A sample of gaseous sulfur has a mass of 2.5 g and is held at 130 kPa and 10.0 °C. What is the density of the gas under these conditions?

• A. 0.052 g/L
• B. 0.66 g/L
• C. 0.018 g/L
• D. 1.2 g/L

Answer: (B)

Verified step by step guidance

1. Identify the known variables: mass (m) = 2.5 g, pressure (P) = 130 kPa, temperature (T) = 10.0 °C. Convert temperature to Kelvin using the formula \(T(K) = T(°C) + 273.15\).
2. Recall the ideal gas law equation: \(P V = n R T\), where \(P\) is pressure, \(V\) is volume, \(n\) is number of 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 the molar mass of sulfur. Determine the molar mass of sulfur (S) from the periodic table.
4. Substitute \(n = \frac{m}{M}\) into the ideal gas law and solve for volume \(V\): \(V = \frac{n R T}{P} = \frac{m R T}{M P}\).
5. Calculate the density \(\rho\) using the formula \(\rho = \frac{m}{V}\). Substitute \(V\) from the previous step to get \(\rho = \frac{m}{\frac{m R T}{M P}} = \frac{M P}{R T}\). Use consistent units for \(P\), \(R\), and \(T\) to find the density.