The apparatus shown consists of three temperature-jacketed 1.000-L bulbs connected by stopcocks. Bulb A contains a mixture of H₂O(g), CO₂(g), and N₂(g) at 25 °C and a total pressure of 564 mm Hg. Bulb B is empty and is held at a temperature of -70 °C. Bulb C is also empty and is held at a temperature of -190 °C. The stopcocks are closed, and the volume of the lines connecting the bulbs is zero. CO₂ sublimes at -78 °C, and N₂ boils at -196 °C.

(b) How many moles of H₂O are in the system?

Video transcript

Welcome back everyone. We're told that the following apparatus shows three enclosed 30.500 liter bulbs connected by stop cocks bulb X at 200 degrees Celsius has a total pressure of 650 millimeters of mercury and contains bromine gas, gas and chlorine gas while Y and Z are both empty and held at a temperature of 95 25 degrees Celsius, respectively. Initially the stop cocks are closed and assumed that the volume of the lines joining the bulbs is negligible. When the stop cock between X&Y are opened and was allowed to reach equilibrium. X&Y has a total of 270 of mercury of pressure, calculate the moles of iodine gas present in the system. So we're going to also given from the prompt we have are useful information being are boiling point and melting point of our three gasses, chlorine, bromine and iodine gas. Our first step is to recall our relation where pressure and volume are equal to our molds of our gas times the gas constant R times temperature. We're going to utilize this formula to first calculate our initial moles of gas present in bulb X. And so beginning with the temperature for bulb X Given in the prompt, we have a temperature according to our Diagram of 200°C. We want temperature to be in kelvin. So we're going to add to 73.15. And this is going to give us our temperature of 473.15 kelvin for bulb X. And now we want to get its pressure being in units of a t M's. So from the prompt we're told that bulb X has a pressure of 650 millimeters of mercury which we're going to multiply by our conversion factor where 760 millimeters of mercury has an equivalent of 1 80 M. From our notes. So canceling out units of millimeters of mercury were left with a tm for pressure and for our pressure of bulb X. Initially we have a pressure of 800.8553 A t M's. So now that we have these units in their proper or these variables in their proper units. Going to calculate initial moles of gas and bulb X. We have our term end for moles of gas isolated so that we can take pressure times volume and divided by r gas constant R times temperature meaning plugging in our pressure. We have 0.8553 A T M's for bulb X multiplied by bulb X's volume given in the prompt, which is actually the same for all of our flasks given or sorry, are all of our bulbs above according to the prompt. That volume. For bulbs X, Y and Z should all be 0.500 leaders. This is then divided by R gas constant R. Which we should recall is a value of 0. leaders times a t M's divided by moles times kelvin, which is then multiplied by our temperature for bulb X. Being 473.15 kelvin as we converted it. So now we want to cancel out our units of Kelvin as well as ATMs. And leaders leaving us with moles, which is what we want. And this tells us that our moles of gas present initially is going to be 0.011014 moles. So now that we have this initial moles of gas, we need to consider what happens with the moles of gas after opening the stop cock according to our prompt. And so we would say that after opening the stop cock, we need to figure out our moles of gas first in bulbs X. Sorry, in bob. Let's fix that. So first in bulb X. And second in bulb Y. But let's begin with bulb X. First. So we would say that still the temperature is still 473.15 Kelvin as we converted earlier. And now we have a pressure where according to the prompt. After opening the stop cock, our pressure is now 270 millimeters of mercury, which we need to convert to a T. M's. Where again, we have 760 millimeters of mercury equal to 1 80 M canceling out millimeters of mercury leaving us with a T. M's. We have a pressure and a tm. After the stop cock opens of 800.3553 A. T. M's. And so now going into our formula, we would say that our moles of gas present In Bulb X. is now equal to our pressure being .355. And yes 0.3553 A t. M's multiplied by its volume, which is now going to be still given in the prompt as 0.500 liters, which is then divided by our gas constant R again being 0.8206. Leaders times A. T. M's, divided by moles, times kelvin and then multiplied by our final temperature. Because things are at equilibrium, we have a temperature of 473.15 Kelvin still. And so simplifying this, canceling out our units. We get rid of leaders A T. M's and we get rid of Kelvin leaving us with moles. And what we'll have is that our moles of gas left in Bulb X would be 0. 75 moles. Now, after opening the stop cock, we want to consider our moles of gas left in bulb Y. And This is where we consider bulbs wide temperature given in the Diagram as 95°C. So we have Our temperature 95°C converted to Kelvin adding to 73.15. We have a kelvin temperature of 368.15 Kelvin. Now going to its and sorry, going to bulb wise pressure, which according to the prompt after the stop cock opens and reaches equilibrium, should also be equal to 270 millimeters of mercury as we saw with bulb X. Which converting to a t. M's. We were not going to repeat that since we did that above. We said that that is equal to .35538cms. So this was from above at this step. And so since we have these proper units, we're now going to calculate the moles of our gas present in bulb Y where we would have Our pressure being zero again, 3553 A T. M's multiplied by the volume in bulb y still being 35530. liters as given in the prompt, divided by our gas constant 0. Leaders, times A t. M's divided by moles. Times kelvin multiplied by our Temperature of Bulb Y, which we converted to 368.15 Kelvin canceling out our units. We get rid of a T. M's. We get rid of leaders, We get rid of kelvin. We're left with moles and this gives us our most left in bulb Y of gas being 0. moles. And now for our final answer, we need our moles of our iodine gas that is left and this is once our system reaches equilibrium. So we're going to take the, we're going to calculate this by setting this equal to our moles of gas present initially. And we'll use the color blue actually for that, since we calculated that. So our moles of gas initially subtracted from our moles of gas left over in bulb X. After the stop cock is opened, which is then subtracted from our moles of gas left in bulb Y. After the stop cock is opened. And so plugging in what we calculated from above, we have our initial moles of gas which we found to be this value here. So we have 0.01, one will say because we want to just shorten it to just 666 figs. And now we're going to subtract this from our molds left in bulb X. After the stop cock is opened, which we found to be 0.4575 moles from the step here And sorry, we need 6/6 figs. So we're going to just cut it off at 457 here. And this is then subtracted from our moles left in bulb Y. Once the stop caucus opened, which we found here, below in purple as 0. moles. So from this difference, we get our moles of iodine gas equal to 5.60 times 10 to the negative fourth power moles. And this would complete this example as our final answer for the moles of our iodine gas that is present in the system after the stop cocks are opened and allowed to reach equilibrium. So what's highlighted in yellow is our final answer. I hope that everything I went through is clear. If you have any questions, please leave them down below and I'll see everyone in the next practice video.