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A container with volume 1.64 L is initially evacuated. Then it is filled with 0.226 g of N2N 2 . Assume that the pres
Question
A container with volume 1.64 L is initially evacuated. Then it is filled with 0.226 g of N2N
2
. 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 182 m/s, what is the pressure of the gas?
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2021-07-15T03:29:29+00:00
2021-07-15T03:29:29+00:00 1 Answers
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Answers ( )
Answer:
0.015 atm
Explanation:
The pressure of the gas can be calculated using Ideal Gas Law:
Where:
n: is the number of moles of the gas
R: is the gas constant = 0.082 L*atm/(K*mol)
V: is the volume of the container = 1.64 L
T: is the temperature
We need to find the number of moles and the temperature. The number of moles is:
Where:
M: is the molar mass of the N₂ = 14.007 g/mol*2 = 28.014 g/mol
m: is the mass of the gas = 0.226 g
Now, the temperature can be found using the following equation:
Where:
R: is the gas constant = 0.082 L*atm/K*mol = 8.314 J/K*mol
By solving the above equation for T, we have:
Finally, we can find the pressure of the gas:
Therefore, the pressure of the gas is 0.015 atm.
I hope it helps you!