Number of moles from gas volume

For gases, SPM Chemistry lets you measure amount by volume instead of by mass, using the molar volume. Our online one-to-one teachers focus on the two things students actually lose marks on here: choosing the right molar volume, and converting cm cubed to dm cubed before dividing.

When you use it

Use this whenever a gas is described by a volume, in a reacting-gas question, a gas collected over water, or a “what volume of gas is produced” problem where you first need the moles. It is the gas partner of n = m / M for solids and n = c x V for solutions.

The formula

n = V / molar volume

• n = number of moles, in mol
• V = volume of gas, in dm cubed (dm³)
• molar volume = the volume of one mole of any gas at the stated conditions

The molar volume is 24 dm³ mol⁻¹ at room conditions and 22.4 dm³ mol⁻¹ at STP.

Units

Volume must be in dm cubed. If a volume is given in cm cubed, divide by 1000 to convert to dm cubed first (1 dm³ = 1000 cm³). The answer is in mol. The same molar volume applies to any gas, because equal volumes of gases contain equal numbers of molecules at the same conditions.

Worked example 1 (easy), oxygen at room conditions

Find the number of moles in 12 dm³ of oxygen gas at room conditions.

• Step 1, n = V / molar volume = 12 / 24.
• Step 2, n = 0.5 mol.

Worked example 2 (medium), carbon dioxide in cm cubed

Find the number of moles in 480 cm³ of carbon dioxide at room conditions.

• Step 1, convert the volume: 480 cm³ / 1000 = 0.48 dm³.
• Step 2, n = V / molar volume = 0.48 / 24 = 0.02 mol.

(Equivalently, divide by 24 000 cm³: 480 / 24 000 = 0.02 mol.)

Worked example 3 (SPM level), hydrogen at STP

Find the number of moles in 5.6 dm³ of hydrogen gas measured at STP, then the number of molecules.

• Step 1, choose the STP molar volume, 22.4 dm³ mol⁻¹.
• Step 2, n = V / molar volume = 5.6 / 22.4 = 0.25 mol.
• Step 3, molecules: N = n x NA = 0.25 x (6.02 x 10²³) = 1.505 x 10²³ molecules.

The examiner switches to STP precisely to see whether you notice the conditions and swap to 22.4.

Common traps

• Using 24 when the question says STP (should be 22.4), or 22.4 for room conditions.
• Forgetting to convert cm cubed to dm cubed; dividing 480 by 24 gives 20, which is wrong by a factor of 1000.
• Trying to use a molar volume for a substance that is not a gas at those conditions.
• Dropping the unit mol on the answer.
• Confusing molar volume with molar mass, one is dm cubed per mole, the other grams per mole.

How we help

Our teachers deliberately mix room-conditions and STP questions, and slip in cm cubed values, so you build the two-second habit of checking the conditions and the units before you divide, the exact discipline SPM Chemistry rewards. Lessons are one-to-one, taught in English, from RM50 per hour, with a paid one-hour trial so you can try the method first. Once this is secure, gas-volume questions in reacting-mass problems stop being the place careless marks disappear.