QuestionJune 3, 2025

At what temperature does sulfur tetrafluoride have a density of 0.310g/L at 0.0721 atm?

At what temperature does sulfur tetrafluoride have a density of 0.310g/L at 0.0721 atm?
At what temperature does sulfur tetrafluoride
have a density of 0.310g/L at 0.0721 atm?

Solution
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Answer

T \approx 413.5 K Explanation 1. Use Ideal Gas Law The formula is PV = nRT. Rearrange to find T: T = \frac{PV}{nR}. 2. Calculate Moles from Density Density \rho = \frac{m}{V}. For 1 L, mass m = 0.310 g. Molar mass of SF_4 is 146.06 g/mol. Moles n = \frac{0.310}{146.06}. 3. Substitute Values into Ideal Gas Law P = 0.0721 atm, V = 1 L, R = 0.0821 L·atm/(mol·K), n = \frac{0.310}{146.06} mol. Calculate T = \frac{(0.0721)(1)}{\left(\frac{0.310}{146.06}\right)(0.0821)}.

Explanation

1. Use Ideal Gas Law<br /> The formula is $PV = nRT$. Rearrange to find $T$: $T = \frac{PV}{nR}$.<br />2. Calculate Moles from Density<br /> Density $\rho = \frac{m}{V}$. For 1 L, mass $m = 0.310$ g. Molar mass of SF$_4$ is $146.06$ g/mol. Moles $n = \frac{0.310}{146.06}$.<br />3. Substitute Values into Ideal Gas Law<br /> $P = 0.0721$ atm, $V = 1$ L, $R = 0.0821$ L·atm/(mol·K), $n = \frac{0.310}{146.06}$ mol. Calculate $T = \frac{(0.0721)(1)}{\left(\frac{0.310}{146.06}\right)(0.0821)}$.
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