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A container containing 5.00 L of a gas is collected at 100 K and then allowed to expand to 20.0 L. What must the new temperature be in order to maintain the same pressure (as required by Charles' Law)?

Question

A container containing 5.00 L of a gas is collected at 100 K and then allowed to expand to 20.0 L. What must the new temperature be in order to maintain the same pressure (as required by Charles' Law)?

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Solution

Charles' Law states that the volume of a given amount of gas is directly proportional to its temperature on the absolute temperature scale (Kelvin) if pressure is kept constant. This can be expressed as V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.

Given in the problem:

V1 = 5.00 L T1 = 100 K V2 = 20.0 L T2 = ?

We are asked to solve for T2.

Rearranging the formula to solve for T2 gives us T2 = V2 * T1 / V1.

Substituting the given values into the formula gives us T2 = 20.0 L * 100 K / 5.00 L.

Solving for T2 gives us T2 = 400 K.

Therefore, the new temperature must be 400 K in order to maintain the same pressure.

This problem has been solved

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