20 L of a gas at 303K and 1.00 atm was heated to 498Kwith a final pressure of 1.50 atm. What is the final volume of the gas?

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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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  1. 20 L of a gas at 303K and 1.00 atm was heated to 498Kwith a final pressure of 1.50 atm. What is the final volume of the gas?
Expert Solution
Step 1

For the ideal gas, the temperature pressure and the volume are related by the ideal gas equation. The ideal gas equation is given by:

Chemistry homework question answer, step 1, image 1

For the change in the state of the ideal gas, we can write the above equation as follows:

Chemistry homework question answer, step 1, image 2

Here P1, V1, and T1 are the initial pressure, volume, and temperature of the gas.

Chemistry homework question answer, step 1, image 3

Here P2, V2, and T2 are the final pressure, volume, and temperature of the gas.

Step 2

Dividing the above equation, we get:

Chemistry homework question answer, step 2, image 1

By rearranging the above equation, we get:

Chemistry homework question answer, step 2, image 2

The initial volume of gas = 20 L

The initial temperature of gas = 303 K

The initial pressure of gas = 1.00 atm

 

The final volume of gas =?

Thefinal temperature of gas =498 K

The final pressure of gas = 1.50 atm

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