How do you Calculate the Molar Mass of a Substance?

How do you Calculate the Molar Mass of a Substance?

1. Molar mass of a substance is the mass of one mole of the substance in grams. It has a unit of grams per mole (g mol^-1).
2. One mole of any substance contains 6.02 × 10²³ particles. Therefore, the molar mass of a substance contains 6.02 × 10²³ particles of the substance.
3. The molar mass of any substance is numerically equal to its relative atomic, molecular or formula mass.
   (a) This means, to measure 1 mole of atoms of any element, we only need to weigh a mass equal to its relative atomic mass in grams.
   (b) Similarly, the mass of 1 mole of molecules of any molecular substance is equal to its relative molecular mass in grams.
   (c) The mass of 1 mole of any ionic substance is equal to its relative formula mass in grams.
4. Based on Table below, 1 mole of magnesium can be measured by weighing 24 g of magnesium.
   This amount of magnesium contains 6.02 × 10²³ magnesium atoms.

   Substance	Relative mass	Molar mass (g mol-1)
   Magnesium, Mg	Ar = 24	24
   Helium, He	Ar = 4	4
   Hydrogen gas, H2	Mr = 2(1) = 2	2
   Methane, CH4	Mr = 12 + 4(1) = 16	16
   Sodium chloride, NaCl	Fr = 23 + 35.5 = 58.5	58.5
   Zinc bromide, ZnBr2	Fr = 65 + 2(80) = 225	225

   [Relative atomic mass: H, 1; He, 4; C, 12; Na, 23; g Mg, 24; Cl, 35.5; Zn, 65; Br, 80]

5. The mass of any number of moles of a substance or vice versa can be calculated easily using the following relationship.
   
6. Equal numbers of moles of substances always contain the same number of particles even though they differ in mass and size.
   
   Figure: Both blocks of magnesium and iron contain 0.5 x 6.02 x 10²³ atoms. [Relative atomic mass: Mg, 24; Fe,56]
7. For this reason, we can compare the number of particles in substances by comparing the number of moles of the substances.

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Molar Mass of a Substance Problems with Solutions

1. Find the mass of the following.
(a) 0.5 mole of copper
(b) 1.5 moles of carbon dioxide
[Relative atomic mass: C, 12; O, 16; Cu, 64]
Solution:
(a) Relative atomic mass of copper = 64
So, the molar mass of copper = 64 g mol^-1
Mass of 0.5 mole of copper = number of moles x molar mass
= 0.5 x 64 = 32g
(b) Relative molecular mass of carbon dioxide, CO₂ = 12 + 2(16) = 44
So, the molar mass of CO₂ = 44 g mol^-1
Mass of 1.5 moles of CO₂ = number of moles x molar mass
= 1.5 x 44 = 66g

2. Find the number of moles of sodium hydroxide with the mass of 2.0 g.
[Relative atomic mass: H, 1; O,16; Na, 23]
Solution:
Relative formula mass of sodium hydroxide, NaOH = 23+16+1 = 40
So, the molar mass of NaOH = 40 g mol^-1
Therefore, the number of moles of NaOH
= mass of NaOH ÷ molar mass
= 2/40
= 0.05 mol

3. What is the number of moles of calcium nitrate in 49.2 g of calcium nitrate, Ca(NO₃)₂?
[Relative atomic mass: O, 16; Ca, 40; N, 14]
A. 0.30 mol
B. 0.36 mol
C. 0.45 mol
D. 0.48 mol
Solution:
Relative formula mass of Ca(NO₃)₂ = 40 + 2[14 + 3(16)] = 164
So, molar mass of Ca(NO₃)₂ = 164 g mol^-1
Number of moles of Ca(NO₃)₂ = Mass of Ca(NO₃)₂ ÷ molar mass of Ca(NO₃)₂
= 49.2/164
= 0.3 mol
Answer: A

4. What is the mass of gold that has the same number of atoms as in 4 g of oxygen?
[Relative atomic mass: O, 16; Au, 197]
Solution:
Number of moles of oxygen atoms, O = mass of O ÷ molar mass of O
= 4/16 = 0.25 mol
0.25 mole of gold will have the same number of atoms with 0.25 mole of oxygen.
Therefore, the mass of gold, Au
= number of moles of Au x molar mass of Au
= 0.25 x 197
= 49.25 g

5. What is the mass of hydrogen gas that has twice the number of molecules as in 1.6 g of oxygen gas?
[Relative atomic mass: H, 1; O,16]
Solution:
Relative molecular mass of oxygen gas, O₂ = 2(16) = 32
Therefore, the molar mass of O, = 32 g mol^-1
Number of moles of O₂ = mass of O₂ ÷ molar mass of O₂
= 1.6/32 = 0.05 mol
Thus, the number of moles of hydrogen gas, H₂ that contains twice the number of molecules in 0.05 mole of O₂
= 2 x 0.05 mol = 0.1 mol
Mass of 0.1 mole of H₂
= number of moles of H₂ x molar mass of H₂
= 0.1 x 2(1) = 0.2 g

6. How many times more is the number of atoms in 7 g of nitrogen gas compared to that in 7 g of iron? [Relative atomic mass: N, 14; Fe, 56]
Solution:
Here, we need to compare the number of moles of atoms in both substances.

Therefore, the number of atoms in 7 g of nitrogen gas is 4 times more than that in 7 g of iron.

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