The apparatus shown consists of three bulbs connected by stopcocks. What is the pressure inside the system when the stopcocks are opened? Assume that the lines connecting the bulbs have zero volume and that the temperature remains constant. (LO 10.3, 10.7) (a) 1.10 atm (b) 1.73 atm (c) 4.14 atm (d) 1.41 atm

Video transcript

hi everyone for this problem. It reads three bulbs containing three gasses at varying pressures are connected by stop cox. And the apparatus displayed what happens to the system's pressure when the stop cocks are opened. Assume that the temperatures stay constant and that the lines connecting the bulbs have a volume of zero. So the question that we want to answer here is what happens to the system's pressure when the stop cocks are opened. And because the volume and temperature are constant, we're only paying attention to pressure and volume here. And so the way that we want to to think about this is that the initial pressure times the initial volume is going to equal the final pressure times the final volume. So the initial pressure and initial volume is when the stop cocks are closed and then the final pressure and final volume is when the stop cocks are opened. Okay. And so we're particularly interested in the systems pressure when the stop cocks are opened. And so we're interested in the final pressure. Okay. And so let's go ahead and rearrange this so that we're solving for the final pressure. So we're gonna go ahead and divide both sides by the final volume. And so we get the final pressure is going to equal the initial pressure times the initial volume over the final volume. Okay, So we have everything that we need in this problem here to go ahead and plug in these values. So let's go ahead and calculate first the value for the initial pressure times the initial volume for the entire system. Okay, so we're going to take the pressure and volume for each A. B and C and take the some of this. Okay, so let's go ahead and do that first. All right, so we have four A. The pressure is 1. atmospheres times the volume is 1. liters. Plus for B the pressure is 0.893 atmospheres times one liter and plus see the pressure is 1.23 atmospheres Times 1.25 L. So we're going to take the sum and so the initial pressure times volume Is going to be, the total is going to be four . atmospheres Leader. Okay, that's our final unit. So let's go ahead and plug that value in here. So our numerator is going to be 4. atmosphere leaders. And our final volume is going to be the sum of all the volumes. Okay, so the final is going to be so for a we have 1.50 liters for B. It's one liter and four C. It's 1.25 liters. Okay, so our final volume is 3. liters. So let's go ahead and plug that in. Alright, so once we do the calculation we're going to get our final pressure is going to equal 1.32 atmospheres. So this is going to be the pressure when the stop cocks are opened. This is going to be the systems pressure when the stop cocks are opened. Okay, So that is it for this problem. I hope this was helpful.