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Chapter 5: Problem 58

A \(2.5-\mathrm{L}\) flask at \(15^{\circ} \mathrm{C}\) contains a mixture of three gases, \(\mathrm{N}_{2},\) He, and \(\mathrm{Ne},\) at partial pressures of \(0.32 \mathrm{~atm}\) for \(\mathrm{N}_{2}, 0.15 \mathrm{~atm}\) for \(\mathrm{He},\) and \(0.42 \mathrm{~atm}\) for Ne. (a) Calculate the total pressure of the mixture. (b) Calculate the volume in liters at STP occupied by He and Ne if the \(\mathrm{N}_{2}\) is removed selectively.

Short Answer

Expert verified
The total pressure of the gas mixture is \(0.89~atm\) and the volume of the He and Ne gases at STP (after removal of \(\mathrm{N}_{2}\)) is approximately \(2.27~L\).

Step by step solution

01

Calculate Total Pressure

The total pressure of a mixture of gases is the sum of the individual pressures of each gas. This principle is known as Dalton’s law. Simply add up the given pressures of the three gases: \(P_{total} = P_{N2} + P_{He} + P_{Ne} = 0.32 atm + 0.15 atm + 0.42 atm\).
02

Calculate Volume at Standard Temperature and Pressure (STP)

Now, you want to calculate the volume the He and Ne gases occupy at STP when you remove the \(\mathrm{N}_{2}\) gas. We use \(STP = 273.15 K\) and \(1 atm\). The combined pressure of He and Ne is \(P_{He} + P_{Ne} = 0.15 atm + 0.42 atm\). The volume these gases occupy at STP can be found using the Ideal Gas law, formulated as \(V = nRT/P\). Here, you need to find the number of moles (n) of He and Ne using the given volume and temperature, then recalculate its volume at STP using the partial pressure of only He and Ne. As we know, \(n = PV/RT\). Then put the computed value into the Ideal Gas law to find the volume.
03

Converting the Temperature to Kelvin

Temperature must be in Kelvin when working with gas laws. So, convert the Celsius temperature to Kelvin by adding 273.15. \(T = 15^{\circ}C + 273.15 = 288.15 K\).
04

Calculating the number of moles of He and Ne

Calculate the number of moles \(n\) of He and Ne in the flask using the Ideal Gas Law in the format of \(n = PV/RT\). The values should be put in as follows: \(n = 0.57~atm * 2.5~L / (0.08206~L*atm/(mol*K) * 288.15~K)\).
05

Calculate the Volume of Ne and He at STP

After finding the number of moles, place it in the Ideal Gas Law as we knew from step 2 formulated as \(V = nRT/P\). Replacing the values, we get \(V = n * 0.08206 L*atm/(mol*K) * 273.15~K / 1 atm\).

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Most popular questions from this chapter

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