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Mass, Moles and Direct Calculations

Choose and rearrange the mass–amount relationship, keeping the units and magnitude consistent.

  • SEC G2 Science Chemistry component 2027
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Learning objectives

  • perform calculations involving the relationship between the amount of substances in moles, mass and molar mass (calculations of stoichiometric reacting masses and volumes of gases are not required).

A mass tells you how much material was weighed. An amount in moles counts specified particles. Molar mass connects them:

n = m/M, m = nM, M = m/n.

Use m in g and M in g mol⁻¹ to obtain n in mol. If a mass is given in kg, convert it to g first. These are direct relationships for one substance; reacting ratios, gas-volume calculations and solution concentration belong outside this G2 calculation sequence.

From a formula to molar mass to amount

Guided practice 1

Calculate Amount from Mass

About 5 min

Problem

Calculate the amount in 9.00 g of water. Use Aᵣ(H) = 1.0 and Aᵣ(O) = 16.0.

Complete the calculation

Hints

Hint 1: formula-mass
Count two H atoms and one O atom.
Hint 2: relationship
Use n = m/M.
View solution step by step

  1. Find molar mass

    Method

    Add the relative masses represented by H₂O.

    Reason

    The subscript 2 applies to hydrogen.

    Working

    M(H₂O) = 2(1.0) + 16.0 = 18.0 g mol⁻¹

  2. Calculate amount

    Method

    Divide mass by molar mass.

    Reason

    n = m/M converts grams to moles directly.

    Working

    n = 9.00/18.0 = 0.500 mol

Before using a calculator, compare the sample mass with the mass of one mole. Since 9.00 g is less than 18.0 g, the water sample must contain less than one mole. This catches an inverted division such as 18.0/9.00.

Reverse the calculation

Challenge 2

Calculate Mass from Amount

Minimal support

Reverse calculation

Calculate the mass of 0.300 mol of ammonia, NH₃. Use Aᵣ(N) = 14.0 and Aᵣ(H) = 1.0.

Reverse the relationship

Hints

Hint 1: molar-mass
M(NH₃) = 14.0 + 3(1.0).
Hint 2: rearrange
From n = m/M, use m = nM.
View solution step by step

  1. Find molar mass

    Method

    Count one N and three H atoms.

    Reason

    The chemical formula fixes the molar mass.

    Working

    M = 14.0 + 3(1.0) = 17.0 g mol⁻¹

  2. Reverse the relationship

    Method

    Multiply amount by molar mass.

    Reason

    Mass is the unknown, so m = nM.

    Working

    m = 0.300(17.0) = 5.10 g

Choose the quantity and check it

A sample contains 0.250 mol of CO₂. Use Aᵣ(C) = 12.0 and Aᵣ(O) = 16.0 to calculate its mass. State why the answer’s unit is g.

Check the direct calculation

M = 12.0 + 2(16.0) = 44.0 g mol⁻¹. Mass is unknown, so m = nM = 0.250(44.0) = 11.0 g. The units are mol × g mol⁻¹ = g; one-quarter of a mole has one-quarter of the molar mass in grams.

Repair a formula-to-amount calculation

A learner uses M(Mg(OH)₂) = 24 + 16 + 2 = 42 g mol⁻¹, then n = 5.80/42. With Aᵣ(Mg) = 24, Aᵣ(O) = 16 and Aᵣ(H) = 1, identify the first error and recompute the amount.

Check the first error and its consequence

The outside 2 multiplies both O and H: M = 24 + 2(16 + 1) = 58 g mol⁻¹. The learner’s division method is valid, but its denominator is wrong. Correcting it gives n = 5.80/58 = 0.100 mol. An underestimated molar mass overestimates the amount.

Submit a direct calculation and error repair, then use the topic check to choose what to revisit.