QuestionJuly 3, 2025

13) What is the molar mass of a 0.726 g sample of gas that occupies 855 mL at 1 .20 atm and 18^circ C

13) What is the molar mass of a 0.726 g sample of gas that occupies 855 mL at 1 .20 atm and 18^circ C
13) What is the molar mass of a 0.726 g sample of gas that occupies
855 mL at 1 .20 atm and 18^circ C

Solution
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Answer

16.73 g/mol Explanation 1. Convert Volume to Liters Convert 855 mL to liters: 855 \, \text{mL} = 0.855 \, \text{L}. 2. Convert Temperature to Kelvin Convert 18^{\circ}C to Kelvin: T = 18 + 273.15 = 291.15 \, \text{K}. 3. Use Ideal Gas Law to Find Moles Use **PV = nRT** where P = 1.20 \, \text{atm}, V = 0.855 \, \text{L}, R = 0.0821 \, \text{L atm/mol K}, and T = 291.15 \, \text{K}. Solve for n: \[ n = \frac{PV}{RT} = \frac{1.20 \times 0.855}{0.0821 \times 291.15} \approx 0.0434 \, \text{mol} \] 4. Calculate Molar Mass Molar mass M = \frac{\text{mass}}{n} = \frac{0.726 \, \text{g}}{0.0434 \, \text{mol}} \approx 16.73 \, \text{g/mol}.

Explanation

1. Convert Volume to Liters<br /> Convert 855 mL to liters: $855 \, \text{mL} = 0.855 \, \text{L}$.<br /><br />2. Convert Temperature to Kelvin<br /> Convert $18^{\circ}C$ to Kelvin: $T = 18 + 273.15 = 291.15 \, \text{K}$.<br /><br />3. Use Ideal Gas Law to Find Moles<br /> Use **$PV = nRT$** where $P = 1.20 \, \text{atm}$, $V = 0.855 \, \text{L}$, $R = 0.0821 \, \text{L atm/mol K}$, and $T = 291.15 \, \text{K}$.<br /> Solve for $n$: <br />\[ n = \frac{PV}{RT} = \frac{1.20 \times 0.855}{0.0821 \times 291.15} \approx 0.0434 \, \text{mol} \]<br /><br />4. Calculate Molar Mass<br /> Molar mass $M = \frac{\text{mass}}{n} = \frac{0.726 \, \text{g}}{0.0434 \, \text{mol}} \approx 16.73 \, \text{g/mol}$.
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