[anshu]

A 2.0-L helium tank at a pressure of 15.0 MPa in a room kept at 22 °C is used to blow up balloons. The balloons, once blown up, have a volume of 2.0 L and maintain a pressure of 115 kPa without breaking. What is the maximum number of balloons that can be filled with this tank?

[stewie griffin]

You need to show your attempt first to get help on these forums.
Here's a tip though... the number of moles in the tank will be the same as what's used to fill up all the balloons. Find the number of moles in the tank, find how many moles are in one balloon, then find how many balloons you can fill.

[Grundalizer]

Ok, so first things first.  We have to figure out how MUCH gas we have in the tank.  To do that, we need to use the idea gas law PV=nRT where: P=pressure (in atm), V = Volume (in L), n = number of moles, R=ideal gas constant (which changes depending on your units), T = temperature (in K)

Go to any textbook/wikipedia and find the gas constant R that has the most units you are given.  In this case, we are given; L, C^o,Pa

So the gas constant I chose was 0.082 057 46(14)   L* atm K−1 mol−1 so we don't have to convert L into anything.

First, convert degrees C to Kelvin, just add 273 to the degrees C to get Kelvin, so we get 273+22 = 295K.

Next, convert MPa into atm, we have 15.0 x 10⁶ Pa x 9.869 x 10 ^-6 atm/Pa

Tell me what you get for that conversion.

Then plug the numbers into PV=nRT and SOLVE for n.  So do PV/RT (remember to use the right units!)

Tell me how many moles of gas you get.

Then do the same thing for the 2 L ballon, its all the same numbers except for Pressure.  Solve for n to get mols.  Then do the moles in the tank divided by the moles per balloon, and you got your answer.  Remember to not round your numbers too early to avoid rounding error.  Tell me what you get and we'll see if we confirm eachothers calculations.

[Grundalizer]

In case you never come back, I got 1300 balloons

[billnotgatez]

Grundalizer -

Do we really need to do all that?

The temp is the same for both the balloon and the tank.
The moles are the same for both the balloon and the tank.
All that has changed is the volume and pressure.
The R is a constant.

anshu -

Note what the units are for all measurments

[billnotgatez]

Grundalizer -

I get far less

I divided one number by another

[Grundalizer]

What do you get?  How did you get it?  I don't see what the shorter way is if there is one.

[billnotgatez]

I divided

15000000 by 115000 to get about 130
Can you explain why or shall I

[Grundalizer]

Nicely done. V, T, n, R all constant, P is the only variable.  And it was so painful using the calculator application on this laptop!  Since my answer is off by a factor of 10, I'm guessing I missed a zero somewhere, but that looks right to me.  Gj +1, I hang my head in shame

[billnotgatez]

MPa v.s. kPa
I think I did this correctly

They always try to make it tricky by mixing units of measurements

By the way the first time I did this I multilied by 2 and later took half of the result.

[Borek]

In case you never come back, I got 1300 balloons

And you have posted it less then 3 hours after the thread was started... sigh.

[anshu]

i got 131 as my number of balloons . thanks for all your help.

[Borek]

i got 131 as my number of balloons

Assuming half filled balloon still counts...

[billnotgatez]

130.43478260869565217391304347826

i guess significant figures is important

[savy2020]

Hey,
You're all missing something important.
You can NOT fill the balloons till whole of the gas in the cylinder is filled in the baloons
You CAN the balloons only till the pressure in the balloon being filled equalises that in the cylinder.
Without pressure difference there is no way of filling the balloons.

After you will 129 balloons, pressure in the cylinder will be 165kPa. If you try to fill the 130th balloon, you can't get it to 2L. YOu can fill it only till 0.869L. Because at that point pressure inside the cylinder becomes 115kPa and further movement of gas from Cylinder to the 130th balloon doesn't takes place.

Hope this helps