2000cm3 of a gas is collected at 27oC and 700mmHg. What is the volume of the gas at standard temperature and pressure?

Analyze the question: A fixed mass of gas changes from given conditions to STP (0°C, 760 mmHg). This calls for the combined gas law.

Concept:

P₁V₁/T₁ = P₂V₂/T₂

Temperature must be in Kelvin.

Solution:

• V₁ = 2000 cm³, P₁ = 700 mmHg, T₁ = 27 + 273 = 300 K
• P₂ = 760 mmHg, T₂ = 0 + 273 = 273 K, V₂ = ?

V₂ = (P₁V₁T₂) / (T₁P₂)

V₂ = (700 × 2000 × 273) / (300 × 760)

• Numerator: 700 × 2000 = 1,400,000; 1,400,000 × 273 = 382,200,000
• Denominator: 300 × 760 = 228,000

V₂ = 382,200,000 / 228,000 ≈ 1676.3 cm³

Answer: The volume at STP is about 1676.3 cm³, which is option C.

Tip: Always convert to Kelvin first. Remember STP = 273 K and 760 mmHg. Since the pressure is lower than 760 mmHg and the temperature is higher than 273 K, the volume must shrink, so 1676.3 (less than 2000) makes sense. A quick estimate also helps: 2000 × (700/760) × (273/300) ≈ 2000 × 0.921 × 0.91 ≈ 1676.