A balloon holds 30.0 kg of helium. What is the volume of the balloon if the final pressure is 1.

step 1 Oh boy, I love this problem. It's problem 18 from chapter 12 where we have a balloon. I love bal

A balloon holds 30.0 kg of helium. What is the volume of the...

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Key Concepts

Temperature Conversion (Celsius to Kelvin)

The ideal gas law requires the temperature to be in Kelvin, an absolute temperature scale. Converting from Celsius to Kelvin is essential because the Kelvin scale starts at absolute zero, ensuring that the gas laws are applied correctly.

Molar Mass and Conversion of Mass to Moles

Before applying the ideal gas law, it is necessary to determine the number of moles of the gas by dividing the given mass by the molar mass. This conversion is crucial because the ideal gas law relates the amount of substance in moles to the other state variables.

Ideal Gas Law

The ideal gas law relates the pressure, volume, number of moles, gas constant, and temperature of a gas using the equation PV = nRT. This law is fundamental in understanding how changes in one state variable affect the others in ideal gases, and it provides a framework for calculating unknown properties when the rest are known.

Transcript

00:01 Oh boy, i love this problem.

00:04 It's problem 18 from chapter 12 where we have a balloon.

00:08 I love balloons.

00:09 This is great.

00:09 It's a lovely day.

00:10 It's 22 degrees celsius.

00:12 We're on a different planet because there's 1 .2 atmospheres of pressure, but it's a nice planet.

00:16 So we'll be fine.

00:19 Now, this particular balloon is very special because it contains 30 kilograms of helium.

00:27 Oh, my.

00:29 We might need to change the scale of our balloon.

00:33 Here.

00:35 We're being asked to find out how large is this balloon? what's its volume? and to do this we're going to make use of pivnard, our ideal gas law.

00:47 Pressure times the volume times the number of moles, multiply that by the gas constant, and the temperature in kelvin.

00:54 So let's get straight down into it.

00:56 Because we're solving for volume, we'll divide the pressure over, bam.

01:02 And this is what we're going to be plugging into our calculator.

01:05 Once we get our values in their correct units.

01:09 We'll start off by finding the number of moles.

01:11 To do this, we're going to take the mass of our helium...