What is the density (in g/L) of xenon (Xe) gas at a pressure of 788 mmHg and a temperature of 25°C? (Molar mass of Xe = 131.3 g/mol; R = 0.0821 L·atm/(mol·K))

• A. 7.95 g/L
• B. 6.80 g/L
• C. 5.10 g/L
• D. 4.25 g/L

Answer: (B)

Verified step by step guidance

1. Convert the given pressure from mmHg to atm using the conversion factor: \$1\ \text{atm} = 760\ \text{mmHg}\(. Use the formula: \)P_{\text{atm}} = \frac{P_{\text{mmHg}}}{760}$.
2. Convert the temperature from Celsius to Kelvin using the formula: \(T(K) = T(^\circ C) + 273.15\).
3. Use the ideal gas law in the form that relates density to pressure, molar mass, gas constant, and temperature: \(\rho = \frac{PM}{RT}\), where \(\rho\) is the density in g/L, \(P\) is pressure in atm, \(M\) is molar mass in g/mol, \(R\) is the gas constant in L·atm/(mol·K), and \(T\) is temperature in K.
4. Substitute the values of \(P\), \(M\), \(R\), and \(T\) into the equation \(\rho = \frac{PM}{RT}\) to set up the expression for density.
5. Calculate the numerical value of the density from the expression, ensuring units are consistent, to find the density of xenon gas in g/L.