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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?

1 Answer

4 votes

Answer:

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

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