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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
Yes, according to the ideal gas law, if the volume of an ideal gas is increased (and the quantity of gas and temperature remain constant), the pressure will drop proportionately. They are inversely proportional.

Step by step solution

01

Understand the Ideal Gas Law

The ideal gas law is given by \( PV = nRT \), where \( P \) represents the pressure of the gas, \( V \) is the volume, \( n \) is the number of moles of gas, \( R \) is the universal gas constant, and \( T \) is the temperature. In our case, the number of moles of gas and the temperature are considered constant.
02

Investigate the relationship between Pressure and Volume

Rearranging the Ideal Gas Law equation for the two variables, we get the formula \( P = \frac{nRT}{V} \). This demonstrates that the pressure \( P \) and volume \( V \) of an ideal gas are inversely proportional, assuming the number of moles \( n \) and temperature \( T \) are constant.
03

Apply the Inverse Proportional Relationship

An inverse proportion means that as one quantity increases, the other decreases. Thus, increasing the volume of the gas in our exercise will indeed lead to a proportional decrease in pressure.

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