A gas occupies a volume of 2.4 L at 14.1 kPa. What volume will the gas occupy at 84.6 kPa?

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BlackTom AI · Accepted Answer

Start by identifying the governing relationship for this problem: Boyle's Law, which states that for a gas at constant temperature, P1V1 = P2V2.

Now restate the given values clearly: initial pressure P1 = 14.1 kPa, initial volume V1 = 2.4 L; final pressure P2 = 84.6 kPa, and we need to find the final volume V2.

Option 1: 497 L. This option suggests an enormous increase in volume as pressure rises, which contradicts Boyle's Law. When pressure increases, volume should decrease, not explode upward to hundreds of liters. This makes it an implausible result given the data.

Option 2: 2.5 L. This is a very small change from the initial 2.4 L, implying that pressure change had almost no effect on volume. Since the final pressure is about six times larger than the initial (84.6 / 14.1 ≈ 6), we would expect a notable decrease in volume, not a near-constant one. So this is inconsistent with the expected inverse relationship.

Option 3: 14 L. A volume of 14 L would imply a dramatic increase in volume despite a much higher pressure, which goes directly against the inverse proportionality dictated by Boyle's Law. It is not compatible with the given P1, P2 values.

Option 4: 0.40 L. This option reflects the correct inverse relationship: as pressure increases from 14.1 kPa to 84.6 kPa (a factor of about 6), the volume should decrease by roughly the same factor, and 2.4 L ÷ (84.6/14.1) ≈ 2.4 L ÷ 6 ≈ 0.40 L. The calculation is V2 = (P1 × V1) / P2 = (14.1 kPa × 2.4 L) / 84.6 kPa = 33.84 / 84.6 ≈ 0.40 L, which matches this option exactly.

In summary, the other three choices fail to satisfy the inverse P–V relationship described by Boyle’s Law under the given conditions, whereas 0.40 L aligns with the expected outcome once the pressures are correctly applied in the equation.

Chemistry (H) - Varnold - Preparatory Academy - 2nd Semester - 2024/2025 Gases Practice Test for the Final

A gas occupies a volume of 2.4 L at 14.1 kPa. What volume will the gas occupy at 84.6 kPa?

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