Ideal Gas Law: messing with ratios

In summary, the problem involves calculating the number of moles of air that must be pumped into a bicycle tire to raise the gauge pressure from 1 atm to 5 atm. Using the ideal gas law and assuming constant volume and temperature, the equation P1/n1 = P2/n2 is used to solve for n2. However, since the given pressures are in terms of gauge pressure, the equation must be adjusted to account for this. After reworking the problem, the correct answer is determined to be 129 moles added.
  • #1
Night-san
5
0

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?
 
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  • #2
You are given the pressures in terms of gauge pressures. Are these the correct units to use with the ideal gas law?
 
  • #3
SteamKing said:
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.
 
  • #4
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
 
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  • #5
Night-san said:
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.
 
  • #6
Ok, I see the problem. thank you guys for the help. Much appreciated. ^_^
 
  • #7
Well, I went back and re-did my work and came out with 129 moles. It was still wrong.
 
  • #8
Nevermind, error on my part. I needed the amount of moles that was added, not the amount of moles in the end.
 

1. What is the Ideal Gas Law?

The Ideal Gas Law is a mathematical equation that describes the relationship between the pressure, volume, temperature, and amount of a gas. It is often written as PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

2. How does the Ideal Gas Law relate to gas behavior?

The Ideal Gas Law can be used to predict and understand the behavior of gases under different conditions. It states that at a constant temperature, increasing the pressure on a gas will decrease its volume, and vice versa. It also shows that at a constant pressure, increasing the temperature of a gas will increase its volume, and vice versa.

3. What happens when the ratio of pressure to volume changes in the Ideal Gas Law?

According to the Ideal Gas Law, if the ratio of pressure to volume changes, either the temperature or the amount of gas must also change in order to maintain equilibrium. For example, if the pressure is increased and the volume is decreased, the temperature must also increase in order to keep the equation balanced.

4. How does the Ideal Gas Law apply to real gases?

The Ideal Gas Law is an idealized equation that assumes gases behave perfectly under all conditions. In reality, real gases deviate from the ideal behavior at high pressures and low temperatures. However, the Ideal Gas Law is still a useful tool for approximating gas behavior in many situations.

5. How can the Ideal Gas Law be used in scientific research?

The Ideal Gas Law is a fundamental equation in the study of gases and is used in many areas of scientific research. It can be used to predict the behavior of gases in chemical reactions, to calculate the volume of a gas at a specific pressure and temperature, and to determine the amount of gas in a given sample. It is also used in industries such as chemistry, physics, and engineering to design and optimize processes involving gases.

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