Question

Nicotine is found in tobacco leaf and is mainly responsible for the addictive property of cigarette smoking. Nicotine is made up of carbon, hydrogen, and nitrogen atoms. When a \(2.500-\mathrm{g}\) sample of nicotine is burned, \(6.782 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(1.944 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are obtained. What is the simplest formula for nicotine?

Short answer

Answer: The simplest formula for nicotine is C₅H₇N.

Step-by-step solution

Calculate moles of carbon from moles of CO₂

First, let's find the moles of carbon in nicotine. Since we know that CO₂ is produced by burning the carbon in nicotine, we can calculate the moles of carbon in nicotine using the mass of CO₂ produced. The molar mass of CO₂ is (12.01 g/mol for C) + (2 × 16.00 g/mol for O) = 44.01 g/mol. We have 6.782 g of CO₂, so to find the moles: moles of CO₂ = (mass of CO₂) / (molar mass of CO₂) moles of CO₂ = 6.782 g / 44.01 g/mol ≈ 0.154 mol Since each molecule of CO₂ contains one carbon atom, there are 0.154 mol of carbon in the nicotine sample.

Calculate moles of hydrogen from moles of H₂O

Next, we need to find the moles of hydrogen in nicotine. Since H₂O is produced by burning the hydrogen in nicotine, we can calculate the moles of hydrogen using the mass of H₂O produced. The molar mass of H₂O is (2 × 1.01 g/mol for H) + (16.00 g/mol for O) = 18.02 g/mol. We have 1.944 g of H₂O, so to find the moles: moles of H₂O = (mass of H₂O) / (molar mass of H₂O) moles of H₂O = 1.944 g / 18.02 g/mol ≈ 0.108 mol Since each molecule of H₂O contains two hydrogen atoms, there are 2 × 0.108 mol = 0.216 mol of hydrogen in the nicotine sample.

Calculate moles of nitrogen in nicotine

We are given that the mass of the nicotine sample is 2.500 g. We have already calculated the moles of carbon and hydrogen in the sample; now we can find the moles of nitrogen. First, determine the mass of carbon and hydrogen in the nicotine sample: mass of carbon = moles of carbon × molar mass of carbon = 0.154 mol × 12.01 g/mol ≈ 1.848 g mass of hydrogen = moles of hydrogen × molar mass of hydrogen = 0.216 mol × 1.01 g/mol ≈ 0.218 g Now, calculate the mass of nitrogen: mass of nitrogen = mass of nicotine - mass of carbon - mass of hydrogen mass of nitrogen = 2.500 g - 1.848 g - 0.218 g ≈ 0.434 g To find the moles of nitrogen, use the molar mass of nitrogen (14.01 g/mol): moles of nitrogen = (mass of nitrogen) / (molar mass of nitrogen) moles of nitrogen = 0.434 g / 14.01 g/mol ≈ 0.031 mol

Find the mole ratio and simplest formula

To find the simplest formula, we need to find the mole ratio of C, H, and N in nicotine. Divide the moles of each element by the smallest value (0.031 mol for N): C: 0.154 mol / 0.031 mol ≈ 5 H: 0.216 mol / 0.031 mol ≈ 7 N: 0.031 mol / 0.031 mol = 1 The mole ratio of C, H, and N is about 5:7:1. Therefore, the simplest formula for nicotine is C₅H₇N.