So they tell us that we have four giggle years of flue gas and they're wanting us to find out how much calcium Sophia in kilograms we can obtain from this. So we know that one Giga Leader is equal to one time 10 to the nine leaders.
and they inform us that our stress is equal to one surroundings and that our temperature is equal to 25 degrees Celsius. i am just gonna add to seventy three Calvin to this. So our temperature goes to be 98. Calvin. All proper, so we are simply gonna plug the whole thing into our equation. So one atmosphere times our quantity so four times, 10 to the nine leaders. we're gonna divide this through ours. i'm just gonna use artwork zero.8 to 1 leader's atmosphere per mole, Kelvin.
and then we are gonna times that by way of our temperature. so to 98 Calvin. All right, so when we calculate this out, are moles of flue gasoline is gonna identical to one.6 35 instances generally tend to the 8 moles of our flue gasoline. So now that we've got our moles of flue gas, we need to find a connection between the most of flue fuel and the mass of our calcium selfie.
So if we pass up here, we see that one more of our silver dioxide is equal to at least one mole of our calcium sulfate. So we're gonna use that connection to help us discover the big calcium selfie. So we want to locate the moles of our sulfur dioxide and they provide us the mole fraction for silver dioxide. they say it's a thousand times that of clean air, and we recognize that the mole fraction for easy air is two instances 10 to the negative 10.
So our mole fraction to be able to is equal to two instances 10 to the poor, 10 times a thousand. So our new mole fraction for S 02 goes to be instances 10 to the terrible seven. Hurry. And we realize our moles of sulfur dioxide are identical to its mole fraction times the full wide variety of moles. So we do recognise the full variety of moles.
it's what number of moles of our flue gas we have. So our moles of eso to is gonna be too instances 10 to the negative seven instances 1.635 times tend to the 8 moles. So our moles of sulfur dioxide goes to be 32.7 moulds. So now that we've maximum of the sulfur dioxide, we are able to get the moles of our calcium, Sophie, and that's just gonna be the moles of our sulfur dioxide. And we're gonna times that by means of that one toe, one-mole ratio. So one mole, calcium Sophie to at least one-mole sulfur dioxide.
So the moles of our calcium sulphate is the same at 32.7 maximum. So now, to get the mass of our calcium selfie, we simply take our range of maximum of 32.7 moles. I worked inside the times that via its molar mass, that's 136.14 grams in keeping with mole.
So our mass of calcium sulfate is equal to four hundred or 4451.eight g. They need this in kilograms. Sword goes to divide this by way of hundreds. So when we do this, it is gonna equal 4 factors for 518 kilograms of our calcium. So toes and that is Thea amount or the mass of calcium sulphate we will get from four Giga leaders of flue gasoline.
All right, so for the second a part of this question, they're asking us the quantity of air needed to react with all the calcium sulphides. as a way to figure that out, we're gonna need to parent out the moles of 02 They do give us the mole fraction for 02 and it is identical to 0.2 09 after which we're searching out the quantity of air in leaders. All proper, so we recognize that moles of 02 are identical to its small fraction times the full moles of air So maximum of 02 is gonna be 0 factor 209 times all through moles of air.
So allow's simply use that variety for our Mueller ratio to discern out our moles of calcium sulphate. So we are gonna use 32.7 of our calcium, so fight as it's simply gonna be a 1 to one ratio. Oh, we recognize that for each 1.five moles of 02 we've one mole, our calcium sulfate. and then we also know that for each one mole of air, we've got zero.209 moles of 02 So we calculate this out. Are moles of air goes to same 78.2 moles of air?
So then, to get the volume we are simply gonna use PV is same to N. R. T. So we're solving for quantity. So n r t divided through the pressure. They tell us that the pressure is same to 1 environment and we are gonna be using a temperature equal to 2 98 Calvin.
So our extent is gonna identical 78.2 moles of air while times that through our cost of zero.8 to one leaders surroundings in keeping with greater Calvin or in times that fireplace temperature, which is to ninety eight Calvin, I might not divide all of this through one surroundings. So our extent of air is gonna identical to 1913 leaders of air this is had to react absolutely with calcium sulfate. and that's how we noticed the second part of this problem.
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