Math  /  Algebra

Question1. Write a balanced chemical equation, including physical state symbols, for the combustion of liquid nonane into gaseous carbon dioxide and gaseous water. C9H20(l)+14O2(g)9CO2(g)+10H2O(g)\mathrm{C}_{9} \mathrm{H}_{20}(l)+14 \mathrm{O}_{2}(g) \rightarrow 9 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)
2. Suppose 0.340 kg of nonane are burned in air at a pressure of exactly 1 atm and a temperature of 15.0C15.0^{\circ} \mathrm{C}. Calculate the volume of carbon dioxide gas that is produced. Round your answer to 3 significant digits. \square L

Studdy Solution
Use the ideal gas law to calculate the volume of carbon dioxide. The ideal gas law is given by:
PV=nRT PV = nRT
Where: - P=1atm P = 1 \, \text{atm} - V=?L V = ? \, \text{L} - n=23.85mol n = 23.85 \, \text{mol} - R=0.0821L atm/mol K R = 0.0821 \, \text{L atm/mol K} - T=15.0C=288.15K T = 15.0^{\circ} \mathrm{C} = 288.15 \, \text{K}
Rearrange the ideal gas law to solve for V V :
V=nRTP V = \frac{nRT}{P}
V=23.85mol×0.0821L atm/mol K×288.15K1atm V = \frac{23.85 \, \text{mol} \times 0.0821 \, \text{L atm/mol K} \times 288.15 \, \text{K}}{1 \, \text{atm}}
V563.5L V \approx 563.5 \, \text{L}
Round to 3 significant digits:
V564L V \approx 564 \, \text{L}
The volume of carbon dioxide gas produced is:
564L \boxed{564} \, \text{L}

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