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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 sample is \(127.81 K\).

Step by step solution

01

Convert the initial temperature from Celsius to Kelvin

Converting the initial temperature from Celsius to Kelvin can be done with this formula: \( K = ^{\circ}C + 273.15 \). Substitute \( 88^{\circ}C \) into the formula: \( K = 88 + 273.15 = 361.15 K \). The initial temperature in Kelvin is \(361.15 K\).
02

Apply Charles's Law to calculate the final temperature

Charles's Law can be written as: \(V_1 / T_1 = V_2 / T_2\), where \(V_1\) and \(T_1\) correspond to the initial volume and temperature, \(V_2\) is the final volume, and \(T_2\) is the final temperature we want to determine. Now it's time to substitute our values into the equation: \(9.6 L / 361.15 K = 3.4 L / T_2\).
03

Solve for the final temperature \(T_2\)

To solve for \(T_2\), multiply both sides of the equation by \(T_2\), and then divide by the left side to get: \(T_2 = (3.4 L * 361.15 K / 9.6 L)\). Calculate the value: \(T_2 = 127.81 K\).

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Most popular questions from this chapter

The following procedure is a simple though somewhat crude way to measure the molar mass of a gas. A liquid of mass \(0.0184 \mathrm{~g}\) is introduced into a syringe like the one shown here by injection through the rubber tip using a hypodermic needle. The syringe is then transferred to a temperature bath heated to \(45^{\circ} \mathrm{C},\) and the liquid vaporizes. The final volume of the vapor (measured by the outward movement of the plunger) is \(5.58 \mathrm{~mL}\) and the atmospheric pressure is \(760 \mathrm{mmHg}\). Given that the compound's empirical formula is \(\mathrm{CH}_{2}\), determine the molar mass of the compound.

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