How Do You Calculate Final Pressure in a Compressed and Cooled Ideal Gas?

[dnl65078]

Homework Statement

A sample of an ideal gas is both compressed and cooled. The given variables for the gas are: P1 = 90.0 kPa, V1 = 0.0800 m3, V2 = 0.0400 m3, T1 = 300. K, T2 = 260. K. Calculate the final pressure.

Homework Equations

PV=nRT
P1 V1 /T1 = P2V2 / T2

The Attempt at a Solution

P2 = T1 V / P1V T2
= 299*1.29 / 1.40 *315 * 1.29
P2 = 0.67 atm

***I thought i was doing this right, but webassign says it's wrong... please advise?

 

[willem2]

P1 V1 /T1 = P2V2 / T2

The Attempt at a Solution

P2 = T1 V / P1V T2

this is wrong already. mulitply your first equation by T2 and then divide by V2.

299*1.29 / 1.40 *315 * 1.29
P2 = 0.67 atm

What are all those numbers that aren't in the problem statement?
I suppose the answer should be in kPa as well.

 

[kerimek]

I would first check that all the units are consistent in the equations and calculations being used. In this case, it looks like the units for pressure and volume are not consistent (kPa and m3 in the given variables, but atm and cm3 in the attempted solution). It is important to use the same units throughout the calculations to ensure accuracy.

Additionally, I would check that the equations being used are appropriate for the given problem. In this case, the ideal gas law (PV=nRT) may not be the best equation to use since the problem does not mention the number of moles of gas. It may be more appropriate to use the combined gas law (P1V1/T1 = P2V2/T2) to calculate the final pressure.

Using the given variables and the combined gas law, the final pressure can be calculated as follows:

P2 = (P1V1T2)/(V2T1) = (90.0 kPa * 0.0800 m3 * 260 K) / (0.0400 m3 * 300 K) = 156 kPa

Therefore, the final pressure is 156 kPa. This answer is consistent with the units used in the given variables (kPa) and is also in the correct range for the given problem (between the initial pressure of 90 kPa and the final temperature of 260 K). I would recommend double checking the units and equations used in the attempted solution to ensure accuracy.