Answer:
moles B = 2.32 moles
Explanation:
In this case, we can assume that both gases are ideals, so we can use the expression for an ideal gas which is:
PV = nRT
From here, we can calculate the total moles (n) that are in the container, and then, by difference, we can calculate how much we have of gas B.
For this case, we will use R = 0.082 L atm / mol K. Solving for n:
n = PV/RT
n = 5 * 20 / 0.082 * 303
n = 4.02 moles
If we have 4.02 moles between the two gases, and we have 1.70 from gas A, then from gas B we simply have:
Total moles = moles A + moles B
moles B = Total moles - moles A
moles B = 4.02 - 1.70
moles B = 2.32 moles
We have 2.32 moles of gas B
Considering the ideal gas law, 2.32 moles of Gas B are present in the mixture.
Ideal gases are a simplification of real gases that is done to study them more easily. It is considered to be formed by point particles, do not interact with each other and move randomly. It is also considered that the molecules of an ideal gas, in themselves, do not occupy any volume.
The pressure, P, the temperature, T, and the volume, V, of an ideal gas, are related by a simple formula called the ideal gas law:
P×V = n×R×T
where P is the gas pressure, V is the volume that occupies, T is its temperature, R is the ideal gas constant, and n is the number of moles of the gas. The universal constant of ideal gases R has the same value for all gaseous substances.
In this case, you know:
Replacing in the ideal gas law:
5 atm× 20 L= n× 0.082[tex]\frac{atmL}{molK}[/tex]× 303 K
Solving:
[tex]n=\frac{5 atmx20 L}{0.082\frac{atmL}{molK}x303 K }[/tex]
n= 4.02 moles
You have 4.02 moles between the two gases, and you have 1.70 from gas A. Then the number of moles of gas B can be calculated as:
Total moles = moles A + moles B
4.02 moles= 1.70 moles + moles B
4.02 moles - 1.70 moles= moles B
2.32 moles= moles B
Finally, 2.32 moles of Gas B are present in the mixture.
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