A chemist finds that \(30.82 \mathrm{~g}\) of nitrogen will react with 17.60 , \(35.20,70.40,\) or \(88.00 \mathrm{~g}\) of oxygen to form four different compounds. (a) Calculate the mass of oxygen per gram of nitrogen in each compound. (b) How do the numbers in part (a) support Dalton's atomic theory?

To find the ratio of the mass of oxygen to the mass of nitrogen in a compound, we divide the mass of oxygen in the compound by the mass of nitrogen. For the given problem, there are four different compounds formed, and we can calculate the oxygen-to-nitrogen mass ratio for each of them. Mass of Nitrogen = 30.82 g Compound 1: Mass of Oxygen: 17.60 g Oxygen-to-nitrogen mass ratio = \( \frac{17.60}{30.82} \) Compound 2: Mass of Oxygen: 35.20 g Oxygen-to-nitrogen mass ratio = \( \frac{35.20}{30.82} \) Compound 3: Mass of Oxygen: 70.40 g Oxygen-to-nitrogen mass ratio = \( \frac{70.40}{30.82} \) Compound 4: Mass of Oxygen: 88.00 g Oxygen-to-nitrogen mass ratio = \( \frac{88.00}{30.82} \) Now, let's compute these ratios.

Compute the oxygen-to-nitrogen mass ratios by dividing the mass of oxygen by the mass of nitrogen for each compound. Compound 1: Oxygen-to-nitrogen mass ratio = \( \frac{17.60}{30.82} \approx 0.571 \) Compound 2: Oxygen-to-nitrogen mass ratio = \( \frac{35.20}{30.82} \approx 1.142 \) Compound 3: Oxygen-to-nitrogen mass ratio = \( \frac{70.40}{30.82} \approx 2.284 \) Compound 4: Oxygen-to-nitrogen mass ratio = \( \frac{88.00}{30.82} \approx 2.855 \)

Dalton's atomic theory states that elements combine in simple whole-number ratios to form compounds. Therefore, if a pattern exists in the ratios obtained in step 2, it would support Dalton's atomic theory. Let's examine the oxygen-to-nitrogen mass ratios calculated previously: Compound 1: 0.571 Compound 2: 1.142 Compound 3: 2.284 Compound 4: 2.855 Observe that these mass ratios can be approximated by simple whole-number ratios: Compound 1: 1 Compound 2: 2 Compound 3: 4 Compound 4: 5 These approximations show that the compounds are formed according to simple whole-number ratios of oxygen to nitrogen atoms, which supports Dalton's atomic theory.