If the density of an unknown gas Z is 4.50 g/L at STP, what is the molar mass of gas Z?

• A. 101 g/mol
• B. 22.4 g/mol
• C. 4.50 g/mol
• D. 44.8 g/mol

Answer: (A)

Verified step by step guidance

1. Recall that at STP (Standard Temperature and Pressure), one mole of any ideal gas occupies 22.4 liters. This is a key fact to relate volume, moles, and molar mass.
2. Use the definition of density, which is mass per unit volume. Here, the density (d) is given as 4.50 g/L, meaning each liter of gas weighs 4.50 grams.
3. Express the molar mass (M) in terms of density and molar volume using the formula: \(M = d \times V_m\), where \(V_m\) is the molar volume at STP (22.4 L/mol).
4. Substitute the known values into the formula: \(M = 4.50 \text{ g/L} \times 22.4 \text{ L/mol}\) to set up the calculation for molar mass.
5. Perform the multiplication to find the molar mass of gas Z, which will give you the mass of one mole of the gas in grams.