Molecular formula: from empirical and structural formulas

How many empirical units in one molecule?

A molecular formula is a whole number n of empirical formula units. Find n by dividing the molar mass by the empirical formula mass.

Hydrogen peroxide: empirical formula HO has mass 17 and the molar mass is 34, so n is 2 and the molecule is H₂O₂. Benzene: CH has mass 13, molar mass 78, so n is 6: C₆H₆.

If n comes out as 1, the molecular and empirical formulas are the same.

From a structural formula, count each kind of atom, write the symbols with the totals as subscripts, and drop any 1. Acetic acid CH₃COOH has 2 C, 4 H and 2 O: C₂H₄O₂.

The empirical formula alone cannot tell CH₂O (30) from glucose (180); the molar mass decides.

Key terms

n

Scaling the empirical formula up.

Empirical formula mass

The bottom of the n fraction.

Molar mass

The top of the n fraction.

Structural formula

Counting atoms to get the molecular formula.

Short questions with model answers

1. Q1. Empirical formula CH, molar mass 78 g mol⁻¹. Find the molecular formula. (p. 56)

   • CH = 12 + 1 = 13
   • n = 78 ÷ 13 = 6
   • (CH)₆ = C₆H₆

   C₆H₆ (benzene)

2. Q2. Find the molecular formula of n-propyl alcohol, CH₃–CH₂–CH₂–OH. (p. 57)

   • C: 1 + 1 + 1 = 3
   • H: 3 + 2 + 2 + 1 = 8
   • O: 1

   C₃H₈O

Common mistakes

• ✗ n = empirical formula mass ÷ molar mass.

  ✓ n = molar mass ÷ empirical formula mass, so n is 1 or more.

• ✗ (CH₂O)₆ is C₆H₂O₆: only the first symbol is multiplied.

  ✓ Every subscript is multiplied by n: C₆H₁₂O₆.

• ✗ CH₃–CH₂–CH₂–OH has 7 hydrogen atoms.

  ✓ Count the H in OH too: 8.

MCQs

1. 1. Empirical formula HO, molar mass 34. Molecular formula?

   1. (a) HO
   2. (b) H₂O
   3. (c) H₂O₂
   4. (d) H₃O₃
   Show answer

   (c) n = 34 ÷ 17 = 2 (p. 55).

2. 2. Empirical formula CH₂O, molar mass 60. n is:

   1. (a) 1
   2. (b) 2
   3. (c) 3
   4. (d) 6
   Show answer

   (b) 60 ÷ 30 = 2, giving C₂H₄O₂ (exercise 2, p. 56).

3. 3. (CH₂O)₆ is written as:

   1. (a) C₆H₂O₆
   2. (b) C₆H₁₂O₆
   3. (c) CH₁₂O
   4. (d) C₆H₁₂O
   Show answer

   (b) Multiply every subscript by 6.

4. 4. The molecular formula of acetic acid, CH₃COOH, is:

   1. (a) C₂H₄O₂
   2. (b) CH₄O₂
   3. (c) C₂H₃O₂
   4. (d) C₂H₄O
   Show answer

   (a) 2 C, 4 H, 2 O (p. 57).

5. 5. If n = 1, the molecular formula is:

   1. (a) Half the empirical formula
   2. (b) Double the empirical formula
   3. (c) The same as the empirical formula
   4. (d) Impossible to find
   Show answer

   (c) p. 56: if n is one, both formulas are the same.

Quick revision

• Molecular formula = n × empirical formula.
• n = molar mass ÷ empirical formula mass; multiply every subscript by n.
• From a structural formula, count each kind of atom and drop subscripts of 1.