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Chapter 5: Problem 6

A tank is filled with a gas to a pressure of \(977 \mathrm{~mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C}\). When the tank is heated, the pressure increases to \(1.50 \mathrm{~atm}\). To what temperature was the gas heated?

Short Answer

Expert verified
Answer: The final temperature of the gas when heated is approximately \(86.12^{\circ}\mathrm{C}\).

Step by step solution

01

Write down the initial conditions

The initial pressure \(P_1 = 977 \mathrm{~mm Hg}\), the initial temperature \(T_1=25^{\circ} \mathrm{C}\), and the final pressure \(P_2=1.50 \mathrm{~atm}\).
02

Convert pressures and temperatures to proper units

For consistency, let's convert pressures to atmospheres and temperatures to Kelvins. We know that \(1 \mathrm{~atm} = 760 \mathrm{~mm Hg}\) and to convert Celsius to Kelvin we just add \(273.15\). Therefore, \(P_1 = \frac{977}{760} \mathrm{~atm}\) and \(T_1 = 25 + 273.15 = 298.15\mathrm{~K}\).
03

Apply the ideal gas law in the form of \(P_1 / T_1 = P_2 / T_2\)

Now we can write the equation for the final temperature: $$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$.
04

Solve for the final temperature \(T_2\)

We can rearrange the equation to solve for \(T_2\): $$T_2 = \frac{P_2 \cdot T_1}{P_1} = \frac{1.50 \mathrm{~atm} \cdot 298.15 \mathrm{~K}}{\frac{977}{760} \mathrm{~atm}}$$ Now, we can calculate the value of \(T_2\) for the final temperature: $$T_2 = \frac{1.50 \cdot 298.15}{\frac{977}{760}} \approx 359.27 \mathrm{~K}$$
05

Convert the final temperature to Celsius

Let's convert the final temperature in Kelvins to Celsius: $$T_2^{\circ}C = 359.27 \mathrm{~K} - 273.15 \approx 86.12^{\circ} \mathrm{C}$$ So, the gas was heated to a temperature of approximately \(86.12^{\circ}\mathrm{C}\).

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Most popular questions from this chapter

Nitroglycerine is an explosive used by the mining industry. It detonates according to the following equation: $$ 4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}(l) \longrightarrow 12 \mathrm{CO}_{2}(g)+6 \mathrm{~N}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{O}_{2}(g) $$ What volume is occupied by the gases produced when \(10.00 \mathrm{~g}\) of nitroglycerine explodes? 'The total pressure is \(1.45 \mathrm{~atm}\) at \(523^{\circ} \mathrm{C}\).

In Calculate the densities (in grams per liter) of the following gases at \(97^{\circ} \mathrm{C}\) and \(755 \mathrm{~mm} \mathrm{Hg}\) (a) hydrogen chloride (b) sulfur dioxide (c) butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\)

A mixture of \(3.5 \mathrm{~mol}\) of \(\mathrm{Kr}\) and \(3.9 \mathrm{~mol}\) of He occupies a \(10.00-\mathrm{L}\) container at \(300 \mathrm{~K}\). Which gas has the larger (a) average translational energy? (b) partial pressure? (c) mole fraction? (d) effusion rate?

Cyclopropane mixed in the proper ratio with oxygen can be used as an anesthetic. At \(755 \mathrm{~mm} \mathrm{Hg}\) and \(25^{\circ} \mathrm{C}\), it has a density of \(1.71 \mathrm{~g} / \mathrm{L}\). (a) What is the molar mass of cyclopropane? (b) Cyclopropane is made up of \(85.7 \% \mathrm{C}\) and \(14.3 \% \mathrm{H}\). What is the molecular formula of cyclopropane?

A 1.58-g sample of \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{X}_{3}(g)\) has a volume of \(297 \mathrm{~mL}\) at \(769 \mathrm{~mm} \mathrm{Hg}\) and \(35^{\circ} \mathrm{C}\). Identify the element \(\mathrm{X}\).
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