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Chapter 17: Problem 1

If the volume of an ideal gas is increased, must the pressure drop proportionately? Explain.

Short Answer

Expert verified
No, the pressure does not have to drop proportionately when the volume of an ideal gas is increased. While the ideal gas law predicts an inverse relationship between pressure and volume, in real-world scenarios, the temperature and amount of gas often change, meaning the relationship isn't necessarily strictly proportional.

Step by step solution

01

Establish the ideal gas law

Begin by setting up the problem using the ideal gas equation \(PV = nRT\) where P is the pressure, V is the volume, n is the number of moles, R is the gas constant and T is the temperature.
02

Theoretical assumption

If the temperature and amount of gas, denoted by n, are held constant, you find from the ideal gas law that pressure and volume are inversely proportional, i.e., as volume goes up, pressure goes down, due to the multiplication of P and V remaining constant (鈭� 1/V). If we double the volume, the pressure will be halved.
03

Real life scenarios

In reality, it's difficult to maintain constant temperature when changing the volume of a gas sample. Increasing the volume of gas without letting it exchange heat with the environment will decrease its temperature, as the gas molecules will have to spread out in a larger volume, lowering their average kinetic energy. This will also decrease the pressure further due to a decreased temperature.
04

Conclusion

In conclusion, the ideal gas law tells us that increases in volume should lead to decreases in pressure, but the relationship is not necessarily strictly proportional because temperature and amount of gas might not be constant. Therefore, it is incorrect to say that the pressure must drop proportionately when the volume of an ideal gas is increased.

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