A gas has a density of 0.890 g/L at 1.00 atm and 75.0 °C. What is its molar mass in g/mol?

• A. 18.0
• B. 28.9
• C. 44.0
• D. 22.0

Answer: (B)

Verified step by step guidance

1. Identify the known variables: density (d) = 0.890 g/L, pressure (P) = 1.00 atm, temperature (T) = 75.0 °C. Convert the temperature to Kelvin using the formula \(T(K) = T(°C) + 273.15\).
2. Recall the ideal gas law equation: \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.
3. Express the number of moles \(n\) in terms of mass and molar mass: \(n = \frac{m}{M}\), where \(m\) is mass and \(M\) is molar mass.
4. Rewrite the ideal gas law in terms of density \(d = \frac{m}{V}\) by substituting \(n = \frac{m}{M}\) into \(PV = nRT\), resulting in \(P = \frac{dRT}{M}\), and then solve for molar mass \(M\) as \(M = \frac{dRT}{P}\).
5. Plug in the values for density \(d\), gas constant \(R\) (use \$0.0821\ \text{L}\cdot\text{atm}/\text{mol}\cdot\text{K}\(), temperature \)T\( in Kelvin, and pressure \)P\( to calculate the molar mass \)M$.