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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

Hydrogen sulfide gas \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\) is responsible for the foul odor of rotten eggs. When it reacts with oxygen, sulfur dioxide gas and steam are produced. (a) Write a balanced equation for the reaction. (b) How many liters of \(\mathrm{H}_{2} \mathrm{~S}\) would be required to react with excess oxygen to produce \(12.0 \mathrm{~L}\) of \(\mathrm{SO}_{2}\) ? The reaction yield is \(88.5 \%\). Assume constant temperature and pressure throughout the reaction.

Nitrogen can react with steam to form ammonia and nitrogen oxide gases. A 20.0-L sample of nitrogen at \(173^{\circ} \mathrm{C}\) and \(772 \mathrm{~mm} \mathrm{Hg}\) is made to react with an excess of steam. The products are collected at room temperature \(\left(25^{\circ} \mathrm{C}\right)\) into an evacuated flask with a volume of \(15.0 \mathrm{~L}\). (a) Write a balanced equation for the reaction. (b) What is the total pressure of the products in the collecting flask after the reaction is complete? (c) What is the partial pressure of each of the products in the flask?

The air is said to be "thinner" in higher altitudes than at sea level. Compare the density of air at sea level where the barometric pressure is \(755 \mathrm{~mm} \mathrm{Hg}\) and the temperature is \(0^{\circ} \mathrm{C}\) with the density of air on top of \(\mathrm{Mt}\). Everest at the same temperature. The barometric pressure at that altitude is \(210 \mathrm{~mm} \mathrm{Hg}\) (3 significant figures). Take the molar mass of air to be \(29.0 \mathrm{~g} / \mathrm{mol}\).

A mixture in which the mole ratio of hydrogen to oxygen is \(2: 1\) is used to prepare water by the reaction $$ 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) $$ The total pressure in the container is \(0.950 \mathrm{~atm}\) at \(25^{\circ} \mathrm{C}\) before the reaction. What is the final pressure in the container at \(125^{\circ} \mathrm{C}\) after the reaction, assuming an \(88.0 \%\) yield and no volume change?

It takes \(12.6 \mathrm{~s}\) for \(1.73 \times 10^{-3} \mathrm{~mol}\) of \(\mathrm{CO}\) to effuse through a pinhole. Under the same conditions, how long will it take for the same amount of \(\mathrm{CO}_{2}\) to effuse through the same pinhole?
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