25.0 g of a hydrocarbon undergoes complete combustion leading to the formation of 77.0  g of CO2. What is the % of carbon in the hydrocarbon?

1. Break Down the Problem

To find the percentage of carbon in the hydrocarbon, we need to:

1. Determine the mass of carbon in the CO2 produced.
2. Calculate the percentage of carbon in the original hydrocarbon.

2. Relevant Concepts

The molar mass of CO2 is: $\text{Molar mass of CO2} = 12.01 \, \text{g/mol (C)} + 2 \times 16.00 \, \text{g/mol (O)} = 44.01 \, \text{g/mol}$

3. Analysis and Detail

1. Calculate moles of CO2 produced: $\text{Moles of CO2} = \frac{\text{mass of CO2}}{\text{molar mass of CO2}} = \frac{77.0 \, \text{g}}{44.01 \, \text{g/mol}} \approx 1.75 \, \text{mol}$

2. Determine mass of carbon in CO2: Each mole of CO2 contains 1 mole of carbon. $\text{Mass of carbon} = \text{moles of CO2} \times \text{molar mass of C} = 1.75 \, \text{mol} \times 12.01 \, \text{g/mol} \approx 21.0 \, \text{g}$

3. Calculate the percentage of carbon in the hydrocarbon: $\text{Percentage of carbon} = \left( \frac{\text{mass of carbon}}{\text{mass of hydrocarbon}} \right) \times 100 = \left( \frac{21.0 \, \text{g}}{25.0 \, \text{g}} \right) \times 100 \approx 84.0\%$

4. Verify and Summarize

The calculations regarding moles of CO2 and the mass of carbon were checked and are correct. The percentage calculation is also verified to be accurate.

Final Answer

The percentage of carbon in the hydrocarbon is approximately 84.0%.