Hydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm 3 at 30°C with a pressure of 1 × 10 5 Pa, calculate how many hydrogen atoms (particles) there are in the sample.

Alright, guys. So let's get started with our problem here. So one of the things I mentioned in an earlier video is that most real gases, for example, like hydrogen gas, behave very closely to actual ideal gases here, and that's what this problem has. So we have a sample of hydrogen gas. We're told the volume is a 1000 centimeters cubed, the temperature is 30 degrees Celsius, and the pressure is 1 times 10 to the 5th. And we're supposed to find out basically how many hydrogen atoms there are in your sample of hydrogen gas. So let's go ahead and use the ideal gas law. We're gonna have to use one of these two equations here. So really if we're looking for how many hydrogen atoms we're looking for, what we're really looking for is big N. So in our ideal gas law equation, remember we have little nRT or big N kBT, and this is the one that we're gonna use here because we use this when we're given or asked for big N. Alright. So let's go ahead and set up our ideal gas law equation. P v equals n k b n t. So we wanna figure out what n is equal to, we just have to move everything over to the other side. So this is gonna be PV divided by kbt, and this is gonna equal big M. Alright? So all you have to do is figure out all these variables. So let's go through and check them off 1 by 1. So we have the pressure. Well, the pressure we're told directly is 1 times 10 to the 5th pascals. That's like normal atmospheric pressure. What about the volume? Well, let's see. The volume here we're told is 1,000 centimeters cubed. Right? So that's we're just told straight from the problem. So we have to convert this to meters because that's SI units. Now you might be thinking that we just have to move the decimal place back twice, but be careful when you do these because you have a unit conversion, for example, centimeters to meters, but you have to do it and shift the decimal place as many times as there are exponents in your number. So for example, we have to shift the decimal place back twice. We're we're gonna have to do that 3 times though. So you're gonna have to do 12, 12 and then 12. So really what this becomes is 0.001 meters cubed. Alright? So that's a very common mistake, make sure you don't make that. So that's what the volume is. What about the temperature? Well, the temperature here is just 30 degrees Celsius. So to convert that, we're gonna add 2 73 and you're gonna get 303 Kelvin. So remember, we have to plug in all of our temperatures in Kelvin and now we can do that. So we plug everything in. We're gonna get 1 times 10 to the 5th, then the volume is gonna be point 1. The, the kv, the Boltzmann's constant is gonna be 1.38 times 10 to the minus 23, and then finally our temperature is 303. When you go ahead and work everything out, what you should get here is 2.39 times 10 to the 22, and that's how many particles. This is a huge number, but that makes sense. Atoms are really really really tiny and you get a lot of them if you have a sample of gas. Alright, guys. So that's it for this one. Let me know if you have any questions. The answer choice is gonna be answer B. That's it for this one.

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21. Kinetic Theory of Ideal Gases

The Ideal Gas Law

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21. Kinetic Theory of Ideal Gases

The Ideal Gas Law

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Multiple Choice

Hydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm³ at 30°C with a pressure of 1 × 10⁵ Pa, calculate how many hydrogen atoms (particles) there are in the sample.

2.42 × 10²²

2.39 × 10²²

2.39 × 10²⁸

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Hydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm3 at 30°C with a pressure of 1 × 105 Pa, calculate how many hydrogen atoms (particles) there are in the sample.

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Hydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm³ at 30°C with a pressure of 1 × 10⁵ Pa, calculate how many hydrogen atoms (particles) there are in the sample.