An unknown diatomic gas has a density of 3.164 g/L at STP. What is the identity of the gas?

• A. H2
• B. N2
• C. O2
• D. Cl2

Answer: (D)

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 given density of the gas to find its molar mass. The relationship between density (d), molar mass (M), and molar volume (V_m) is given by the formula: \[d = \frac{M}{V_m}\] Rearranged to solve for molar mass: \[M = d \times V_m\]
3. Substitute the given density (3.164 g/L) and the molar volume at STP (22.4 L/mol) into the equation to calculate the molar mass of the unknown gas (do not calculate the final value, just set up the expression).
4. Compare the calculated molar mass to the molar masses of the given diatomic gases: - H\_2 (approximately 2 g/mol) - N\_2 (approximately 28 g/mol) - O\_2 (approximately 32 g/mol) - Cl\_2 (approximately 70.9 g/mol)
5. Identify the gas whose molar mass is closest to the calculated value. Since the problem states the correct answer is Cl\_2, the molar mass you calculate should be close to 70.9 g/mol, confirming the identity of the gas.