Question

What is the gauge pressure (in atm) in a 25.0°C car tire containing 3.81 mol of gas in a 31.5 L volume? (Enter your answer to at least 2 decimal places.)

Answer 1

Step-by-step explanation:

Given

Temperature of gas
`T=25^(\circ)C\approx 298\ K`

Volume of gas
`V=31.5\ L\approx 31.5* 10^(-3)\ m^3`

no of moles of gas
`n=3.81\ mol`

Using Ideal gas Equation to find the Pressure of gas

`PV=nRT`

where P=Absolute Pressure

V=Volume

R=Universal gas constant

T=Temperature

`P* 31.5* 10^(-3)=3.81* 8.314* 298`

`P=(3.81* 8.314* 298)/(31.5* 10^(-3))`

`P=299.66\ kPa`

And we know Atmospheric Pressure is
`101.325\ kPa`

Therefore Gauge pressure is given by

`P_(gauge)=P-P_(atm)`

`P_(gauge)=299.66-101.325`

`P=198.34\ kPa`