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Chapter 12: Problem 48

A sample of hydrogen exerts a pressure of 0.329 atm at \(47^{\circ} \mathrm{C}\) . What will the pressure bo at \(77^{\circ} \mathrm{C},\) assuming constant volume?

Short Answer

Expert verified
The pressure of the hydrogen at \(77^{\circ} \mathrm{C}\), assuming constant volume, will be approximately \(0.361 atm\).

Step by step solution

01

Convert temperatures to Kelvin

First, convert the temperatures from Celsius to Kelvin. The Kelvin temperature is the Celsius temperature plus 273.15. Thus, \(T1 = 47^{\circ} \mathrm{C} + 273.15 = 320.15 K\) and \(T2 = 77^{\circ} \mathrm{C} + 273.15 = 350.15 K\).
02

Apply pressure-temperature relationship

According to the law of gases, at a constant volume, the pressure of a gas is directly proportional to its temperature. That is \(\frac{P1}{T1} = \frac{P2}{T2}\). Where, \(P1 = 0.329 atm\) and \(T1 = 320.15 K\) are the initial pressure and temperature, and \(T2 = 350.15 K\) is the final temperature. The task is to solve for \(P2\), the pressure at \(77^{\circ} \mathrm{C}\).
03

Solve for the final pressure P2

Rearrange the equation to solve for the final pressure: \(P2 = P1 \times \frac{T2}{T1}\) = \(0.329 atm \times \frac{350.15 K}{320.15 K}\) = \(0.361 atm\)

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