Mass-Mole Calculations (n=m/M) Chemistry Tutorial - AUS-e-TUTE
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Mass-Mole Calculations (n=m/M) Chemistry TutorialKey Concepts
⚛ 1 mole of a pure substance has a mass equal to its molecular mass(1) expressed in grams.
· This is known as the molar mass, M, and has the units g mol-1 (g/mol, grams per mole of substance)
⚛ The relationship between molar mass, mass and moles can be expressed as a mathematical equation as shown below:
g mol-1 = g ÷ mol
molar mass = mass ÷ moles
M = m ÷ n
where:
M = molar mass of the pure substance (measured in g mol-1)
m = mass of the pure substance (measured in grams, g)
n = amount of the pure substance (measured in moles, mol)
⚛ This mathematical equation can be rearranged to give the following:
(i) n = m ÷ M
moles = mass ÷ molar mass
(ii) m = n × M
mass = moles × molar mass
⚛ To calculate the moles of pure substance: n = m ÷ M
⚛ To calculate mass of pure substance: m = n × M
⚛ To calculate molar mass of pure substance: M = m ÷ n
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Calculating the Mass of a Pure Substance (m=nM)
1 mole of a pure substance is defined as having a mass in grams equal to its relative molecular mass. This quantity is known as the molar mass (symbol M). So, mass of 1 mole of a pure substance = relative molecular mass in grams And, mass of 1 mole of a pure substance = molar mass of the pure substance (g mol-1) Or, mass of 1 mole = M (g mol-1)
The table below gives the mass of 1 mole of a number of common pure substances:
| name | molecularformula | relative molecular mass | molar mass (g mol-1) | mass of 1 mole (g) |
|---|---|---|---|---|
| helium gas | He | 4.003 | 4.003 g mol-1 | 4.003 g |
| oxygen gas | O2 | 2 × 16.00 = 32.00 | 32.00 g mol-1 | 32.00 g |
| carbon dioxide gas | CO2 | 12.01 + (2 × 16.00) = 44.01 | 44.01 g mol-1 | 44.01 g |
| liquid water | H2O | (2 × 1.008) + 16.00 = 18.016 | 18.016 g mol-1 | 18.016 g |
From the table we see that 1 mole of water has a mass of 18.016 grams, which isn't very much (about the mass of water in a couple of small ice-cubes you'd make in your family freezer).
But what if you had 10 moles of water? What would be the mass of 10 moles of water? If 1 mole of water has a mass of 18.016 g, then 10 moles of water must have ten times more mass: mass of 10 moles of water = 10 × mass of 1 mole of water mass of 10 moles of water = 10 × 18.016 = 180.16 g (about the mass of water you could put in a small glass)
So, if we only had ½ mole of water, what mass of water would we have? If 1 mole of water has a mass of 18.016 g, then ½ mole of water must have ½ the mass: mass of ½ mole of water = ½ × mass of 1 mole of water mass of ½ mole of water = ½ × 18.016 = 9.008 g
In both of the examples above, we can calculate the mass of water in grams by multiplying the moles of water by the mass of 1 mole of water in grams:
mass water = moles of water × mass of 1 mole water
because the mass of 1 mole of water in grams is known as its molar mass, we can write:
mass water = moles of water × molar mass of water
The table below compares the mass of different amounts of water in moles:
| mass of water (g) | = | moles of water (mol) | × | mass of 1 mole of water (molar mass of water) (g mol-1) |
|---|---|---|---|---|
| 0 | = | 0.00 | × | 18.016 |
| 9.008 | = | 0.50 | × | 18.016 |
| 18.016 | = | 1.00 | × | 18.016 |
| 27.024 | = | 1.50 | × | 18.016 |
| 180.16 | = | 10.00 | × | 18.016 |
| 270.24 | = | 15.00 | × | 18.016 |
From the data in the table we can generalise and say that for any pure substance the mass of substance in grams is equal to the moles of substance multiplied by the mass of 1 mole of the substance:
mass = moles × mass of 1 mole
and since mass of 1 mole of a substance (in grams) = molar mass (in grams per mole)
mass (g) = moles × molar mass (g mol-1)
m = n × M
where
m = mass of pure substance in grams
n = amount of pure substance in moles
M = molar mass of pure substance in grams per mole
We could also plot the data in the table above on a graph as shown below: