A sample of oxygen gas occupies 47.2 litres under a pressure of 1240 mm Hg at 25oC. What volume would it occupy at 25oC if the pressure were decreased to 730 mm Hg?

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BlackTom AI · Accepted Answer

The problem presents a scenario at constant temperature, so we can apply Boyle's law: P1 V1 = P2 V2. 
First, identify the given values: P1 = 1240 mm Hg, V1 = 47.2 L, P2 = 730 mm Hg, and T is constant (25°C). 
Next, solve for V2 using V2 = (P1 × V1) / P2. Substituting in, V2 = (1240 × 47.2) / 730.
Compute the ratio 1240/730 ≈ 1.6986. Multiply by 47.2 L to obtain V2 ≈ 1.6986 × 47.2 ≈ 80.2 L. This shows the volume increases when the pressure decreases, as expected from Boyle's law. 
Option 1: 80.2 L — This matches the calculation exactly, so it is correct. 
Option 2: 29.3 L — If one used the inverse of the pressure ratio incorrectly or kept V1 constant, you might get a smaller volume, but that contradicts Boyle's law for a drop in pressure at constant temperature.
Option 3: 27.8 L — This value is not consistent with P1V1 = P2V2; it implies a much larger pressure change or a miscalculation in the proportionality, which is not supported by the given numbers.
Option 4: 47.8 L — This is almost the original volume, which would occur only if pressure remained unchanged; since P2 ≠ P1, the volume must change, so this is incorrect.
In summary, the proper application of P1V1 = P2V2 yields V2 ≈ 80.2 L, aligning with Option 1.

A sample of oxygen gas occupies 47.2 litres under a pressure of 1240 mm Hg at 25oC. What volume would it occupy at 25oC if the pressure were decreased to 730 mm Hg?

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