6.4.1 Gram Atomic Mass, Gram Molecular Mass and Gram Formula Mass

This topic explains three closely related quantities — gram atomic mass, gram molecular mass, and gram formula mass — all of which tell you the mass of one mole of a substance.

Definition

Gram Atomic Mass

Atomic mass of an element expressed in grams is called gram atomic mass.

Simple explanation: Gram atomic mass is the atomic mass of an element, but written in grams instead of amu.

Gram Molecular Mass

Molecular mass of a molecular compound expressed in grams is called gram molecular mass.

Simple explanation: Gram molecular mass is the molecular mass of a compound, but written in grams instead of amu.

Gram Formula Mass

Formula mass of an ionic compound expressed in grams is called gram formula mass.

Simple explanation: Gram formula mass is the formula mass of an ionic compound, but written in grams instead of amu.

Main Idea

The book shows this with a simple pattern:

• Atomic mass of C = 12 amu → Gram atomic mass of C = 12 g
• Atomic mass of Na = 23 amu → Gram atomic mass of Na = 23 g
• Atomic mass of Zn = 63.54 amu → Gram atomic mass of Zn = 63.54 g

So:

Gram atomic mass of an element contains 1 mole of atoms.

Mass of 1 mole of C-atoms = 12 g

Mass of 1 mole of Na-atoms = 23 g

Mass of 1 mole of Zn-atoms = 63.54 g

Simple explanation: If you take the atomic mass and change "amu" to "grams," you get the mass of one mole of that element.

Core Concept

Detailed Explanation

Gram Atomic Mass

The atomic mass of an element expressed in grams is called its gram atomic mass.

Gram atomic mass of an element contains 1 mole of atoms.

Examples from the book:

Atomic mass of C = 12 amu ⇒ Gram atomic mass of C = 12 g

Atomic mass of Na = 23 amu ⇒ Gram atomic mass of Na = 23 g

Atomic mass of Zn = 63.54 amu ⇒ Gram atomic mass of Zn = 63.54 g

So:

Mass of 1 mole of C-atoms = 12 g

Mass of 1 mole of Na-atoms = 23 g

Mass of 1 mole of Zn-atoms = 63.54 g

Simple explanation: 1 mole of carbon weighs 12 g; 1 mole of sodium weighs 23 g; 1 mole of zinc weighs 63.54 g.

Gram Molecular Mass

The molecular mass of a molecular compound expressed in grams is called its gram molecular mass.

Gram molecular mass contains 1 mole of molecules.

Examples:

Simple explanation: 1 mole of water molecules weighs 18 g; 1 mole of glucose molecules weighs 180 g.

Gram Formula Mass

The formula mass of an ionic compound expressed in grams is called its gram formula mass.

Gram formula mass contains 1 mole of formula units.

Examples:

Simple explanation: 1 mole of NaCl formula units weighs 58.5 g.

Book Example: Mass of One Mole

The book gives this example (Figure 6.2):

• Mass of 6.022 × 10²³ S-atoms = 32.1 g → this is the gram atomic mass of sulphur.
• Mass of 6.022 × 10²³ C-atoms = 12.0 g → this is the gram atomic mass of carbon.

• What is the mass of 6.022 × 10²³ S-atoms? → 32.1 g
• Is this mass equal to its atomic mass? → No — it is equal to the gram atomic mass (atomic mass in grams).
• What is the mass of one mole of C-atoms? → 12.0 g
• Is this mass equal to its atomic mass? → No — it is equal to the gram atomic mass (12 g).

Simple explanation: The number 6.022 × 10²³ tells you how many particles are in one mole. The mass of that mole depends on the substance.

Why Do Different Moles Have Different Masses?

The book asks:

> "If each of the carbon and sulphur sample shown above contains one mole of atoms, why do the samples have different masses?"

Answer: Because carbon and sulphur have different atomic masses.

• Carbon's atomic mass = 12 amu → 1 mole of carbon = 12 g
• Sulphur's atomic mass = 32.1 amu → 1 mole of sulphur = 32.1 g

One mole always contains the same number of particles (6.022 × 10²³), but different elements have different masses per atom, so one mole of each has a different mass.

Simple explanation: Same number of atoms, but different masses per atom → different total masses.

Intermediate Level

Why These Terms Matter

These terms connect the microscopic world (atoms, molecules) to the macroscopic world (grams) in a practical way.

• Find the atomic/molecular/formula mass in amu.
• Weigh out that many grams of the substance.

Simple explanation: You can't count 6.022 × 10²³ particles, but you can weigh them.

Relation to Avogadro's Number

Key relationship:

Gram atomic mass = atomic mass in grams = mass of 1 mole of atoms

Gram molecular mass = molecular mass in grams = mass of 1 mole of molecules

Gram formula mass = formula mass in grams = mass of 1 mole of formula units

Examples from the Book

Example 6.3: Calculating the molar masses of (a) Na, (b) Nitrogen, (c) Sucrose C₁₂H₂₂O₁₁

Solution:

(a) Na (metal): Molar mass = atomic mass in grams = 23 g/mol

• Molecular mass of N₂ = 14 × 2 = **28 amu**
• Mass of 1 mole of N₂ = **28 g**

• Molecular mass = 12 × 12 + 1 × 22 + 16 × 11
• = 144 + 22 + 176
• = **342 amu**
• Mass of 1 mole of sucrose = 342 g

Comparison Table

Important Points

• - Gram atomic mass: atomic mass of an element expressed in grams.
• - Gram molecular mass: molecular mass of a molecular compound expressed in grams.
• - Gram formula mass: formula mass of an ionic compound expressed in grams.
• - Gram atomic mass of C = 12 g (1 mole of C atoms).
• - Gram atomic mass of Na = 23 g (1 mole of Na atoms).
• - Gram atomic mass of Zn = 63.54 g (1 mole of Zn atoms).
• - Gram molecular mass of H₂O = 18 g (1 mole of H₂O molecules).
• - Gram formula mass of NaCl = 58.5 g (1 mole of NaCl formula units).
• - One mole always contains 6.022 × 10²³ particles.
• - Different substances have different masses per mole because their particles have different masses.

Remember

• - Gram atomic mass = atomic mass in grams → 1 mole of atoms.
• - Gram molecular mass = molecular mass in grams → 1 mole of molecules.
• - Gram formula mass = formula mass in grams → 1 mole of formula units.
• - **C** = 12 g; **Na** = 23 g; **Zn** = 63.54 g.
• - **H₂O** = 18 g; **CO₂** = 44 g; **C₆H₁₂O₆** = 180 g.
• - **NaCl** = 58.5 g; **Mg(OH)₂** = 58 g.
• - **1 mole** = 6.022 × 10²³ particles.

Common Mistakes

• 1. Thinking gram atomic mass and atomic mass are the same. Atomic mass is in amu; gram atomic mass is in grams.
• 2. Thinking 1 mole of all substances has the same mass. Different substances have different molar masses.
• 3. Forgetting to use the correct term. Use gram atomic mass for elements, gram molecular mass for molecular compounds, gram formula mass for ionic compounds.
• 4. Forgetting to multiply by subscripts. For H₂O, molecular mass = 2(1) + 16 = 18 amu.
• 5. Thinking diatomic elements like N₂ have the same molar mass as N atoms. N₂ = 28 g/mol; N = 14 g/mol.
• 6. Forgetting Avogadro's number. 1 mole = 6.022 × 10²³ particles.

Quick Revision

• Gram atomic mass: atomic mass of an element expressed in grams.
• Gram molecular mass: molecular mass of a molecular compound expressed in grams.
• Gram formula mass: formula mass of an ionic compound expressed in grams.
• Examples:
• C: atomic mass = 12 amu → gram atomic mass = 12 g
• Na: atomic mass = 23 amu → gram atomic mass = 23 g
• Zn: atomic mass = 63.54 amu → gram atomic mass = 63.54 g
• H₂O: molecular mass = 18 amu → gram molecular mass = 18 g
• NaCl: formula mass = 58.5 amu → gram formula mass = 58.5 g
• Gram atomic mass of an element contains 1 mole of atoms.
• **1 mole** = 6.022 × 10²³ particles.

60-Second Revision

• Gram atomic mass = atomic mass in grams (C = 12 g, Na = 23 g).
• Gram molecular mass = molecular mass in grams (H₂O = 18 g).
• Gram formula mass = formula mass in grams (NaCl = 58.5 g).
• **1 mole** = 6.022 × 10²³ particles.
• Warning: gram atomic mass is in grams, not amu.