M19 Question

[Roma Patel 1K]

Hello, for the following question, I understand the process that is required, but can someone explain why we have to solve for every other amount before we can find oxygen? More specifically, why do we have to find the total grams and subtract? Is there another way to solve?

[mohammada1f]

We subtract to find oxygen because its mass is not directly measured in the combustion products (CO₂, H₂O, and N₂). Using the law of conservation of mass, the total mass of the caffeine sample must equal the sum of the masses of its elements (C, H, N, and O). Since carbon, hydrogen, and nitrogen are accounted for in the measured masses of the combustion products, the remaining mass belongs to oxygen. This approach avoids the complexity of tracking oxygen atoms individually across multiple products, making subtraction the simplest method.