1 a balloon with a volume of 150 l at 25c and 10 atm is...

1. A balloon with a volume of 15.0 L at 25°C and 1.0 atm is released. It rises to a height of 5,000 feet where the pressure is 632 mmHg and the temperature is 5°C. What is the new volume of the balloon? 2. A balloon with a volume of 550 mL at 1.0 atm rises to a height of 6.5 km where the pressure is 305 mmHg. Assuming the temperature remains constant, what is the new volume of the balloon? 3. A sample of oxygen gas occupies a volume of 1.2 L at 22°C. Calculate the temperature (in °C) at which the volume will reduce to 254 mL.

Transcript

00:01 Okay, so for all these questions, we're going to be using the ideal gas law and variations of that law.

00:06 So for the first problem, we were given the initial volume, temperature, and pressure, and then asked to find the final volume.

00:14 So the equation that we're going to use for this is that the initial pressure times the initial volume divided by the initial temperature is equal to the final pressure times the final volume divided by the final temperature.

00:27 So we just have to make sure all of our units are the same and that the temperature is always in.

00:33 In kelvin.

00:34 So the units for pressure and volume doesn't matter as long as they are the same, but the units for temperature always have to be in kelvin.

00:45 So let's convert our temperature into kelvin, which we just add 273.

00:49 So 273 plus 25 is going to be 298 kelvin, and then 5 degrees celsius plus 273 is just going to be 278 kelvin.

01:00 Now, the initial pressure, the initial pressure, is an atmosphere and the final pressure is in millimeters of mercury.

01:06 So let's convert millimeters of mercury into atmosphere.

01:09 So for one atmosphere, we have 760 millimeters of mercury.

01:15 So our pressure is 632 divided by 760, which is 0 .83 atmospheres.

01:23 So let's go ahead and plug those values in.

01:28 So our initial pressure of one atmosphere times our initial volume of 15 liters divided by an initial temperature of 298 kelvin is equal to the final temperature of 0 .83 atmospheres times our final volume which is what we're trying to find divided by our final temperature of 278 kelvin and then now we just use some algebra and solve for our final volume so 1 times 15 divided by 298 times the 278 divided by the 0 .83 and our final volume.

02:06 Should be 16 .9 liters.

02:10 We're going to do a similar thing for the next two problems.

02:13 So in number two, we have the initial volume of 550 milliliters, initial pressure of one atmosphere, and a final pressure of 305 millimeters of mercury.

02:24 So the temperature is constant.

02:25 So we can throw that out of the equation.

02:28 So we can just say the initial pressure times the initial volume is equal to the final pressure times the final volume, right? the temperature is constant.

02:36 So it's the same, it's the same so it'll cancel each other out so we don't need to include it.

02:40 Now we just can make sure our units are the same.

02:42 So we have atmospheres here and millimeters of mercury here...

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