If a sample of CO_2 contains 48 grams of oxygen, what is the mass of the CO_2 sample?

• A. 22 grams
• B. 88 grams
• C. 44 grams
• D. 64 grams

Answer: (B)

Verified step by step guidance

1. Identify the chemical formula of carbon dioxide, which is \(\mathrm{CO_2}\). This means each molecule contains 1 carbon atom and 2 oxygen atoms.
2. Calculate the molar mass of oxygen in \(\mathrm{CO_2}\). Since oxygen has an atomic mass of approximately 16 g/mol, the total mass of oxygen in one mole of \(\mathrm{CO_2}\) is \$2 \times 16 = 32$ grams.
3. Recognize that the total molar mass of \(\mathrm{CO_2}\) is the sum of the molar masses of carbon and oxygen: \$12\( g/mol for carbon plus \)32\( g/mol for oxygen, giving \)44$ g/mol total.
4. Set up a proportion relating the given mass of oxygen in the sample (48 grams) to the total mass of the \(\mathrm{CO_2}\) sample. Since oxygen makes up 32 grams out of every 44 grams of \(\mathrm{CO_2}\), use the ratio \(\frac{32}{44} = \frac{48}{x}\), where \(x\) is the total mass of the \(\mathrm{CO_2}\) sample.
5. Solve the proportion for \(x\) to find the total mass of the \(\mathrm{CO_2}\) sample: \(x = \frac{48 \times 44}{32}\). This will give the mass of the \(\mathrm{CO_2}\) sample corresponding to 48 grams of oxygen.