Problem — Pressure of an ideal gas

Problem

$n = 2{,}0$ moles of ideal gas at $T = 300$ K occupy $V = 50$ L. Calculate the pressure and compare with the standard value of one atmosphere.

Solution

From the ideal gas law $pV = nRT$ I solve for the pressure: $p = \frac{nRT}{V}$ I convert the volume to SI units: $V = 50\ \text{L} = 0{,}050\ \text{m}^3$. $p = \frac{2{,}0 \cdot 8{,}31 \cdot 300}{0{,}050} = 9{,}97\cdot10^{4}\ \text{Pa}$ Comparison with $1\ \text{atm} = 1{,}013\cdot10^{5}$ Pa: $\frac{p}{p_\text{atm}} = \frac{9{,}97\cdot10^{4}}{1{,}013\cdot10^{5}} \approx 0{,}99$ $\ev{p \approx 0{,}99\ \text{atm}}$

Links

Topics: Kinetic theory of gases Concepts: Ideal gas law · Pressure Skills: Symbolic setup