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A balloon that is 100.21 L at 21 °C and 0.981 atm is released and just barely clears the top of Mount Crumpet in British Columbia. If the final volume of the balloon is 144.53 L at a temperature of 5.24 °C, what is the pressure experienced by the balloon as it clears Mount Crumpet?

0.644 $\mathrm{atm}$

01:29

Aadit S.

00:55

Charotte M.

Chemistry 101

Chapter 9

Gases

My C.

May 19, 2021

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Yeah. So let's say that we have a balloon and it starts out with a volume Of 100.21 leaders. And that that balloon is at 21°C. And the pressure of the balloon to start out with is .98 one atmospheres. So, we have our balloon at these conditions and now it goes up into the sky and it goes and gets near the top of a mountain. And when you get to that second set of conditions, what you know at that point is that the volume of the balloon Is now bigger. It's 144.53 leaders. And the temperature up there is cooler 5.24°C. So, we want to know boy, what's the pressure up there? All right, so, we know the set of conditions, volume temperature pressure at the beginning. We don't know all of them at the end, but we're dealing with volume and temperature and pressure. So what we can do is we can use the combined gas law to be able to solve this. P one V one over T one is equal to P two V two over T two. Now, when you're using the combined gas law, you need and when you're doing anything in gas laws, your temperature has to be in kelvin, kelvin is the temperature in degrees Celsius Plus 2 73. So, we're going to add to 73 to our temperatures to get our value in kelvin. So when we take 2 73 plus R 21 We get our value of 294 Kelvin. And when we add our to 73 to 5.24, we get 278 .24 Kelvin, I'm going to keep the extra significant figures here until we finish the math and the combined gas law. And then I will answer uh, the final answer to the combined gasol to the correct number of significant figures. All right. So, we know the equation, We know the values we're gonna need to plug in. So let's go ahead and do that. So, we're going to have our P one Times are V one Over our new value of T one Is equal to we don't know P two times V two. That's a four over T two. Now we can cross multiply too to get our values and so we're going to have 294 times 144.53 times p two, Which is 42491 82 times p two equals. And let's take the other part of the cross multiply. So 20.981 times 100.21 times 2 78.24 Is 27,352 66. We'll divide both sides By our 42 4 91.82. Sure. And we'll get our answer P two. Now, if we go back to our values here, Three significant figures is the lowest number of significant figures. So we're gonna answer to three 0.644. And then when we go back here, we can see that atmospheres was our unit to start with. So atmospheres is going to be your unit to end with, So our new pressure at the top of the mountain is .644 atmospheres.

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