Many laboratory gases are sold in steel cylinders with a volume of 43.8 L. What is the mass in grams of argon inside a cylinder whose pressure is 17,180 kPa at 20 °C? (LO 10.4) (a) 1.83 * 107 g (b) 1.81 * 105 g (c) 1.23 * 104 g (d) 122 g

Video transcript

Hi everyone for this problem, we're told argon in the atmosphere has a partial pressure of 946.4 pascal's at the standard sea level temperature of 288 kelvin determine the number of argon atoms present and one liter of argon. Okay, so our goal for this problem is to determine the number of argon atoms. Okay. And we're dealing with a gas here and an equation that we're going to want to use to solve this problem is the ideal gas law and the ideal gas law is pressure times volume is equal to the number of most times our ideal gas constant times temperature. In order for us to determine the number of argon atoms will first want to figure out how many moles of argon we have and that is represented by N in this equation. So we're going to want to rearrange this equation so that we're solving for N. Which is our number of moles. So let's go ahead and divide both sides of our equation by R. T. And when we do that, we get N. Is equal to P. V. Over R. T. So from this we'll be able to get the number of moles and we'll start there. So p represents pressure. And they told us that the pressure is 946.4 pascal's. Okay, so let's go ahead and write that here. 946.4 pascal's but the unit that we're going to want for pressure is atmospheric pressure. Okay, A T. M. And so we need to do a conversion here. Okay, so in 1 80 M there is 100 there's 10,325 past scouts. Okay, so looking at our units here are pascal's cancel and we're left with unit of A T. M. So that gives us 9.3412 times 10 to the negative third A T. M. Okay. So we know our pressure V represents volume. We are told our volume is one leader. Okay, so that is good. We're in the correct units here and here. Our represents our gas constant which is 0.08-06 leaders times atmosphere over Mall Times Kelvin. Okay. And this is basically the constant that we want to make sure all of our units match too. Okay. And so our is good. And then our temperature we're told in the problem is 288 Kelvin. And this is in the right unit. So we have everything we need to plug into our ideal gas law that was rearranged so that we can solve for moles. So let's go ahead and do that now. So we have N is equal to our pressure, which we said is 9.314. No excuse me. 9.3 times 10 to the negative third A. T. M. Times one leader over r times T. So we said our is 0.8 to 06 liters Times atmosphere over More Times Kelvin Times our temperature of 288 Kelvin. So we should only have the unit of moles left over. So let's just make sure all of our units cancel this cancels with this. Our leaders cancel here are kelvin cancels. And as you can see we're left with our unit of mole, which is correct. We always want to make sure we do that. So let's go ahead and solve. And when we solve we get 3. to 6 times 10 to the negative four moles of argon. Okay, so the question asked us to determine the number of argon atoms. So we're close here here we have moles and we need to go from moles to atoms. And there is a conversion that we can use to go from moles to atoms and that conversion is avocados number. Okay. And so let's go ahead and do this final step here. So we know we have 3.95 to 6 times 10 to the negative four moles of argon. And what avocados number tells us is and one mole of anything. So here we have argon there is 6.22 times 10 to the 23 atoms. Okay, so using that conversion we see that our moles cancel and we're left with the unit of atoms. So let's go ahead and do this last step here and we're almost done. So we get an answer of 2.38 times 10 to the 20 argon atoms. Okay, And this is going to be our final answer. This is the number of organs present Argon atoms present and one leader of argon. That's it for this problem. I hope this was helpful.