Modern vacuum pumps make it easy to attain pressures of the order...

Question

Modern vacuum pumps make it easy to attain pressures of the order of 10^-13 atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of 
9.00 * 10^-14 atm and an ordinary temperature of 300.0 K, how many molecules are present in a volume of 1.00 cm^3?

Accepted Answer

welcome back everybody. We are forming experiments on a cryo stat chamber and we are looking at the pressure of nitrogen gas inside. Now we find that the pressure is 10 to the negative seventh millibars. We are also told that the temperature is 50 degrees kelvin and we are told that the volume of the car that chamber is 10 centimeters cute. And we are tasked with finding how many nitrogen molecules are present inside the cryo stat chamber. Well, the number of molecules is just going to be equal to the number of moles of the nitrogen times God Rose number. But what is the the number of moles in the chamber where we are actually going to use our ideal gas law. That states that PV is equal to N. R T. And you see if you divide by R. T. On both sides, we get that N or a number of moles is equal to the pressure times the volume over our ideal gas constant times temperature. Wonderful. Now that we have this, we can plug in these numbers. But before we do, let's make sure we're working with the correct units here for our pressure up here here, we actually need to be working in pascal's. Right. So what I'm gonna do is I'm going to convert this real quick. So in one bar, there is 1000 millibars and in one bar there is tend to the fifth pascal's if you multiply straight across and you see that these units cancel out, we get that the pressure inside the chamber is 10 to the negative fifth pascal's great temperature is in kelvin, which is exactly what we needed to be and our volume we actually needed to be in meters cube. So I'm going to multiply by centimeters cubed on the bottom and one m cubed on top. This is going to give us a volume of 10 times 10 to the negative six m cubed. Wonderful. Now it looks like we have everything in the right units. So we are good to go on finding the number of moles here. So N is equal to our pressure of 10 to the negative fifth pascal's times are volume of 10 times 10 to the negative six m Cubed. All divided by our ideal gas constant of 8.314 times our temperature of Kelvin. When you plug all of this into your calculator, you get 2.405 times to the negative 13th great. Now that we have that we can go ahead and find the number of molecules of nitrogen inside the chamber as a reminder, this is just going to be the number of moles times of a God Rose number. So let's go ahead and do that. So we have a number of moles is 2.405 times 10 to the negative, 13th times avocados. Number of six point oh 22 times 10 to the 23rd. And this gives us a final answer of 1.44 times 10 to the 11th molecules inside the cryo stat chamber corresponding to our answer choice of C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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