8B Caffeine (M = 194.2 g/mol) is a stimulant found in coffee, tea, many soft drinks, and chocolate. Elemental…

Question

8B Caffeine (M = 194.2 g/mol) is a stimulant found in coffee, tea, many soft drinks, and chocolate. Elemental analysis of caffeine shows 49.47 mass % C, 5.19 mass % H, 28.86 mass % N, and 16.48 mass % O. What is the molecular formula of caffeine?

ScanSolve AI Tutor · Accepted Answer

To find the molecular formula of caffeine, we will first determine its empirical formula from the given mass percentages and then use the molar mass to find the molecular formula.

Assume a 100 g sample to convert mass percentages to grams.
- Mass of C = $49.47 \text{ g}$
- Mass of H = $5.19 \text{ g}$
- Mass of N = $28.86 \text{ g}$
- Mass of O = $16.48 \text{ g}$
Convert the mass of each element to moles using their respective atomic masses (C = 12.01 g/mol, H = 1.008 g/mol, N = 14.01 g/mol, O = 16.00 g/mol).
$\text{Moles of C} = \frac{49.47 \text{ g}}{12.01 \text{ g/mol}} = 4.119 \text{ mol}$ $\text{Moles of H} = \frac{5.19 \text{ g}}{1.008 \text{ g/mol}} = 5.149 \text{ mol}$ $\text{Moles of N} = \frac{28.86 \text{ g}}{14.01 \text{ g/mol}} = 2.060 \text{ mol}$ $\text{Moles of O} = \frac{16.48 \text{ g}}{16.00 \text{ g/mol}} = 1.030 \text{ mol}$
Divide the number of moles of each element by the smallest number of moles (1.030 mol for O) to find the simplest whole-number ratio.
$\text{Ratio for C} = \frac{4.119 \text{ mol}}{1.030 \text{ mol}} \approx 4.00$ $\text{Ratio for H} = \frac{5.149 \text{ mol}}{1.030 \text{ mol}} \approx 5.00$ $\text{Ratio for N} = \frac{2.060 \text{ mol}}{1.030 \text{ mol}} \approx 2.00$ $\text{Ratio for O} = \frac{1.030 \text{ mol}}{1.030 \text{ mol}} = 1.00$
Write the empirical formula based on these ratios.
The empirical formula is $\text{C}_4\text{H}_5\text{N}_2\text{O}$ .
Calculate the empirical formula mass.
$\text{Empirical formula mass} = (4 \times 12.01) + (5 \times 1.008) + (2 \times 14.01) + (1 \times 16.00)$ $= 48.04 + 5.040 + 28.02 + 16.00 = 97.10 \text{ g/mol}$
Determine the ratio between the given molar mass and the empirical formula mass.
The given molar mass ( $\mathcal{M}$ ) of caffeine is 194.2 g/mol.
$n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}} = \frac{194.2 \text{ g/mol}}{97.10 \text{ g/mol}} \approx 2.00$
Multiply the subscripts in the empirical formula by this ratio ( $n=2$ ) to get the molecular formula.
$\text{Molecular Formula} = (\text{C}_4\text{H}_5\text{N}_2\text{O})_2 = \text{C}_{4 \times 2}\text{H}_{5 \times 2}\text{N}_{2 \times 2}\text{O}_{1 \times 2} = \text{C}_8\text{H}_{10}\text{N}_4\text{O}_2$
The molecular formula of caffeine is $\text{C}_8\text{H}_{10}\text{N}_4\text{O}_2$ .

8B Caffeine (M = 194.2 g/mol) is a stimulant found in coffee, tea, many soft drinks, and chocolate. Elemental analysis of caffeine shows 49.47 mass % C, 5.19 mass % H, 28.86 mass % N, and 16.48 mass % O. What is the molecular formula of caffeine?

Answer

Step-by-step solution

Assume a 100 g sample to convert mass percentages to grams.

Convert the mass of each element to moles using their respective atomic masses (C = 12.01 g/mol, H = 1.008 g/mol, N = 14.01 g/mol, O = 16.00 g/mol).

Divide the number of moles of each element by the smallest number of moles (1.030 mol for O) to find the simplest whole-number ratio.

Write the empirical formula based on these ratios.

Calculate the empirical formula mass.

Determine the ratio between the given molar mass and the empirical formula mass.

Multiply the subscripts in the empirical formula by this ratio ( $n=2$ ) to get the molecular formula.

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8B Caffeine (M = 194.2 g/mol) is a stimulant found in coffee, tea, many soft drinks, and chocolate. Elemental analysis of caffeine shows 49.47 mass % C, 5.19 mass % H, 28.86 mass % N, and 16.48 mass % O. What is the molecular formula of caffeine?

Answer

Step-by-step solution

Assume a 100 g sample to convert mass percentages to grams.

Convert the mass of each element to moles using their respective atomic masses (C = 12.01 g/mol, H = 1.008 g/mol, N = 14.01 g/mol, O = 16.00 g/mol).

Divide the number of moles of each element by the smallest number of moles (1.030 mol for O) to find the simplest whole-number ratio.

Write the empirical formula based on these ratios.

Calculate the empirical formula mass.

Determine the ratio between the given molar mass and the empirical formula mass.

Multiply the subscripts in the empirical formula by this ratio (n=2n=2n=2) to get the molecular formula.

Try one yourself

Still stuck on this one?

More Chemistry Questions

Multiply the subscripts in the empirical formula by this ratio ( $n=2$ ) to get the molecular formula.