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Chapter 5: Problem 34

A certain amount of gas at \(25^{\circ} \mathrm{C}\) and at a pressure of 0.800 atm is contained in a glass vessel. Suppose that the vessel can withstand a pressure of \(2.00 \mathrm{~atm} .\) How high can you raise the temperature of the gas without bursting the vessel?

Short Answer

Expert verified
The final temperature (\(T_2\)) that can be reached without bursting the vessel is approximately 745 K

Step by step solution

01

Convert Temperatures to Kelvin

Before proceeding the calculation, convert the initial temperature from Celsius to Kelvin. The Celsius to Kelvin conversion is done by adding 273 to the Celsius temperature. Thus, the initial temperature is \( 25^{\circ} \mathrm{C} + 273 = 298 \mathrm{K} \) .
02

Apply the Ideal Gas Law

The ideal gas law equation is \( P \propto T \), implying that \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \). Here, \(P_1\) and \(T_1\) are the initial pressure and temperature, and \(P_2\) and \(T_2\) are the final pressure and temperature. Plug in the known values: \( \frac{0.800 \mathrm{atm}}{298 \mathrm{K}} = \frac{2.00 \mathrm{atm}}{T_2} \)
03

Solve for Final Temperature

Rearrange the equation from step 2 to solve for \(T_2\). Then calculate \( T_2 = \frac{2.00 \mathrm{atm} \times 298 \mathrm{K}}{0.800 \mathrm{atm}} \)

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Most popular questions from this chapter

In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at \(43^{\circ} \mathrm{C}\) : $$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(g)$$ This reaction separates nickel from other solid impurities. (a) Starting with \(86.4 \mathrm{~g}\) of \(\mathrm{Ni}\), calculate the pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a container of volume \(4.00 \mathrm{~L}\). (Assume the above reaction goes to completion.) (b) On further heating the sample above \(43^{\circ} \mathrm{C}\), it is observed that the pressure of the gas increases much more rapidly than predicted based on the ideal gas equation. Explain.

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