You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds $0.900$ L. The pressure of the gas inside the balloon equals air pressure ( $1.00$ atm). If the air inside the balloon is at a constant $22.0$ °C and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts?

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Hey everyone in this problem. We have a worker using a hand air pump to inflate an air mattress. The worker notices the volume of the mattress is 160 L. The temperature of the air inside the mattress is 25°C. And the absolute pressure inside the mattress is 1.0272 atmospheres. Were asked what is the mass of air in the mattress? Okay Let's start out by just writing all of the information we've been given in the problem. Okay so we're given the volume of 160 l in problems like this. We typically want the volume to be in meters cubed. So let's go ahead and convert that two m cubed. Okay so this is going to be 160 divided by to convert to meters cubed. We get 0.16 m cubed. Alright. The next piece of information we're given is the temperature and the temperature is going to be 25°C. And we're gonna take that we're gonna add 273.15 Calvin. To give us 298.15 Calvin. Okay. Again putting everything in our standard units And we're told the pressure p is 1.0272 atmospheres. And again converting to our standard unit. We want this to be in pascal's. So we take it And we multiply by 1.013 Times to the five Pascal's. Okay. And this is going to give us 1. 05536 Times 10 to the five Pascal's. Alright, so we have the volume, the temperature and the pressure we've been given. We want to find the mass M. Well let's recall. We're talking about air so we can treat it as an ideal gas. But the ideal gas law that's going to relate the volume temperature and pressure that we have PV is equal to N. R. T. Okay, but you'll see in this equation we don't have the mass M. Okay? So we can use this information we have but we're not going to be able to find the mass M. Using this equation as it is. Okay well let's recall we can relate and the number of moles to the mass M. Through the following and is equal to the mass M divided by the molar mass. Big. Um If we replace N. In our equation with little M. The mass over big M. The molar mass. Okay, We now have a way to find the mass. We're looking for little m. Okay. We know the pressure, we know the volume, the molar mass of air. We can find our is the gas constant, which we know and t is the temperature which we've been told. Okay, so we can plug in all of our values and so for em so we're going to have the pressure 1. times 10 to the five pascal's times the volume. 0.16 m cubed is equal to little in the mass divided by big. Um now this is the molar mass in this case of air. You can look this up in a table in your textbook or that your professor provided and it's going to be 0. 896 kg per mole Times are the gas constant which is 8.314. The unit here is jewel per mole Calvin. Okay, times the temperature T. Which is 298.15 Calvin. Okay so on the left hand side we have pascal times meters cubed. This is going to give us a unit of jewel. And when we do the multiplication we're gonna get 1. Times 10 to the four. OK Jules on the right hand side we have m the mass we're looking for. We have jewel Permal Calvin times Calvin. So the unit of Calvin will cancel. And then we have divided by kilogram per mole. So the unit of mole will also cancel. We're gonna be left with the union of jewel per kilogram. And when we do the multiplication we get 8. Times 10 to the four jewels per kilogram. Now let's go ahead and divide and when we divide the unit of jewel will cancel we're gonna be left with approximately 0.194 kg. And we'll see that our answer choices are in grams. So let's convert this to grams. Okay, So we're gonna multiply by 1000 To get to 194 g. And so the mass of air inside of the mattress is going to be answered. C- 194 g. Thanks everyone for watching. I hope this video helped see you in the next one.

Verified video answer for a similar problem:

Key Concepts

Ideal Gas Law

Conversion of Temperature to Kelvin

Molar Mass of Air