How many moles of air are in the rocket?

Question

A 2.0 L soda bottle is used as a water rocket. If 0.30 L of water is in the bottle and it is pumped with air to a pressure of 3.8 atm at a temperature of 25ºC, how many moles of air are in the rocket?

Answer 1

Hi Grace,

I'm not sure why you have a down vote on this question... but I'll answer it since I see nobody did, and I hope that it helps (of course you might not even need it any more).

 

If the soda bottle holds 2.0 L and there is 0.30 L of water in the bottle, then 1.7 L remains to be filled with air.

 

Now according to the ideal gas law (assuming you are approximating an ideal gas here):

 

PV = nRT

 

You want to find n, so solve the ideal gas law for n:

 

n = PV/(RT)

 

We know that:

P = 3.8 atm

V = 1.7 L

T = 25 degrees C which equals 25 + 273 = 298 Kelvins

And thus we should use R = 0.082 L*atm/mol/K for our gas constant because of the units of P,V, and T above

 

Therefore:

 

n = (3.8 atm) * (1.7 L) / (0.082 L*atm/mol/K * 298K)

 

n = (6.46 atm * L) / ( 24.4 L*atm/mol/K*K)

 

canceling out the units, you'll see that you get:

 

n =  (6.46 atm * L) / ( 24.4 L*atm/mol/K*K)

 

n = 0.26 moles of air

 

Remember, when dealing with gas laws, it doesn't matter what the gas is. 

Hope this helped!

Hank