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)?
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.
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