A 20.0-L tank contains 4.86 * 10^-4 kg of helium at 18.0°C. The molar mass of helium is 4.00 g/mol. (b) What is the pressure in the tank, in pascals and in atmospheres?

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everyone in this problem. We have an empty aerosol sprayer with a volume of 0.3 liters filled with 0.3 g of carbon dioxide at a temperature of degrees Celsius. They were told the molecular mass of carbon dioxide is 44 g per mole. We're asked to find the pressure inside the sprayer and we're asked to express their answer in pascal's and then in atmospheres. Alright, so let's start just by writing out what we've been given. Okay, so we've been given a volume Of 0.3 L. We can write this 0.3 divided by 1000. Okay, meters cute. So to go from leaders two m cube to divide by 1000 we're going to have a volume of three times 10 to the negative four meters cubed. We're giving a mass of 0.3 g. M. is equal to 0.3 g. We're gonna have temperature t of 25°C. And if we add 273.15 we can convert this into Calvin. Our standard unit 298.15 Calvin. We're also told the molecular mass of carbon dioxide so big. M is equal to 44 g per. Okay, now we want to find the pressure P so we have volume, we have temperature, we want to find pressure. Okay, we have carbon dioxide. We can treat this as an ideal gas. So let's recall. We have our ideal gas law P. V. Equals N. R. T. So P. Is what we want to find. We have information about V. We have information about our that's the gas constant. We have information about T. We don't know. We don't have information about the number of moles N. Okay, but let's recall that we can write N. Is equal to the mass M divided by the molar mass. Big M. Times are T. Okay, So we replace N with little M over big M. Now we have the information we need. Okay, we have the we have little M. We have big M. R. Is the gas constant which we know where we can look up and T. Is the temperature which we've been given? So now we have all the information we need. We can plug into the equation and solve for the pressure. P. Alright, so substituting the information we have we have the pressure p times the volume which is three times 10 to the negative four m cubed is equal to. And here you'll notice that our mass M and our molecular mass big M are both both have units with grams. Okay, so we just want to be sure that those are consistent If one is in kilograms and one is in grams, there's going to be an issue there. Okay, so just be sure that those are have the same unit. Okay, so we have 0.3 g Divided by 44 g per mole. And you'll see now that the unit of Graham will cancel. So that's what we wanted. Okay, we have are the gas constant which is 8.314 time. Oops, not times anything. 8.314 with a unit jewels prime or Calvin. Okay. Times the temperature T. Which is 298.15 Calvin. See here the unit of Calvin will cancel. Okay? And the unit here we have Permal Permal. So those will also cancel. So let's give ourselves some more room to work. All right. We're gonna leave the left side alone. So we have the pressure p times three times 10 to the negative four m cubed Is equal to OK. We're gonna multiply these all together. We get 16. in our unit. The only unit we're left with is jewel. And then we can divide and if we divide jewel by meters cubed, we're left with the unit of pascal which is a unit we wanted for pressure. So, our units work out. Um And that's good. That's a good check. And then we're gonna get a pressure p of 1003 136.8 pascal's. And in scientific notation, we can approximate this to 5.63 times 10 To the four pascal's. So that is our pressure and pascal's. And now remember that for part two. They wanted us to convert the pascal's into atmospheres. Okay. And so we're gonna have 5.63 times 10 to the four pascal's. Okay? And we divide this By 1.013 Times 10 to the five Okay, Pascal's per atmosphere. And this is gonna give us 0. atmospheres. So now we have our answer in both pascal's and and atmospheres. So let's go back up to the top and look at our answer choices and we'll see that we have answers. See the pressure is 5.63 times 10 to the four pascal's or 0.56 atmospheres. Thanks everyone for watching. I hope this video helped see you in the next one.

A 20.0-L tank contains 4.86 * 10^-4 kg of helium at 18.0°C. The molar mass of helium is 4.00 g/mol. (b) What is the pressure in the tank, in pascals and in atmospheres?

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Key Concepts

Ideal Gas Law

Molar Mass

Pressure Units