Question

You have two samples of the same gas in the same size container, with the same pressure. The gas in the first container has a Kelvin temperature four times that of the gas in the other container.

1) The ratio of the number of moles of gas in the first container compared to that in the second is?
2) The ratio of the average velocity of particles in the first container compared to that in the second is?

Please explain.

Answer 1

PV=nRT Since P, V and R are constant, when T goes up, n must go down by the same factor.

Answer 2

So the gas at the higher temp would have to have 4 times less moles.

Answer 3

1:4

Answer 4

Thank you! How about the second question, can you explain that also please

Answer 5

No problem. For the second question, I know the root mean squared speed = sqrt(3RT/M)

Answer 6

So, when T1=4T2, root mean squared speed 1 = 2*root mean squared speed 2. But I'm not sure exactly how root mean squared speed relates to average velocity of particles.

Answer 7

so then what would you use?

Answer 8

the answer is 2:1, but i don't get how

Answer 9

That is what I got using the root mean squared formula. So, I guess it is the same.

Answer 10

when you used sort(3RT/M) what exactly was R, T and M equal to?

Answer 11

R is always constant and M would be the same for the same compound. T1=4T2

Answer 12

So, in comparison, root mean squared speed1 ratio to root mean squared speed2 is 2:1.

Answer 13

Is the constant (R) = 0.08206? and what would the number for M be?

Answer 14

We don't know since we don't know what the compound is, but it doesn't matter since it will be the same for both.

Answer 15

Another way to think of it is (I will use u for root mean squared speed) u1=sqrt(3RT1/M) and u2=Sqrt(3RT2/M)

Answer 16

T1=4T2, so u1=sqrt(3R*4T2/M)

Answer 17

Simplifying gives 2*sqrt(3RT2/M) since sqrt(4)=2

Answer 18

So, we can substitute to give u1=2*u2

Answer 19

For example, if u2 were 1, u1 would be 2. So the ratio is 2:1.

Answer 20

Hm i'll have to do that on paper but thank you very much for helping out!

Answer 21

Yes, it is easier to see when you write it out on paper. Good luck and happy studies!