Solving Ideal Gas Problem: Find # of Balloons Filled

[Jamessamuel]

Homework Statement

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. Homework Equations
pV=nRT

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.

 

[BvU]

Very good. How close ?

 

[Jamessamuel]

Off by about 5 balloons

 

[theodoros.mihos]

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

 

[SteamKing]

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

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

 

[theodoros.mihos]

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

 

[SteamKing]

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

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.

 

[theodoros.mihos]

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

 

[SteamKing]

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

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).

 

[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.

 

[SteamKing]

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.

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.

 

[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?

 

[rolotomassi]

a

 

[theodoros.mihos]

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

 

[SteamKing]

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

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

 

[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 ?

 

[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 $n$.

 

[SteamKing]

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 ?

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

 

[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

 

[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.

 

[BvU]

Off by about 5 balloons

five balloons is about the volume of the cylinder. Doesn't that ring a bell ?

 

[Jamessamuel]

What you say about the gas changing volume with pressure makes sense.

I do not understand the pink line.

 

[Jamessamuel]

Apologies for the upside down - nature of the image.

 

[rolotomassi]

That pink line doesn't make sense. The number on the left is the volume the gas in the cylinder will occupy while subject to the new pressure. Now you can forget about the cylinder and think about how many balloons this volume can fill.

Also its good practice in general to not write out numbers and use letters instead, use the letter p, for pressure, V for volume and label them 1, 2 etc.. This way you can check your working.

 

[Jamessamuel]

So the additon on the pink line is incorrect?

Also, is it better to work algebraically before involing numbers because a bunch of numbers make the method more vague?

 

[rolotomassi]

Think about what it all means. You have some pressurised gas then you de-pressurise it and it expands. This new volume, V, you have calculated is at the correct pressure to fill a balloon of a volume u. So how many balloons?

Yes that's also true, its more difficult for other people to follow your working.