A gas with a molar mass of 26.54 g/mol is at a pressure of 172 torr and a temperature of 27 °C. What is its density in g/L?

• A. 0.32 g/L
• B. 0.20 g/L
• C. 0.15 g/L
• D. 0.25 g/L

Answer: (B)

Verified step by step guidance

1. Convert the given pressure from torr to atmospheres because the ideal gas law constant R is typically given in units involving atm. Use the conversion factor: \$1\ \text{atm} = 760\ \text{torr}\(. So, calculate \)P(\text{atm}) = \frac{172}{760}$.
2. Convert the temperature from Celsius to Kelvin since the ideal gas law requires temperature in Kelvin. Use the formula: \(T(K) = T(^\circ C) + 273.15\). So, calculate \(T = 27 + 273.15\).
3. Recall the relationship between the density (\(\rho\)) of a gas, its molar mass (\(M\)), pressure (\(P\)), temperature (\(T\)), and the ideal gas constant (\(R\)). The formula is: \(\rho = \frac{PM}{RT}\) where \(\rho\) is in g/L, \(P\) in atm, \(M\) in g/mol, \(R = 0.0821\ \text{L atm mol}^{-1} \text{K}^{-1}\), and \(T\) in K.
4. Substitute the values of \(P\), \(M\), \(R\), and \(T\) into the formula to set up the expression for density: \(\rho = \frac{(P)(M)}{(R)(T)}\).
5. Perform the calculation to find the density in g/L. This will give you the density of the gas under the given conditions.