Final answer:
To calculate the percentage of carbon in the sample, the carbon in the CO₂ produced is found to be 0.9 grams by using the molecular mass of CO₂ and the proportion of carbon in it. This value is then divided by the initial sample mass of 3.6 grams and multiplied by 100% to yield a 25% carbon content.
Step-by-step explanation:
To determine the percentage of carbon in the sample from the combustion that produced 3.3 grams of CO₂, we need to calculate the mass of carbon in the CO₂ and then find what percentage this mass is of the original 3.6-gram sample.
First, we know that CO₂ consists of one carbon atom and two oxygen atoms. The atomic mass of carbon is approximately 12 u (atomic mass units), and that of oxygen is about 16 u. Therefore, CO₂ has a molecular mass of 12 u + (2 × 16 u) = 44 u.
Since the mass of carbon in CO₂ is 12 u out of the total 44 u, the proportion by mass of carbon in CO₂ is ³/₄₄. By multiplying the mass of CO₂ (3.3 grams) by this proportion, we get the mass of carbon in the CO₂ which is (³/₄₄) × 3.3 grams = 0.9 grams.
Finally, to find the percentage of carbon in the original sample, we divide the mass of carbon by the total mass of the sample and multiply by 100%:
Percentage of carbon = (0.9 g / 3.6 g) × 100% = 25%