An unknown diatomic gas has a density of 1.250 g/L at STP. What is the identity of the gas?

• A. N_2
• B. O_2
• C. H_2
• D. Cl_2

Answer: (B)

Verified step by step guidance

1. Recall that at STP (Standard Temperature and Pressure), the molar volume of an ideal gas is 22.4 L/mol. This means 1 mole of any ideal gas occupies 22.4 liters under these conditions.
2. Use the relationship between density (d), molar mass (M), and molar volume (V_m) given by the formula: \(d = \frac{M}{V_m}\) where \(d\) is the density in g/L, \(M\) is the molar mass in g/mol, and \(V_m\) is the molar volume in L/mol.
3. Rearrange the formula to solve for the molar mass \(M\): \(M = d \times V_m\) Substitute the given density (1.250 g/L) and molar volume at STP (22.4 L/mol) into this equation.
4. Calculate the molar mass (without final numeric value) to find the approximate molar mass of the unknown gas.
5. Compare the calculated molar mass to the molar masses of the given diatomic gases: - \(N_2\) (28 g/mol) - \(O_2\) (32 g/mol) - \(H_2\) (2 g/mol) - \(Cl_2\) (71 g/mol) Identify the gas whose molar mass is closest to the calculated value.