5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled.

a. What are the gas volume and temperature after the expansion?

Question

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled.

a. What are the gas volume and temperature after the expansion?

Accepted Answer

Hi, everyone. In this particular practice problem, we're being asked to determine the final temperature of a gas, considering a sample of helium gas with a mass of 7 g, initial pressure of two ATM and initial temperature of 25 degrees Celsius. The helium is going to be compressed at constant pressure until its volume is reduced to one third of its initial value. And we're being asked to determine the final temperature of the gas. And the options given are a 75 degrees Celsius, B, 100 and 10 degrees Celsius C negative 100 and 74 degrees Celsius and D negative 75 degrees Celsius. So in this particular practice problem, let's consider the initial uh condition to have the properties of P one, P one and P one and the final to have the properties of P two, P two and T two, the process will be an isobaric process at constant pressure. So in this case, we know that P two will come out to be having the same value of P one or P two equals to P one. The compression reduces the volume to one third of its initial value. So P two will be equal to P one divided by three T one is given to be 25 degrees Celsius and converting that into Kelvin, we will have 2 25 plus 273. Kelvin, which will come out to be 298. Kelvin T two is what we are interested to find, which is the final temperature of the gas. So according to the isobaric compression at constant pressure, the ideal gas relationship can be reduced into P two, divided by T two M equals to P one divided by T one. What we are interested to find is T two. So T two will then come out to B equal to P two multiplied by T one divided by P one. So let's substitute RP two, P two will be equals to P one divided by three. So P one divided by three, multiplied by T one divided by P one will then equal to T one divided by three, which will then be equal to P one is 298. Kelvin divided by three and T two will then come out to a value of 99. Kelvin. So then we wanna convert that into Celsius. So 99.338 Kelvin minus 273 will come out to be the final temperature of the gas in Celsius, which will come out to a value of negative 100 and 74 degrees Celsius. So there we have the final temperature of the gas T two which will come out to be negative 100 and 74 degrees Celsius, which will correspond to option C in our answer choices. So option C will be the answer to this particular practice problem and that will be it for this video. If you guys still have any sort of confusion, please feel free to check out our adolescent videos on similar process, but other than that a bit for this one and thank you so much for watching. Bye bye.

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. a. What are the gas volume and temperature after the expansion?

Verified Solution

Key Concepts

Ideal Gas Law

Isobaric Process

Charles's Law