What is the pressure in atmospheres inside a container of gas
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Question

What is the pressure in atmospheres inside a container of gas 
connected to a mercury-filled open-end manometer when the 
level in the arm connected to the container is 28.3 cm higher 
than the level in the arm open to the atmosphere and the atmospheric 
pressure reading outside the apparatus is 1.021 atm?

Accepted Answer

Hey everyone in this example, we need to calculate the pressure of the gas sample in this illustration below, given that the atmospheric pressure is 755.5 millimeters of mercury. So we want to recognize this device as a barometer and what we have is our level of our gas within the device. So we want to go ahead and calculate the difference between the side of our device here that is not exposed to the atmosphere versus the level of our gas on the side of our device that is exposed to the atmosphere here. And as you can see, they give us the height and centimeters. So we want to go ahead and look at the side that is not exposed to the atmosphere which is the side here. And based on the measurement here, we can go ahead and draw a circle around here at this point because this is the point at which the level of our guests is at. And this appears to be at about three cm actually because we are up by three ticks. So we can say on the left hand side, we are at 3cm. And then moving on the other hand of our or on the other side of our device, we would recognize that our gas, Is that a negative height value here where we are at about I would say negative 1.5. So we can say negative 1.5 CMS here. Since we're like between the two and the one tick here, that's where our level of the gas sample is on this side of our barometer. So now we want to go ahead and take the difference between these two heights. So we would take the difference of the positive height first. So three CMS minus -1.5 cm. And this is going to give us a value of 4.5 cm as our difference in height. Our next step is to recognize that because we have a negative height difference on the side of our gas sample in the barometer that is exposed to the atmosphere here because we have this negative value here for its height. We would go ahead and recall that our formula to calculate our pressure of the gas sample is going to be that our pressure of our gas is equal to the pressure of the atmosphere minus our height that we calculated. And so we can go ahead and plug in the values that we know to calculate for pressure of our gas sample. So according to the prompt, we have a pressure of 755.5 mm of mercury. So we plug that in for pressure of our atmosphere And we're going to subtract this from our height here and we have a height of 4.5 cm. However, as you recognize, we need the height to be in mm of mercury because technically right now we are at centimeters of mercury. So we want to go ahead and recall our conversion factor that within one centimeter To get two, we would have one or sorry 10 because we should recall that our prefix senti means 10. And so we can go ahead and cancel our units of centimeters. And now we are left with millimeters and then we still have that mercury unit. So what we can go ahead, go ahead and do is calculate our Equation here. So what we're going to have is that our pressure of our gas is equal to 755. millimeters of mercury subtracted from 4.5 times 10, which is going to give us 45 mm of mercury as our conversion from above. And this difference gives us our final pressure of our gas sample equal to a value of 710.5 mm of mercury. And this will be our final answer to complete this example as our sample or our pressure of our gas sample in the barometer for this example. So I hope that everything I reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video

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