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Chapter 4: Problem 6

The volume of gas in a cylinder is \(1098 \mathrm{~cm}^{3}\). Pressure is increased and the volume changes to \(936 \mathrm{~cm}^{3}\). Calculate the percentage change in the volume of gas.

Short Answer

Expert verified
Answer: The percentage change in the volume of the gas after the pressure increase is -14.75%, which indicates that the volume has decreased by 14.75%.

Step by step solution

01

Write down the given information

The initial volume of the gas is \(1098 \mathrm{~cm}^{3}\) and the final volume after the pressure increase is \(936 \mathrm{~cm}^{3}\).
02

Calculate the change in volume

To find the change in volume, subtract the initial volume from the final volume: Change in volume = Final volume - Initial volume = \(936 \mathrm{~cm}^{3} - 1098 \mathrm{~cm}^{3} = -162 \mathrm{~cm}^{3}\).
03

Calculate the percentage change in volume

Now, use the formula for percentage change: Percentage change = \(((\text{Change in volume}) / (\text{Initial volume})) * 100\). Plug in the values: Percentage change = \((\)(-162 \mathrm{~cm}^{3}) / (1098 \mathrm{~cm}^{3})\() * 100 = -14.75\%\).
04

Interpret the result

The percentage change in the volume of the gas is -14.75%. This negative value indicates that the volume of the gas has decreased by 14.75% after the pressure increase.

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