Mass-Mole Calculations (moles = mass ÷ molar mass)

Key Concepts

1 mole of a pure substance has a mass equal to its molecular mass expressed in grams.
This is known as the molar mass, M, and has the units g mol^{-1} So 2 moles of a substance would have a mass = 2 x molar mass
3 moles of a substance would have a mass = 3 x molar mass etc

This leads to the formula: mass = moles x molar mass
If we let:
m = mass of substance in grams,
n = moles of pure substance,
M = molar mass of the pure substance in g mol^{-1} we can write the equation: m = n x M

This equation can be rearranged to give the following:
n = m ÷ M (moles = mass ÷ molar mass)
M = m ÷ n (molar mass = mass ÷ moles)

Examples

1. mass = moles x molar mass

Calculate the mass of 0.25 moles of water

Write the equation:
m (in grams) = n x M

Extract the data from the question:
n = 0.25 mol

Calculate the molar mass of the substance using the periodic table:
M(H_{2}O) = (2 x 1.008) + 16.00 = 18.016 g mol^{-1}

Substitute the values into the equation and solve:
mass = 0.25 x 18.016 = 4.504 g

2. moles = mass ÷ molar mass

Calculate the moles in 124.5 g of oxygen gas.

Write the equation:
n = m ÷ M

Extract the data from the question:
m = 124.5 g

Calculate the molar mass of the substance using the periodic table:
M(O_{2}) = 2 x 16.00 =32.00 g mol^{-1}

Substitute the values into the equation and solve:
n = 124.5 ÷ 32.00 = 3.89 mol

3. molar mass = mass ÷ moles

Calculate the molar mass of a pure substance if 1.75 moles of the substance has a mass of 29.792 g

Write the equation:
M = m ÷ n

Extract the data from the question:
m = 29.792 g
n = 1.75 mol

Substitute the values into the equation and solve:
M = 29.792 ÷ 1.75 = 17.024 g mol^{-1}

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