Answers – Empirical and Molecular Formulas – 2

Answer:

Given: 75.0% carbon, 25.0% hydrogen

Step 1: Convert percentages to masses (assuming 100g of compound)

Carbon: 75.0g

Hydrogen: 25.0g

Step 2: Convert masses to moles

Carbon: 75.0 ÷ 12 = 6.25 mol

Hydrogen: 25.0 ÷ 1 = 25.0 mol

Step 3: Find the simplest ratio by dividing by the smallest value (6.25)

Carbon: 6.25 ÷ 6.25 = 1

Hydrogen: 25.0 ÷ 6.25 = 4

Step 4: Write the empirical formula

The empirical formula is CH₄ (methane)

Answer:

Given: 43.4% sodium, 11.3% carbon, and 45.3% oxygen

Step 1: Convert percentages to masses (assuming 100g of compound)

Sodium: 43.4g

Carbon: 11.3g

Oxygen: 45.3g

Step 2: Convert masses to moles

Sodium: 43.4 ÷ 23 = 1.89 mol

Carbon: 11.3 ÷ 12 = 0.94 mol

Oxygen: 45.3 ÷ 16 = 2.83 mol

Step 3: Find the simplest ratio by dividing by the smallest value (0.94)

Sodium: 1.89 ÷ 0.94 = 2.01 ≈ 2

Carbon: 0.94 ÷ 0.94 = 1

Oxygen: 2.83 ÷ 0.94 = 3.01 ≈ 3

Step 4: Write the empirical formula

The empirical formula is Na₂CO₃ (sodium carbonate)

Answer:

Given: 2.8g silicon and 3.2g oxygen

Step 1: Convert masses to moles

Silicon: 2.8 ÷ 28 = 0.10 mol

Oxygen: 3.2 ÷ 16 = 0.20 mol

Step 2: Find the simplest ratio by dividing by the smallest value (0.10)

Silicon: 0.10 ÷ 0.10 = 1

Oxygen: 0.20 ÷ 0.10 = 2

Step 3: Write the empirical formula

The empirical formula is SiO₂ (silicon dioxide)

Answer:

Element	Number of atoms	Relative atomic mass	Total mass contribution
Carbon	1	12	1 × 12 = 12
Hydrogen	2	1	2 × 1 = 2
Oxygen	2	16	2 × 16 = 32
Relative molecular mass (Mr)			12 + 2 + 32 = 46

The relative molecular mass of methanoic acid (CH₂O₂) is 46.

Answer:

Element	Number of atoms	Relative atomic mass	Total mass contribution
Carbon	4	12	4 × 12 = 48
Hydrogen	10	1	10 × 1 = 10
Relative molecular mass (Mr)			48 + 10 = 58

The relative molecular mass of butane (C₄H₁₀) is 58.

Answer:

Given:

• Empirical formula: CH₂O
• Relative molecular mass: 120

Step 1: Calculate the empirical formula mass

C: 1 × 12 = 12

H: 2 × 1 = 2

O: 1 × 16 = 16

Empirical formula mass = 12 + 2 + 16 = 30

Step 2: Calculate the formula ratio

Formula ratio = Relative molecular mass ÷ Empirical formula mass

Formula ratio = 120 ÷ 30 = 4

Step 3: Calculate the molecular formula

Molecular formula = Empirical formula × Formula ratio

Molecular formula = (CH₂O) × 4 = C₄H₈O₄

The molecular formula is C₄H₈O₄.

Answer:

Given:

• Empirical formula: C₂H₃O
• Relative molecular mass: 86

Step 1: Calculate the empirical formula mass

C: 2 × 12 = 24

H: 3 × 1 = 3

O: 1 × 16 = 16

Empirical formula mass = 24 + 3 + 16 = 43

Step 2: Calculate the formula ratio

Formula ratio = Relative molecular mass ÷ Empirical formula mass

Formula ratio = 86 ÷ 43 = 2

Step 3: Calculate the molecular formula

Molecular formula = Empirical formula × Formula ratio

Molecular formula = (C₂H₃O) × 2 = C₄H₆O₂

The molecular formula is C₄H₆O₂.

Answer:

Given:

• 92.3% carbon and 7.7% hydrogen by mass
• Relative molecular mass: 78

Step 1: Calculate the empirical formula

Carbon: 92.3 ÷ 12 = 7.69 mol

Hydrogen: 7.7 ÷ 1 = 7.70 mol

Dividing by the smaller value (7.69):

Carbon: 7.69 ÷ 7.69 = 1

Hydrogen: 7.70 ÷ 7.69 = 1.001 ≈ 1

Empirical formula = CH

Step 2: Calculate the empirical formula mass

C: 1 × 12 = 12

H: 1 × 1 = 1

Empirical formula mass = 12 + 1 = 13

Step 3: Calculate the formula ratio

Formula ratio = Relative molecular mass ÷ Empirical formula mass

Formula ratio = 78 ÷ 13 = 6

Step 4: Calculate the molecular formula

Molecular formula = Empirical formula × Formula ratio

Molecular formula = (CH) × 6 = C₆H₆

The molecular formula is C₆H₆ (benzene).

Answer:

Given:

• 54.5% carbon, 9.1% hydrogen, and 36.4% oxygen by mass
• Relative molecular mass: 88

Step 1: Calculate the empirical formula

Carbon: 54.5 ÷ 12 = 4.54 mol

Hydrogen: 9.1 ÷ 1 = 9.10 mol

Oxygen: 36.4 ÷ 16 = 2.27 mol

Dividing by the smallest value (2.27):

Carbon: 4.54 ÷ 2.27 = 2.00

Hydrogen: 9.10 ÷ 2.27 = 4.01 ≈ 4

Oxygen: 2.27 ÷ 2.27 = 1.00

Empirical formula = C₂H₄O

Step 2: Calculate the empirical formula mass

C: 2 × 12 = 24

H: 4 × 1 = 4

O: 1 × 16 = 16

Empirical formula mass = 24 + 4 + 16 = 44

Step 3: Calculate the formula ratio

Formula ratio = Relative molecular mass ÷ Empirical formula mass

Formula ratio = 88 ÷ 44 = 2

Step 4: Calculate the molecular formula

Molecular formula = Empirical formula × Formula ratio

Molecular formula = (C₂H₄O) × 2 = C₄H₈O₂

The molecular formula is C₄H₈O₂ (butanoic acid).