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Chapter 5: Problem 24

Under constant-pressure conditions a sample of hydrogen gas initially at \(88^{\circ} \mathrm{C}\) and \(9.6 \mathrm{~L}\) is cooled until its final volume is \(3.4 \mathrm{~L}\). What is its final temperature?

Short Answer

Expert verified
The final temperature of the gas is approximately 127.97 Kelvin.

Step by step solution

01

Convert initial temperature to Kelvin

The Celsius temperature scale is not appropriate to use with gases. Thus, the first step is to convert the initial temperature from Celsius to Kelvin using the relation \(K = ^{\circ}C + 273.15\). The initial temperature, \(T_{i}\), given as \(88^{\circ}C\) in Celsius then equals \(88 + 273.15 = 361.15 K\).
02

Apply Charles’ law

According to Charles’ law, the ratio of initial volume and initial temperature equals the ratio of final volume and final temperature: \(V_{i}/T_{i} = V_{f}/T_{f}\). Substitute the known initial volume, \(V_{i} = 9.6 L\), the initial temperature, \(T_{i} = 361.15 K\), and the final volume, \(V_{f} = 3.4 L\), into the equation and solve for the final temperature, \(T_{f}\). This gives \(T_{f} = V_{f} / (V_{i}/T_{i}) = (3.4/ 9.6) \times 361.15\).
03

Compute the final temperature

Do the math to compute the final temperature: \(T_{f} = (3.4 / 9.6) \times 361.15 \approx 127.97 K\).

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