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

Answer:

Explanation:

Given

Temperature of gas $T=25^{\circ}C\approx 298\ K$

Volume of gas $V=31.5\ L\approx 31.5\times 10^{-3}\ m^3$

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

$P\times 31.5\times 10^{-3}=3.81\times 8.314\times 298$

$P=\frac{3.81\times 8.314\times 298}{31.5\times 10^{-3}}$

$P=299.66\ kPa$

And we know Atmospheric Pressure is $101.325\ kPa$

Therefore Gauge pressure is given by

$P_{gauge}=P-P_{atm}$

$P_{gauge}=299.66-101.325$

$P=198.34\ kPa$