Example 13.9 from College Physics, 13.3 The Ideal Gas Law

Calculating Number of Moles: Gas in a Bike Tire

How many moles of gas are in a bike tire with a volume of $2.00 \times 10^{- 3} m^{3} (2 . 00 L),$ a pressure of $7.00 \times 10^{5} Pa$ (a gauge pressure of just under $90.0 {lb/in}^{2}$ ), and at a temperature of $18.0 º C$ ?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Identify the knowns and unknowns, and choose an equation to solve for the unknown. In this case, we solve the ideal gas law, $PV = nRT$ , for the number of moles $n$ .
Solution
1. Identify the knowns.

$\begin{array}{l} P & = & 7 . 00 \times 10^{5} Pa \\ V & = & 2 . 00 \times 10^{- 3} m^{3} \\ T & = & 18.0 º C = 291 K \\ R & = & 8.31 J/mol \cdot K \end{array}$
13.40

2. Rearrange the equation to solve for $n$ and substitute known values.

$\begin{array}{l} n & = & \frac{PV}{RT} = \frac{(7 . 00 \times 10^{5} Pa) (2 . 00 \times 10^{- 3} m^{3})}{(8.31 J/mol \cdot K) (291 K)} \\ = & 0.579 mol \end{array}$
13.41
Discussion
The most convenient choice for $R$ in this case is $8.31 J/mol \cdot K,$ because our known quantities are in SI units. The pressure and temperature are obtained from the initial conditions in Example 13.6, but we would get the same answer if we used the final values.

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Strategy

Solution

Discussion