A special gas mixture used in bacterial growth chambers contains 1.00% by weight CO2 and 99.0% O2. What is the partial pressure in atmospheres of each gas at a total pressure of 0.977 atm?

Video transcript

Hi everyone. This problem reads 67.5% sulfur dioxide and 32.5% carbon dioxide make up a special gas chamber at 839 atmospheres total pressure. What is each gas is partial pressure in atmospheres. Okay, So we want to know each gas is partial pressure and atmosphere. So our two gasses are sulfur dioxide and carbon dioxide and partial pressure is equal to the mole fraction of the gas times the total pressure. So let's go ahead and write that down. So we have two gasses. So the partial pressure of sulfur dioxide is going to equal the mole fraction of sulfur dioxide where X represents mole fraction times the total pressure. Okay, And the same thing for the partial pressure of carbon dioxide, it's going to equal the mole fraction of carbon dioxide times the total pressure. Okay, So the first thing that we need to do is figure out the mole fraction for both. Okay, And And then we're going to figure out the total, we know what the total pressure is because it's given in the problem. The total pressure is 839 atmospheres. So all we need to do is figure out the mole fraction for each. So, let's assume we have 100 g sample. Alright So let's go ahead and write that down. So we're going to assume that we have 100 g sample. And the reason that we're assuming we have 100 g sample is because we know we have 67.5% sulfur dioxide and 32.5% carbon dioxide. So if we assume that we have 100 g, what that means is the grams of sulfur dioxide is going to equal 67. g. We're taking that percentage and making it grams because we're 67.5 out of 100. Or if we converted it to a percent, it would be the same thing. Okay, So in the same sense, our grams of carbon dioxide is going to equal 32.5 g. Okay, So now what we want to do is we want to go for from grams of each two moles of each. So we want to go from grams of sulfur dioxide, two moles of sulfur dioxide. And we want to go from grams of carbon dioxide, two moles of carbon dioxide. Okay, so let's go ahead and do that. So we have 67.5 g of sulfur dioxide and we want to go to moles of sulfur dioxide. So in one mole of sulfur dioxide, the molar mass of sulfur dioxide is 64.07 g of sulfur dioxide. Alright, so grams of sulfur dioxide cancel. And we're left with unit of moles of sulfur dioxide. So we have 1.0535 moles of sulfur dioxide. Let's go ahead and do the same thing for carbon dioxide. We have 32.5 g of carbon dioxide One mole of carbon dioxide. The molar mass is 44. grams of carbon dioxide. So grams of carbon dioxide cancel. And we're left with unit of moles. Okay, so we have 0. moles of carbon dioxide. So we need to because we need to know what the total amount of moles is. So we know what the moles of each is. And in order for us to calculate the mole fraction we're going to take each and divided by the total number of moles. Okay, so our total number of moles and total is going to equal the sum between the two. So it's going to equal the sum of 1. Plus 0.7385. So our total moles is 1. 920. So now we can calculate the mole fraction of each. So we said mole fraction is represented by X. So the mole fraction of sulfur dioxide is going to equal the moles of sulfur dioxide that we just calculated, which is 1.535 divided by the total number of moles. So 1.7 920. Okay, so let's write that down moles of sulfur dioxide over moles total. Okay, so this ends up coming out to 1. moles. That's the mole fraction for sulfur dioxide, The mole fraction for carbon dioxide is going to equal the moles of carbon dioxide, which is 0. moles of carbon dioxide divided by the total number of moles which is 1.79 to 0 moles total. So this comes out to 0. 21 moles. Okay, so we're going to go ahead and write a so two sulfur dioxide and co two carbon dioxide. So now we have all the information that we need to calculate the partial pressures of each gas. So let's go ahead and do that here. So we know that the partial pressure of sulfur dioxide is equal to the mole fraction of sulfur dioxide. We just calculated the mole fraction of sulfur dioxide, it is 0. Moles. And the total number the total pressure was given in the problem. It's 839 atmospheres. Okay, so that means our partial pressure of sulfur dioxide is equal to 493 atmospheres. And we're gonna do the same thing for the partial pressure of carbon dioxide is going to equal the mole fraction of carbon dioxide, which we calculated is 0.41- moles times the total pressure is atmospheres. So the mole fraction of carbon dioxide is 346 atmospheres. So this is going to be our fine Final answer. So the partial pressure of sulfur dioxide is equal to 493 atmospheres and the partial pressure of carbon dioxide is equal to 346 atmospheres. That is it for this problem, I hope this was helpful.