The volume of a given mass of gas at 27oC and 800 mmHg is 76cm2. Calculate its volume at s.t.p

Analyze the question: A fixed mass of gas changes from one set of conditions (27°C, 800 mmHg) to s.t.p. (0°C, 760 mmHg). We need the new volume. (The "76 cm²" is a typo for 76 cm³.)

Concept: For a fixed mass of gas, the combined gas law applies:

P₁V₁/T₁ = P₂V₂/T₂

Temperature must be in kelvin.

Solution:

Initial conditions:

• P₁ = 800 mmHg
• V₁ = 76 cm³
• T₁ = 27 + 273 = 300 K

At s.t.p.:

• P₂ = 760 mmHg
• T₂ = 273 K
• V₂ = ?

V₂ = (P₁V₁T₂) / (T₁P₂)

V₂ = (800 × 76 × 273) / (300 × 760)

Simplify: 800 × 76 = 60,800, and 300 × 760 = 228,000.

V₂ = (60,800 × 273) / 228,000

60,800 / 228,000 = 0.26667

V₂ = 0.26667 × 273 = 72.8 cm³

Answer: The volume at s.t.p. is 72.8 cm³, which is option B.

Tip: Always convert to kelvin first, and remember s.t.p. = 273 K and 760 mmHg. A quick sanity check: the pressure drops slightly (800 to 760), which would increase volume, while the temperature drops (300 K to 273 K), which would decrease volume. The temperature effect is bigger, so the final volume should be a bit less than 76 cm³. That rules out A immediately, and 72.8 fits.