Chemistry

Chemistry

Problem

Cylinder A contains an ideal gas at 2 atm, 400 K and volume 3 L. Cylinder B contains the same gas at 1 atm and 300 K. What should be the volume of gas in cylinder B so that both cylinders contain the same number of molecules? a) 8.0 L8.0\ \text{L} b) 2.25 L2.25\ \text{L} c) 4.5 L4.5\ \text{L} d) 6.0 L6.0\ \text{L}
Intuitive explanation

The key is recognizing that the number of molecules depends only on pressure, volume, and temperature through the ideal gas law PV=nRTPV = nRT. Since both cylinders hold the same gas (same RR) and you want equal nn, you need PVT\frac{PV}{T} to be identical in both. Set up the ratio for cylinder A and solve for the unknown volume in cylinder B using this constraint.

Intuitive explanation

The key is recognizing that the number of molecules depends only on pressure, volume, and temperature through the ideal gas law PV=nRTPV = nRT. Since both cylinders hold the same gas (same RR) and you want equal nn, you need PVT\frac{PV}{T} to be identical in both. Set up the ratio for cylinder A and solve for the unknown volume in cylinder B using this constraint.

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