A quantity of N2 gas originally held at 531.96 kPa pressure in a 1.00-L container at 26 °C is transferred to a 12.5-L container at 20 °C. A quantity of O2 gas originally at 531.96 kPa and 26 °C in a 5.00-L container is transferred to this same container. What is the total pressure in the new container?

Video transcript

Hi everyone for this problem, we're told to consider helium and neon gas is initially at 405.3. Kill a pascal and 25 degrees Celsius helium was originally held in a 6.5 liter container while neon was held in a two liter container. We need to calculate the Total pressure. If both gasses were transferred to a 15 liter container at 15°C. So for this problem we have helium and neon undergoing changes of condition and they're being mixed. So in order for us to calculate the total pressure, we first need to calculate the new pressure of each gas and then from there we can add those values. But in order to calculate the new pressure, we need the combined gas law And the combined gas law tells us that P one times V one over T. One is equal to P two times V two over T. Two. And in order to calculate the new pressure, that means we're solving for P. Two. We're solving for P. Two for both of our gasses, both helium and neon. So when we when we rearrange this we're going to get P. Two is equal to P one times V one times T. Two over V. two times T one. Okay, so we're going to calculate P2 for both helium and neon. Let's do helium first. So our new pressure of helium is going to equal P one V 1, T two over B two T one. So let's write out what we're given and then saw for anything that we don't know and then we'll plug everything in. So first P. One They tell us in the problem that it's and 5.3 killer pascal's. We need to convert this to A. T. M. So we know that in one killer pascal There is 1000 pascal's and In one a. t. m. There is pascal's. So let's make sure our units cancel our killer pascal's cancel our pascal's cancel and we're left with A T. M. So this gives us four A. T. M. V one, they tell us is 6.5 l Says Helium was originally held in a 6.5 L container. T two we're told is 25. No hold on. It is let's see helium has a temperature of Or T two is our second temperature. So it's going to be 15°C Because our new temp T two is our our new temperature and it says calculate the total pressure of both gasses were transferred to a 15 liter container at 15 degrees Celsius. So that's T. Two and V. Two. Okay, So V two and T two. T two we need to convert to Kelvin. So in order to do that we need to add 273. five and that gives us 288 . Kelvin and V two is 15 Leaders. Okay, So we have everything we need to plug in here. And so the P two of helium is going to be P1 which is four A. T. M's Times v. 6.5 Leaders Times T two to 88.15 Kelvin over B. Two 15 Leaders, times T one T. One. We did not calculate T. one. So let's go ahead and do that. T one is equal to So they tell us It was 25°C. That was the initial 25°C. And we need to convert that to kelvin Is equal to 298.15 Kelvin. Okay, So we have everything here. So to 98.15 Kelvin. All right, so let's go ahead and plug that into our calculator. And when we do we get 1.67 A. T. M. Is our new pressure for helium. Okay, so that is done. We need to do the same thing for neon. So I'll make this a little smaller so that we have the other side to calculate for neon. Mhm. Okay, so are pressure let me make it in a different color. Our pressure or neon, we're going to do the same thing is going to equal P draw a line here. So we can separate what we're doing. It's going to be P one times v one times T two over V two times T one. So P one we're told it is 405.3 killer pascal. So it's the same thing because this was initial P. One is our initial. So we don't need to calculate P. One. It's going to be the same thing that we already calculated. So it's going to be for a T. M. So this is equal to four A. T. M. V one is going to be two leaders Because now we're talking about neon gas and so our helium was 6.5 L and our Neon was two leaders. Okay, our T. Two And our T. one is the same and so is our v. two. Alright so let's go ahead and plug in. Alright that I'll write everything out though so it's going to be the same. So V one is different but T. Two B two and T one is going to be the same. So we have four a. t. m. Times two leaders, times 288. Kelvin. Over 15 liters, times 298. Kelvin. Okay so when we calculate this, we get Our new pressure of Neon is zero 5154 A. T. M. Okay, so now that we have our new pressures of each gas, we're going to add them to get the total pressure of our mixture and so p total is equal to the new pressure of helium plus the new pressure of neon. So p total Is equal to 1.6752 a. T. M. Plus 0. A. T. M. So our p total Is equal to 2.1906 a. T. M. And that is our final answer. We used the combined gas law to solve for our new pressure of each gas and then we added those up to calculate the total pressure of both gasses or the total pressure if both gasses were transferred, that's the end of this problem. I hope this was helpful.