Oxygen has a molar mass of 32 g/mol. If 12 moles of oxygen are in a 0.1-m3 container with an rms speed of 480 m/s, what is the pressure of the gas?
I don't understand what I'm doing wrong Im using p=nM(vrms^2)/3V
and im getting 2.9E8?
someone pls explain
You need to divide the final answer by 1000, as the unit for molar mass is kg/mol rather than g/mol.
you should get 2.9x10^5
i have no idea bro
Well, it seems like you're on the right track with the formula you're using. However, there might be a small error in your calculation. Let's go through it step by step to see what might have gone wrong.
First, we need to calculate the number of moles of oxygen in the container. You mentioned that there are 12 moles of oxygen, so we can use that value directly.
Next, we need to calculate the molar mass of oxygen. You stated that it is 32 g/mol, which is correct.
Then, we have the rms speed of the oxygen molecules, which is 480 m/s.
Finally, we have the volume of the container, which is 0.1 m3.
Now, let's plug these values into the formula:
p = (n * M * (vrms)^2) / (3 * V)
p = (12 * 32 * (480)^2) / (3 * 0.1)
p = (12 * 32 * 230400) / 0.3
p = 883,200 / 0.3
p ≈ 2,944,000 Pa
So it seems like the pressure of the gas is approximately 2,944,000 Pa. It looks like you made a mistake in your calculation, resulting in a different value. Keep in mind that the units need to be consistent throughout the calculation as well.
To find the pressure of the gas using the formula you mentioned: P = (n * M * (vrms^2)) / (3 * V)
Where:
P = Pressure
n = Number of moles
M = Molar Mass
vrms = Root mean square speed of the gas molecules
V = Volume
Given:
n = 12 moles
M = 32 g/mol
vrms = 480 m/s
V = 0.1 m^3
First, let's convert the molar mass from grams/mol to kg/mol:
M = 32 g/mol = 0.032 kg/mol
Next, let's plug in the values into the formula:
P = (12 mol * 0.032 kg/mol * (480 m/s)^2) / (3 * 0.1 m^3)
P = (12 * 0.032 * (480)^2) / (3 * 0.1)
P = (0.4608 * 230,400) / 0.3
P = 106,444.8 / 0.3
P = 354,816 Pa (approximately)
Therefore, the pressure of the gas in the container is approximately 354,816 Pa.
To find the pressure of the gas, you're using the correct formula:
p = (n * M * vrms^2) / (3 * V)
Where:
p = pressure of the gas
n = number of moles of the gas
M = molar mass of the gas
vrms = root mean square speed of the gas molecules
V = volume of the container
Let's plug in the given values into the formula:
n = 12 moles
M = 32 g/mol
vrms = 480 m/s
V = 0.1 m^3
First, let's convert the molar mass to kg/mol by dividing it by 1000:
M = 32 g/mol / 1000 = 0.032 kg/mol
Now, let's substitute the values into the formula:
p = (12 moles * 0.032 kg/mol * (480 m/s)^2) / (3 * 0.1 m^3)
Simplifying the equation gives:
p = (0.384 kg * 230,400 m^2/s^2) / 0.3 m^3
p = 88,473.6 kg m^2/s^2 / 0.3 m^3
p = 294,912 Pa
So the pressure of the gas is 294,912 Pa (Pascal). It seems like you made a mistake in your calculations, which is why you arrived at a different value.