Posted: April 13, 2020
This week we will focus on the mole. The mole is a unit of measurement that is probably the most used in chemistry. I always compare the explanation of the mole with a dozen. Here goes:
One dozen = 12 items
It doesn't matter if you have a dozen eggs, a dozen cars or a dozen feathers. All are equal to 12 items. The masses of each dozen of eggs, cars, feathers are obviously different, the sizes are also different, however, they are all equal to 12 in numbers.
One mole = 6.02 x 1023 particles
So if you have one mole of hydrogen, one mole of potassium or one mole of iron, they are all equal to 6.02 x 1023 particles. The masses are different, the sizes of the molecules are different, but the number of particles are all equal to 6.02 x 1023 particles.
This number is referred to as Avogadro's number, named after the Italian scientist who developed this concept.
In a balanced chemical reaction, the number placed in front of the chemicals, what we call the coefficient, represents the moles of that chemical. For example:
Cl2 + 2 NaBr --> Br2 + 2 NaCl
This is read as 1 mole of chlorine reacts with 2 moles of sodium bromide to produce 1 mole of bromine and 2 moles of sodium chloride.
Calculating the number of particles based on the amount of moles:
To calculate the number of particles of a substance, we simply multiply Avogadro's number by the number of moles.
# particles = moles x Avogadro
Example: How many particles in 3 moles of potassium chloride?
# particles = 3 moles x 6.02 x 1023 particles/mole = 1.806 x 1024 particles
**** Every calculator brand is different for exponents. Learn how to use yours properly. If you can't get the same answer, then please ask.****
The formula can be rearranged to find moles instead. For example: How many moles does 1.65 x 1024 particles of helium represent?
moles = # particles / Avogadro = 1.65 x 1024 particles / 6.02 x 1023 = 2.74 moles of helium
We use the mole in most chemical quantities. If you look at your periodic table, the units for the mass indicated for each element (molar mass) is in g/mol (grams per mole). This is just one simple example of how the mole is used. As you progress in chemistry, you will see it almost everywhere.
Calculating molar mass of a compound: Molar mass is the mass of one mole of a substance. You find the value of individual elements on the periodic table. For example molar mass of hydrogen is 1.01 g/mol; aluminum is 26.98 g/mol; radon is 226.03 g/mol. TO calculate the molar mass of a compound, you just have to add up all the individual masses of the elements inside the compound. For example:
H2O contains 2 hydrogen and 1 oxygen. The molar mass is (2 x mass of hydrogen) + (1 x mass of oxygen)= (2 x 1.01 g/mol) + (1 x 16.00 g/mol) = 18.02 g/mol. This means that one mole of water has a mass of 18.02 grams.
H2SO4 contains 2 hydrogen, 1 sulfur, 4 oxygen. The molar mass is (2 x 1.01 g/mol) + (1 X 32.06 g/mol) + (4 x 16.00 g/mol) = 98.08 g/mol. This means that one mole of hygrogen sulphate has a mess of 98.08 grams.
Molar mass in a mathematical formula is represented with a capital M and is always measured in g/mol.
Mass in a mathematical formula is represented with a lower case m and is measured in g, Kg, mg, etc...
Moles in a mathematical formula is represented with a lower case n and is measured in mol, Kmol, mmol, etc...
Using a formula to calculate mass or moles based on molar mass:
n=m/M
moles = mass divided by molar mass
This formula can be rearranged to find mass is moles is given in the question. m=nM (mass= moles x molar mass)
Molar mass (M) is found on the periodic table. Just add up the elements within the compound as explained earlier.
Example 1: How many moles is 78.23 g of sodium chloride?
First, calculate the molar mass (M) of NaCl from the periodic table by adding Na + Cl = 58.44 g/mol
78.23 g is the mass (m)
n= m/M = 78.23g ÷ 58.44 g/mol = 1.339 mol
Example 2: What is the mass of 1.5 mol of H20?
from the periodic table, M of H2O = 18.02 g/mol
m= nM = 1.5 mol x 18.02 g/mol = 27.03 g
Example 3: What is the mass of 3.8 mol of oxygen?
** Here you must remember that an oxygen molecule never has only one oxygen. It is O2.
m = nM = 3.8 mol x 32.00 g/mol = 121.6 g
Using STP and SATP values of gases to calculate moles: We have seen before that STP stands for Standard Temperature & Pressure of a gas; SATP stands for Standard Ambient Temperature & Pressure.
At STP (0°C and 101.325 kPa) the volume of a gas is 22.4 L/mol.
At SATP (25°C and 100 kPa) the volume of a gas is 24.8 L/mol.
The unit L/mol (liters per mole) represents how much space a gas takes up for each mole of that gas. Imagine the size of a 2 L bottle of pop as a reference when trying to visualize the size of these gas containers. The values mentioned above are also found on the back of your periodic table (bottom righthand side). They can be used to find either the volume or the amount of moles of a gas. For the sake of this section, we are going to refer the STP and SATP values as concentrations (how much gas is in a certain contained area).
c= v/n (concentration = volume ÷ mole)
The formula is rearranged as follows:
v = cn (volume = concentration x moles)
n = v/c (moles = volume ÷ concentraion)
For this type of question, C is measured in L/mol; v is measured in L, kL, mL, etc...; n is measured in mol, kmol, mmol, etc...
Example 1: What is the volume 0.68 mol of neon gas at STP?
Look for the STP value of a gas for c
v = cn = 22.4 L/mol x 0.68 mol = 15.2 L of neon gas
Example 2: How many moles does 5.63 L of hydrogen gas represent at SATP?
Look for the SATP value of a gas fo c
n= v/c = 5.63 L ÷ 24.8 L/mol = 139.6 mol of hydrogen gas
Multistep calculations: You may often need to use more than one formula to get to your final answer. You need to be able to know which formula to use for which problem.
Example 1: What is the mass of 3.49 L of argon gas at SATP?
I didn't give you a formula with mass and volume in it. However, you can first find moles and then convert that to a mass.
step 1: n= v/c = 3.49 L ÷ 24.8 L/mol = 0.140725806 mol (never round off until the very end of your calculation. This is EXTREMELY important)
step 2: m= nM = 0.140725806 mol x 39.95 g/mol = 5.62 g of argon gas.
Hint: Placing your units in your work will be SUPER useful in the future when questions become more complicated. It helps you figure out what the final unit will be and also helps you figure out if you are using the right formula. Units should cancel out in your calculations to leave you with just one in the end.