Ideal Gas Law: messing with ratios

[Night-san]

Homework Statement

Air is pumped into a bicycle tire. The 43 moles of air initially in the tire have a gauge pressure of 1 atm. How many moles of air must be pumped into the tire in order to raise the gauge pressure to 5 atm? Assume that the volume and temperature of the air inside the tire are approximately constant.

Homework Equations

Ideal Gas Law:
PV = nRT

The Attempt at a Solution

Since the V and T were constant, as well as R, I set it up as (P1V1)/(n1T1) = (P2V2)/(n2T2) on the condition that R1 = R2.

V1=V2, T1=T2 So that would leave the equation at P1/n1 = P2/n2.

I decided to plug in and solve. P1=1 atm, n1=43 moles, P2=5 atm. 1/43 = 5/n2

When I solved for n2, I came out with 215 moles. My homework said it was wrong. can someone tell me where I went wrong?

 

[SteamKing]

You are given the pressures in terms of gauge pressures. Are these the correct units to use with the ideal gas law?

 

[Night-san]

You are given the pressures in terms of gauge pressures. Are these the correct units to use with the ideal gas law?

According to my instructor and the lessons/homework, the units should not matter as long as they are uniform throughout the problem and equations.

 

[ehild]

Definition: Gauge pressure refers to the pressure of a system above atmospheric pressure.

Gauge Pressure = Total Pressure - 1 atm.

[PLAIN]http://chemistry.about.com/o...ssure-Definition.htm[Í/url][/PLAIN] ehild

 

[nasu]

According to my instructor and the lessons/homework, the units should not matter as long as they are uniform throughout the problem and equations.

It's not a mater of units. Both absolute and gauge pressure are measured in the same units.
The gas law in the format you used is "designed" to work for absolute pressure. Same as it only works with temperature in Kelvin but not in Celsius.

 

[Night-san]

Ok, I see the problem. thank you guys for the help. Much appreciated. ^_^

 

[Night-san]

Well, I went back and re-did my work and came out with 129 moles. It was still wrong.

 

[Night-san]

Nevermind, error on my part. I needed the amount of moles that was added, not the amount of moles in the end.