QuestionApril 24, 2025

If 2.38 mol of a gas has a volume of 120.0 mL, what is the volume of 1.97 mol of the gas at the same temperature and pressure?

If 2.38 mol of a gas has a volume of 120.0 mL, what is the volume of 1.97 mol of the gas at the same temperature and pressure?
If 2.38 mol of a gas has a volume of 120.0 mL, what is the volume of 1.97 mol of the gas at the same temperature and pressure?

Solution
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Answer

99.3 mL Explanation 1. Use Avogadro's Law Avogadro's Law states that the volume of a gas is directly proportional to the number of moles at constant temperature and pressure. Therefore, \frac{V_1}{n_1} = \frac{V_2}{n_2}. 2. Calculate the Volume Given V_1 = 120.0 mL, n_1 = 2.38 mol, and n_2 = 1.97 mol, solve for V_2: \[ V_2 = \frac{V_1 \cdot n_2}{n_1} = \frac{120.0 \, \text{mL} \times 1.97 \, \text{mol}}{2.38 \, \text{mol}} \]

Explanation

1. Use Avogadro's Law<br /> Avogadro's Law states that the volume of a gas is directly proportional to the number of moles at constant temperature and pressure. Therefore, $\frac{V_1}{n_1} = \frac{V_2}{n_2}$.<br /><br />2. Calculate the Volume<br /> Given $V_1 = 120.0$ mL, $n_1 = 2.38$ mol, and $n_2 = 1.97$ mol, solve for $V_2$: <br />\[ V_2 = \frac{V_1 \cdot n_2}{n_1} = \frac{120.0 \, \text{mL} \times 1.97 \, \text{mol}}{2.38 \, \text{mol}} \]
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