.00g sample of an organic compound requires 11.94g of C, 1.44g H, 7.08g O, 2.08g N, and 4.46g Fe. What is the mass % of each in the compound? Sample Purity • Not in text. • Most real samples are not completely pure. • % purity (by mass) is a measure of how pure a sample of a compound is. – It is defined as the % of the substance (by mass) in an impure sample. Or: % Purity A = (Mass A)/(Total Mass of Impure Sample of A) • Thus a 98.60% pure sample of iron would contain 98.60g of iron per 100.0g sample of impure iron. • Sample purity adds an additional step to any chemical calculations. Sample Purity Problems • What mass of CH4 is there in a 32.00g sample which 80.0% pure CH4? • How many CH4 molecules are there? • How many atoms of carbon are in that same sample? • How many atoms of hydrogen? Empirical vs. Molecular Formulas • There are two types of chemical formulas. • Empirical formulas give only the smallest whole number ratio of atoms in a compound. • Molecular formulas give the actual number of each type of atom within a compound. • Compounds with the same empirical formula but different molecular formulas can have very different properties. • For example, C2H6, C3H9, C4H12, all have the same empirical formula – CH3, but each has different properties. Empirical vs. Molecular Formulas Problems • What is the empirical formula of each of the following compounds? – H2O2 – C4H16 – Na2Cl2 – H2SO4 – Na6(OH)6 Determining an Empirical Formula From Data • It is often much easier to experimentally determine an empirical formula than it is a molecular formula. • Empirical formulas are typically obtained from mass composition (% mass) experiments or raw mass data. • Combustion analysis is another potential source of empirical formula data. Determining an Empirical Formula From Mass Composition Data • The mole ratio of a compound is needed to determine its empirical formula. • First, you need to determine how many moles of each element are in the compound from mass data. • Molar masses are then used to determine the number of moles. • A mole ratio is then determined and converted to whole numbers. • The smallest whole number ratio gives the empirical formula. – Each mole in the ratio is one atom in the empirical formula. Empirical Formula From Mass Composition Data Problems • A salt sample is determined to contain only calcium and chlorine. – What is the empirical formula of the salt if it is 36.0% calcium by mass. Empirical Formula From Mass Composition Data Problems (Cont’d) • Ethanol is 52.17% carbon, 13.05% hydrogen, and 34.78% oxygen. What is the empirical formula of ethanol? Empirical Formula From Mass Composition Data Problems (Cont’d) • A salt sample contains 5.86g of potassium and 19.0g of iodine. What is the empirical formula of the salt? Combustion Analysis • Not in text. • Combustion is a special type of elemental analysis where a compound is burned, along with oxygen, to produce water, carbon dioxide, and solid residue. • All of the hydrogen in the compound forms water. – Thus the moles of water is half the moles of hydrogen (as water has 2 hydrogens). – To get the moles of water, the mass of water is converted to moles. • All of the carbon in the compound forms carbon dioxide. – Thus the moles of carbon dioxide is equal to the moles of carbon. – Likewise, the moles of carbon dioxide is obtained from the mass of carbon dioxide. • The residue will contain any elements that do not readily combust. Combustion Analysis (Cont’d) • The moles of any residue can then be obtained from its molar mass. – The residue, if any, will vary depending on the sample. • Once the moles of hydrogen, carbon, and any residue have been determined, it is possible to determine an empirical formula by using the mole ratio. Combustion Analysis Problems • A 24.0g sample of an unknown hydrocarbon, which contains only carbon and hydrogen, is combusted. It produces 54.0g of water and 66.0g of carbon dioxide leaving no solid residue. – What is the empirical formula of the sample? Combustion Analysis Problems • A 94.0g sample of an unknown hydrocarbon, which contains only carbon, hydrogen, and sulfur is combusted. It produces 54.0g of water and 88.0g of carbon dioxide leaving 64.0g of sulfur residue. – What is the empirical formula of the sample? Determining a Molecular Formula From Data • To determine the molecular, rather than empirical formula, it is necessary to determine the compounds molar mass by a separate experiment. – This is often much more difficult than determining the empirical formula experimentally. • Once both the empirical formula and the molar mass are known the molecular formula can be determined. • This is done by noting that the molar mass of the molecule must be a whole number multiple of the molar mass of the empirical formula. – The multiplier to mass also multiplies the subscripts on the atoms in the formula. Determining a Molecular Formula From Data (Cont’d) • In short: Molecular Formula = Empirical Formula x n Molar Mass = Empirical Formula Molar Mass x n • Where n is a positive whole number. Determining a Molecular Formula From Data Problems • The empirical formula of a compound is CH4. What is its molecular formula if the molar mass is: • 16.0g/mole • 32.0g/mole • 48.0g/mole Determining a Molecular Formula From Data Problems (Cont’d) • A 66.0g sample containing only carbon and oxygen is determined to contain 1.5mol of carbon. A separate experiment determines that the compound has a molar mass of 176.0g/mol. – What is the empirical formula of the sample? – What is the molecular formula of the sample?