Solvequill Blog · chemistry · 3 min read · 19 views

Compress 5.00 L to 2.00 L at constant temperature — what is the pressure?

Two routes reach the same number. One needs the gas constant, the other needs nothing but a ratio — and knowing why they agree is the point.

Published: August 25, 2026

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The Solvequill lesson for this question.

The question

A piston holds 2.00 mol of an ideal gas at 300 K occupying 5.00 L. The gas is compressed isothermally to 2.00 L. Find the initial and final pressures. Use $R = 0.0821$ L·atm· $m o l^{- 1}$ · $K^{- 1}$ .

The bottom row is the whole argument: PV does not move.

What to notice first

Temperature and amount are both constant, so the only two quantities that change are pressure and volume. That is exactly the condition under which the product PV is fixed — which is why the second half of this problem needs no constants at all.

Working it through

Find the initial pressure from the ideal gas law:

P_{1} = \frac{n R T}{V _{1}} = \frac{2.00 \times 0.0821 \times 300}{5.00}

The numerator is 49.26 L·atm, so:

P_{1} = \frac{49.26}{5.00} = 9.85 atm

For the final pressure, note that n, R and T are all unchanged. Their product is a constant, so PV is the same before and after:

P_{1} V_{1} = P_{2} V_{2} = n R T

Solve for P₂. The volume falls by a factor of 2.5, so the pressure must rise by the same factor:

P_{2} = P_{1} \frac{V _{1}}{V _{2}} = 9.85 \times \frac{5.00}{2.00}

The answer

P_{1} = 9.85 atm, P_{2} \approx 24.6 atm

Check it the long way: $\frac{n R T}{V _{2}} = \frac{49.26}{2.00} = 24.6$ atm. The two routes agreeing is the evidence that PV really was constant — it is not an assumption you have to take on faith.

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