a lage compressed air tank contains 325L of air at a pressure of 12.39atm pressure in a 24.82 degree centigrade shop. if the tank is brought outside on a 15.74 degree centigrade fall day and used to fill car tires, how many tires can be filled? assume that a car has a volume of 24.6L and is filled to a pressure of 2.41atm.

common guys

 

Well here is the approach I took:

Since PV = nRT is our main equation we are looking at (Assuming it is an ideal gas problem), we look into what is given to us:

Volume (V) of the tank is 325 L
The Pressure (P) in the tank is 12.39 atm
The Temperature (T) is 24.82^oC = 24.82 + 273.15 = 297.97 K
R is the universal gas constant: 0.08206 L*atm*mol^-1*K^-1

With that information, we can look at how many moles of gas were present in the tank.

Plug the information in, we get

n = (PV)/(RT)
= (12.31 atm * 325 L)/(0.08206L*atm*mol^-1*K^-1 * 297.97K)
= 164.68 mol gas in tank

Now that we know how many moles of gas there are in the tank, we can dig deeper into the problem's second part:

You said assuming each tire fills at 24.6 L and at 2.41 atm. The temperature outside is 15.74^oC. After necessary conversions (C---> K), we can plug the values into our friendly equation from the previous part:

PV = nRT
n= (PV)/(RT)
= (2.41 atm * 24.6 L)/(0.08206 L*atm*mol^-1*K^-1*288.89 K)
n =2.50 mol

Now that we know that's how many moles are there per tire outside, we take the original mole value (of the total tank) and divide it by the mol/tire

So...

(164.68 mol/2.50 mol) = 65.87... tires

We can say that we can fill 65 tires with that much gas.

I think that should be right. I hope it is...

thank u doctorbee. i was stuck at the last part. i highly appreciate ur effort. have a great night. god bless u.