A chemist finds that \(30.82 \mathrm{~g}\) of nitrogen will react with \(17.60 \mathrm{~g}\), \(35.20 \mathrm{~g}, 70.40 \mathrm{~g},\) 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?

We have four compounds with different masses of oxygen reacting with the same mass of nitrogen. We will find the mass of oxygen per gram of nitrogen for each compound by dividing the mass of oxygen by the mass of nitrogen. 1. For the compound with 17.60 g of oxygen: \(\frac{17.60}{30.82} = 0.571\) 2. For the compound with 35.20 g of oxygen: \(\frac{35.20}{30.82} = 1.142\) 3. For the compound with 70.40 g of oxygen: \(\frac{70.40}{30.82} = 2.284\) 4. For the compound with 88.00 g of oxygen: \(\frac{88.00}{30.82} = 2.855\) So the mass of oxygen per gram of nitrogen for the four compounds are approximately 0.571, 1.142, 2.284, and 2.855, respectively.

Dalton's atomic theory states that elements combine in fixed proportions to form compounds. In this case, we can see that the mass ratios of oxygen to nitrogen are related by simple whole numbers. We can observe the following relationships between the mass ratios: 1. The mass ratio in compound 2 is approximately 2 times the mass ratio in compound 1 (1.142 / 0.571 ≈ 2) 2. The mass ratio in compound 3 is approximately 4 times the mass ratio in compound 1 (2.284 / 0.571 ≈ 4) 3. The mass ratio in compound 4 is approximately 5 times the mass ratio in compound 1 (2.855 / 0.571 ≈ 5) This shows that the compounds are formed by combining oxygen and nitrogen in fixed, whole-number ratios, supporting Dalton's atomic theory.