Question

A sample of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) contains \(2.02 \mathrm{~g}\) of hydrogen, \(32.07 \mathrm{~g}\) of sulfur, and \(64.00 \mathrm{~g}\) of oxygen. How many grams of sulfur and grams of oxygen are present in a second sample of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) containing \(7.27 \mathrm{~g}\) of hydrogen?

Short answer

In the first sample, the mass ratio of hydrogen to sulfur is \(\frac{2.02}{32.07}\) and the mass ratio of hydrogen to oxygen is \(\frac{2.02}{64.00}\). In the second sample, containing \(7.27\text{ g}\) of hydrogen, the mass of sulfur is \(\frac{2.02}{32.07} \times 7.27 \approx 4.59\text{ g}\) and the mass of oxygen is \(\frac{2.02}{64.00} \times 7.27 \approx 9.18\text{ g}\).

Step-by-step solution

Calculate the mass ratio between hydrogen and sulfur, and hydrogen and oxygen in the first sample

In the given problem, we have the mass of hydrogen (\(2.02\text{ g}\)), sulfur (\(32.07\text{ g}\)), and oxygen (\(64.00\text{ g}\)) in the first sample of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). Let's find the mass ratio between hydrogen and sulfur, and hydrogen and oxygen. Mass ratio of hydrogen to sulfur: \(\frac{\text{mass of hydrogen}}{\text{mass of sulfur}} = \frac{2.02}{32.07}\) Mass ratio of hydrogen to oxygen: \(\frac{\text{mass of hydrogen}}{\text{mass of oxygen}} = \frac{2.02}{64.00}\) Calculate the values for the mass ratios.

Calculate the mass of sulfur and oxygen in the second sample

In the second sample, we are given the mass of hydrogen as \(7.27\text{ g}\). Using the mass ratios we calculated in the first step (Step 1), we can find the mass of sulfur and oxygen in the second sample. Mass of sulfur in the second sample: \[\text{mass of sulfur} = \text{mass ratio of hydrogen to sulfur} \times \text{mass of hydrogen in the second sample}\] Mass of oxygen in the second sample: \[\text{mass of oxygen} = \text{mass ratio of hydrogen to oxygen} \times \text{mass of hydrogen in the second sample}\] Plug the values of the mass ratios and the mass of hydrogen in the second sample (\(7.27\text{ g}\)) into the equations and calculate the mass of sulfur and oxygen in the second sample.