Download Meeting no

Major chemistry laws. Mole and Avogadro’s number. Calculating
concentrations.
Major chemistry laws
Avogadro's Law
Equal volumes of gases under identical temperature and pressure conditions will contain
equal numbers of particles (atoms, ion, molecules, electrons, etc.).
Boyle's Law
At constant temperature, the volume of a confined gas is inversely proportional to the pressure
to which it is subjected.
PV = k
Charles' Law
At constant pressure, the volume of a confined gas is directly proportional to the absolute
temperature.
V = kT
Combining Volumes
Refer to Gay-Lussac's Law
Conservation of Energy
Energy can be neither created nor destroyed; the energy of the universe is constant. This is the
First Law of Thermodynamics.
Conservation of Mass
Also known as Conservation of Matter. Matter can be neither created nor destroyed, though it
can be rearranged. Mass remains constant in an ordinary chemical change.
Dalton's Law
The pressure of a mixture of gases is equal to the sum of the partial pressures of the
component gases.
Definite Composition
A compound is composed of two or more elements chemically combined in a defined ratio by
weight.
Dulong & Petit's Law
Most metals require 6.2 cal of heat in order to raise the temperature of 1 gram-atomic mass of
the metal by 1°C.
Faraday's Law
The weight of any element liberated during electrolysis is proportional to the quantity of
electricity passing through the cell and also to the equivalent weight of the element.
First Law of Thermodynamics
Conservation of Energy. The total energy of the universe is constant and is neither created nor
destroyed.
Gay-Lussac's Law
The ratio between the combining volumes of gases and the product (if gaseous) can be
expressed in small whole numbers.
Graham's Law
The rate of diffusion or effusion of a gas is inversely proportional to the square root of its
molecular mass.
Henry's Law
The solubility of a gas (unless it is highly soluble) is directly proportional to the pressure
applied to the gas.
Ideal Gas Law
The state of an ideal gas is determined by its pressure, volume, and temperature according to
the equation:
PV = nRT
where
P is the absolute pressure
V is the volume of the vessel
n is the number of moles of gas
R is the ideal gas constant
T is the absolute temperature
Multiple Proportions
When elements combine, they do so in the ratio of small whole numbers. The mass of one
element combines with a fixed mass of another element according to this ratio.
Periodic Law
The chemical properties of the elements vary periodically according to their atomic numbers.
Second Law of Thermodynamics
Entropy increases over time. Another way of stating this law is to say that heat cannot flow,
on its own, from an area of cold to an area of hot.
Molecules and Moles
A molecule is a combination of two or more atoms that are held together by covalent bonds.
A molecule is the smallest unit of a compound that still displays the properties associated with
that compound. Molecules may contain two atoms of the same element, such as O2 and H2, or
they may consist of two or more different atoms, such as CCl4 and H2O. In the study of
chemistry, molecules are usually discussed in terms of their molecular weights and moles.
Ionic compounds, such as NaCl and KBr, do not form true molecules. In their solid state,
these substances form a three-dimensional array of charged particles. In such a case,
molecular weight has no meaning, so the term formula weight is used instead.
Molecular Weight and Formula Weight
The molecular weight of a molecule is calculated by adding the atomic weights (in atomic
mass units) of the atoms in the molecule. The formula weight of an ionic compound is
calculated by adding its atomic weights according to its empirical formula.
The Mole
A mole is defined as the quantity of a substance that has the same number of particles as are
found in 12.000 grams of carbon-12. This number, Avogadro's number, is 6.022x1023. The
mass in grams of one mole of a compound is equal to the molecular weight of the compound
in atomic mass units. One mole of a compound contains 6.022x1023 molecules of the
compound. The mass of 1 mole of a compound is called its molar weight or molar mass. The
units for molar weight or molar mass are grams per mole. Here is the formula to determing
the number of moles of a sample:
mol = weight of sample (g) / molar weight (g/mol)
Exercises
1) How many H2O molecules are there in a snowflake weighing 1 mg?
Solution
Snowflakes are made of water, H2O. First, we need to find the mass of one mole (Avogadro's
number or 6.022 x 1023) of H2O molecules. To obtain this number, first look up the atomic
masses for H and O from the Periodic Table. There are two hydrogen atoms and one oxygen
atom in water, so the mass of one mole of water is:
1.01 g x 2 + 16.00 g x 1 = 18.01 g
This relation is used to determine how many molecules of water there are in 1 gram:
number of molecules per gram = 6.022 x 1023 H2O molecules / 18.01 g
number of molecules per gram = 3.34 x 1016 g
Next, convert grams to milligrams. There are 1000 milligrams in a gram, so move the decimal
point three places to the right or add three to the superscript in exponential notation:
number of molecules in 1 milligram = 3.34 x 1019
Answer
3 x 1019 H2O molecules
2) Calculate the mass in grams of a single carbon (C) atom.
Solution
To calculate the mass of a single atom, first look up the atomic mass for carbon from the
Periodic Table. This number, 12.01, is the mass of one mole of carbon. One mole of carbon is
6.022 x 1023 atoms of carbon (Avogadro's number). This relation is then used to 'convert' a
carbon atom to grams:
mass C atom = 1 C atom x 12.01 g / 6.022 x 1023 C atoms = 1.994 x 10-23 g
Answer
1.994 x 10-23 g
3) Calculate the mass in grams of 2.5 x 109 H2O molecules.
Solution
First, we need to find the mass of one mole (Avogadro's number or 6.022 x 1023) of H2O
molecules. To obtain this number, first look up the atomic masses for H and O from the
Periodic Table. There are two hydrogen atoms and one oxygen atom in water, so the mass of
one mole of water is:
1.01 g x 2 + 16.00 g x 1 = 18.01 g
This relation is used to complete the problem:
mass = 2.5 x 109 H2O molecules x 18.02 g / 6.022 x 1023 H2O molecules
mass = 7.5 x 10-14 g
Answer
7.5 x 10-14 g
4) The mineral cassiterite is a compound of tin and oxygen. Chemical analysis of cassiterite
shows that the mass percentages of tin and oxygen are 78.8 and 21.2, respectively. Determine
the formula of this compound.
Solution
We want to find the number of moles of each element in order to determine the ratios of the
elements and the formula. To make the calculation easy (i.e., let the percentages convert
directly to grams), let's assume we have 100 g of cassiterite. In a 100 gram sample, there are
78.8 g Sn and 21.2 g O. Now, look up the atomic masses for the elements from the Periodic
Table. The atomic masses are found to be:
Sn is 118.7
O is 16.00
The atomic masses provide a moles per gram conversion factor. Using the conversion factor,
we can calculate the moles of each element:
moles Sn = 78.8 g Sn x 1 mol Sn / 118.7 g Sn = 0.664 mol Sn
moles O = 21.2 g O x 1 mol O / 16.00 g O = 1.33 mol O
The numbers of moles of each element are in the same ratio as the number of atoms Sn and O
in cassiterite. To find the simplest whole number ratio, divide each number by the smallest
number of moles:
Sn: 0.664 / 0.664 = 1.00
O: 1.33 / 0.664 = 2.00
The ratios indicate that there is one tin atom for every two oxygen atoms. Thus, the simplest
formula of cassiterite is SnO2.
Answer
SnO2
5) Vitamin C contains three elements: carbon, hydrogen, and oxygen. Analysis of pure
vitamin C indicates that the elements are present in the following mass percentages:
C = 40.9
H = 4.58
O = 54.5
Use the data to determine the simplest formula for vitamin C.
Solution
We want to find the number of moles of each element in order to determine the ratios of the
elements and the formula. To make the calculation easy (i.e., let the percentages convert
directly to grams), let's assume we have 100 g of vitamin C. If you are given mass
percentages, always work with a hypothetical 100 gram sample. In a 100 gram sample, there
are 40.9 g C, 4.58 g H, and 54.5 g O. Now, look up the atomic masses for the elements from
the Periodic Table. The atomic masses are found to be:
H is 1.01
C is 12.01
O is 16.00
The atomic masses provide a moles per gram conversion factor. Using the conversion factor,
we can calculate the moles of each element:
moles C = 40.9 g C x 1 mol C / 12.01 g C = 3.41 mol C
moles H = 4.58 g H x 1 mol H / 1.01 g H = 4.53 mol H
moles O = 54.5 g O x 1 mol O / 16.00 g O = 3.41 mol O
The numbers of moles of each element are in the same ratio as the number of atoms C, H, and
O in vitamin C. To find the simplest whole number ratio, divide each number by the smallest
number of moles:
C: 3.41 / 3.41 = 1.00
H: 4.53 / 3.41 = 1.33
O: 3.41 / 3.41 = 1.00
The ratios indicate that for every one carbon atom there is one oxygen atom. Also, there are
1.33 = 4/3 hydrogen atoms. (Note: converting the decimal to a fraction is a matter of practice!
You know the elements must be present in whole number ratios, so look for common
fractions and become familiar with the decimal equivalents for fractions so you can recognize
them.) Another way to express the atom ratio is to write it as 1 C : 4/3 H : 1 O. Multiply by
three to obtain the smallest whole-number ratio, which is 3 C: 4 H : 3 O. Thus, the simplest
formula of vitamin C is C3H4O3.
Answer
C3H4O3
Concentrations
The concentration of a chemical solution refers to the amount of solute that is dissolved in a
solvent.
Once you have identified the solute and solvent in a solution, you are ready to determine its
concentration. Concentration may be expressed several different ways, using percent
composition by mass, mole fraction, molarity, molality, or normality.
Percent Composition by Mass (%)
This is the mass of the solute divided by the mass of the solution (mass of solute plus mass of
solvent), multiplied by 100.
Example:
Determine the percent composition by mass of a 100 g salt solution which contains 20 g salt.
Solution:
20 g NaCl / 100 g solution x 100 = 20% NaCl solution
Molarity (M)
Molarity is probably the most commonly used unit of concentration. It is the number of moles
of solute per liter of solution (not necessarily the same as the volume of solvent!).
Example:
What is the molarity of a solution made when water is added to 11 g CaCl2 to make 100 cm3
of solution?
Solution:
11 g CaCl2 / (110 g CaCl2 / mol CaCl2) = 0.10 mol CaCl2
100 cm3 x 1 dm3 / 1000 cm3 = 0.10 dm3
molarity = 0.10 mol / 0.10 dm3
molarity = 1.0 mol/ dm3 (M)