A Leak in a Bicycle Tire Problem

[BrainMan]

Homework Statement

Homework Equations

pV = nRT

The Attempt at a Solution

I assumed that volume and temperature would stay constant. I assumed the volume wouldn't change because the volume of the tire doesn't change. This implies that

n₁/p₁ = n₂/p₂

n₁p₂ / p₁ = n₂

I found n₁ by using the ideal gas law

pV/RT = n₁ = 0.0592 moles of gas

Then I used the first equation to find n₂ = 0.0431 moles.

Subtracting n₁ - n₂ I found that 0.0161 moles of gas escaped from the tire.

Converting the amount of moles lost to grams I get

0.0161 x 28 g N₂/ 1 mol N₂ = 0.451 g of N₂ gas

The correct answer should be 1.8 g

 

[Chestermiller]

Show us how you got the initial mass of nitrogen.

 

[BrainMan]

Show us how you got the initial mass of nitrogen.

OK I see. I made an error in calculating the volume of the tire.

 

[Chestermiller]

OK I see. I made an error in calculating the volume of the tire.

The ideal gas law uses absolute pressures, not gauge pressures.