# Ideal gas problem

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1. May 25, 2015

### Jamessamuel

1. The problem statement, all variables and given/known data
A gas cylinder contains 4x10^4 cm cubed of hydrogen at a pressure of 2.5x10^7 Pa and a temperature of 290 K.

The cylinder is used to foll balloons. Each balloon contains 7.24x10^3 cm cubed of hydrogen at a pressure of 1.85x10^5 and a temp of 290K when full.

Find the number of balloons that can be filled from the cylinder.

2. Relevant equations

pV=nRT

3. The attempt at a solution
I came close. I found the amount in mol in the cylinder to be around 415. I divided this by the amount in mol in one balloon.

2. May 25, 2015

### BvU

Very good. How close ?

3. May 26, 2015

### Jamessamuel

Off by about 5 balloons

4. May 26, 2015

### theodoros.mihos

Transform your units to the same than the R units you use.

5. May 26, 2015

### SteamKing

Staff Emeritus
Since the temperature of the gas in the cylinder and in the balloons is the same, what can you say about RT for each?

6. May 26, 2015

### theodoros.mihos

If use $R=0.082 (lt\,atm/mol\,K)$ then convert volumes to litres and pressure to atm.

7. May 26, 2015

### SteamKing

Staff Emeritus
You're still missing the implication of constant temperature here. Since RT is a constant, the value of R doesn't matter. R could be the square root of minus 2, for all the difference it makes to this calculation. As long as RT is a constant, then P and V only need to be measured in the same units for the gas in the cylinder and the gas filling each balloon.

8. May 26, 2015

### theodoros.mihos

I found 750 ballouns. Are you sure than you see the difernence between pressures? They have no the same exponent.

9. May 26, 2015

### SteamKing

Staff Emeritus
Those are just the magnitudes of the pressures. The units of each pressure (pascals) are the same, just like the units of the volumes are the same (cm3).

10. May 26, 2015

### theodoros.mihos

I speak for units because you compute moles. This is not necessary.
There is $n$ moles to balloun and $k\times{n}$ the total moles where $k$ is the ballouns number.

11. May 26, 2015

### SteamKing

Staff Emeritus
Yes, but you are not interested in calculating n, but in calculating k. The fact that n might be 45 or 450 is irrelevant. It's k that you're after, and k can be found just by knowing the pressure and the volume of the cylinder, and the pressure and the volume of each balloon after it has been filled.

If you write the equation PV = nRT for the cylinder and PV = nRT for a single balloon, knowing that T is constant, judicious cancellations take care of n altogether.

12. May 26, 2015

### rolotomassi

The number of moles is not important. pV = nRT so pV = constant because you have a fixed amount of gas at a fixed temperature and R is a constant. What you want to know is how much volume the gas will fill when the pressure is reduced to 1.85* 10^5. If pV is a constant you can find this volume, then how many baloons can be filled with this volume?

13. May 26, 2015

### rolotomassi

a

14. May 26, 2015

### theodoros.mihos

If you write $P_1V_1=knRT$ for the cylinder and $P_2V_2=nRT$ for baloun???

15. May 26, 2015

### SteamKing

Staff Emeritus
Yes. Now solve for k, knowing that RT = constant.

16. May 26, 2015

### rolotomassi

How can that possibly be correct. For a fixed amount of gas pV/T must be a constant. You have pV/T = nR and also pV/T = nkR ?

17. May 26, 2015

### theodoros.mihos

$n\times{k}$ is another integer. What the problem?
I write in this form because the original problem can be $P_1V_1=kP_2V_2$ and take a solve for k without $n$.

18. May 26, 2015

### SteamKing

Staff Emeritus
Through the magic of constant temperature. R is already a constant.

19. May 26, 2015

### rolotomassi

The number of moles is fixed. T is fixed. Therefore pV = const. Under these conditions the product of pressure and volume of an ideal gas must always be constant

20. May 26, 2015

### rolotomassi

I see what your doing now. But its better to look at it as an equation of state and consider what happens to the entirety of the gas as you can pressure, volume, temperature etc... Then you can play around with the values and work out lots of different types of problems.

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