Question

A 7.32 L tire contains 0.448 mol of gas at a temperature of 28 degree Celsius. What is the pressure (in atm) of the gas in the tire?

Answer 1

Assuming the gas behaves as an ideal gas, we can use the Ideal Gas Law to calculate the pressure:

`\begin{gathered} PV=nRT \\ P=(nRT)/(V) \end{gathered}`

We need to use T in absolute terms, so we need to convert it to Kelvin:

`T=(28+273.15)\; K=301.15\; K`

Since we have the volume in L and we want the pressure in atm, we can use the following unit for the R constant:

`R\approx0.082057\; atm\cdot L\cdot K^(-1)\cdot mol^(-1)`

Using the these and the other given values:

`\begin{gathered} V=7.32\; L \\ n=0.448\; mol \end{gathered}`

We have:

`\begin{gathered} P=(nRT)/(V) \\ P=(0.448mol\cdot0.082057atm\cdot L\cdot K^(-1)\cdot mol^(-1)\cdot301.15K)/(7.32L) \\ P=(0.448\cdot0.082057\cdot301.15)/(7.32)\; atm \\ P=1.51239\ldots\; atm \\ P=1.51\; atm \end{gathered}`

So, the pressure is approcimately 1.51 atm.