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Chapter 11: Problem 66

A tank initially at a pressure of \(6.70\) atm contains \(20.0\) moles of oxygen gas at \(25.0^{\circ} \mathrm{C}\). Its temperature is then increased to \(45.0{ }^{\circ} \mathrm{C}\), and an additional \(10.0\) moles of gas are added. What is the final pressure in the tank?

Short Answer

Expert verified
The final pressure in the tank is \(10.35 \ atm\).

Step by step solution

01

Convert temperatures to Kelvin

First, we need to convert the temperatures to Kelvin. To do so, simply add 273.15 to the Celsius temperature: Initial temperature in Kelvin: \(T_1 = 25.0^{\circ}C + 273.15 = 298.15 K\) Final temperature in Kelvin: \(T_2 = 45.0^{\circ}C + 273.15 = 318.15 K\)
02

Determine initial and final moles of gas

We are given the initial number of moles of gas and the additional moles added: \(n_1 = 20.0 \ moles\) \(n_{added} = 10.0 \ moles\) Final moles of gas can be calculated by adding the initial moles and the added moles: \(n_2 = n_1 + n_{added} = 20.0 + 10.0 = 30.0 \ moles\)
03

Use Ideal Gas Law to find initial and final volume

Since the volume stays constant, we can use the Ideal Gas Law to find the initial volume and final volume (both will be the same): Initial conditions: \(P_1V = n_1RT_1\) \(V = \frac{n_1RT_1}{P_1} = \frac{(20.0 \ moles)(0.0821 \ \frac{L⋅atm}{mol⋅K})(298.15 \ K)}{6.70 \ atm}\) Final conditions: \(P_2V = n_2RT_2\) \(P_2 = \frac{n_2RT_2}{V}\) We will calculate these volumes in the next step.
04

Perform calculations and find final pressure (P₂)

Now we can compute the initial and final volumes using the given data and the Ideal Gas Law. Initial volume (V): \(V = \frac{(20.0 \ moles)(0.0821 \ \frac{L⋅atm}{mol⋅K})(298.15 \ K)}{6.70 \ atm} = 73.08 \ L\) Now we can substitute the final number of moles (n₂), final temperature (T₂), and the previous result for volume into the equation for final pressure: Final pressure (P₂): \(P_2 = \frac{(30.0 \ moles)(0.0821 \ \frac{L⋅atm}{mol⋅K})(318.15 \ K)}{73.08 \ L} = 10.35 \ atm\) The final pressure in the tank is 10.35 atm.

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Most popular questions from this chapter

A balloon of methane gas, \(\mathrm{CH}_{4}\), has a temperature of \(-2.0^{\circ} \mathrm{C}\) and contains \(2.35 \mathrm{~g}\) of the gas. What is the temperature of the gas in Kelvin? How many moles of the gas does the balloon contain?

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