The van der Waals constants for methane are a = 2.25 L² . atm/mol² and b =0.0428 L/mol.What is the apparent temperature of 1.0000 mol of CH₄ in a 10.000 L container when it is treated as real relative to the same amount of ideal gas in an identical container at -120.00 $\degree$C?

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The van der Waals equation for real gases is $[P + a(n/V)^2][V - nb] = nRT$, where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles, $R$ is the gas constant, $T$ is the temperature in Kelvin, $a$ and $b$ are the van der Waals constants specific to each gas. Given the constants for methane ($a = 2.25 \, \text{L}^2\text{atm/mol}^2$ and $b = 0.0428 \, \text{L/mol}$), and the conditions ($n = 1.0000 \, \text{mol}$, $V = 10.000 \, \text{L}$), we can solve for $T$ when the gas is considered real. The comparison to an ideal gas at $120.00^\circ C$ (which is $393.15 \, K$) requires adjusting for the real gas behavior, which typically results in a different temperature due to the interactions and volume occupied by the gas molecules. The correct answer involves calculating the temperature using the van der Waals equation and comparing it to the ideal gas scenario, leading to the conclusion that the apparent temperature of the real gas is different from that of the ideal gas, specifically $117.9^\circ C$ in this case.

The Van Der Waals Constants for Methane Are a = °\degree°

The Van Der Waals Constants for Methane Are a = $\degree$