Question

A container with volume 1.77 L is initially evacuated. Then it is filled with 0.226 g of N2. Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy. If the root-mean-square speed of the gas molecules is 178 m/s, what is the pressure of the gas?

Answer 1

P=1587.18 Pa

Step-by-step explanation:

Given that

V= 1.77 L =1.77 x 10⁻³ m³

m = 0.226 g

Vrms= 178 m/s

We know that ideal gas equation

P V = n R T

`n=(m)/(M)`

M=Molecular wight of the gas

P M = m R T -----------1

P=Pressure ,V=Volume ,n=Moles,R=Gas constant ,T=temperature

`V_(rms)=\sqrt{(3RT)/(M)}` ------2

From above two equation we can say that

`P=(m)/(V)* (V_(rms)^2)/(3)`

`P=(0.266* 10^(-3))/(1.77* 10^(-3))* (178^2)/(3)`

P=1587.18 Pa

The pressure of the gas is 1587.18 Pa