The ozone layer in the Earth’s stratosphere has an average total ...

Question

The ozone layer in the Earth’s stratosphere has an average total pressure of 10 mm Hg 11.3 * 10-2 atm2. The partial pressure of ozone in the layer is about 1.2 * 10-6 mm Hg
11.6 * 10-9 atm2. What is the concentration of ozone in
parts per million, assuming that the average molar mass of
air is 29 g/mol?

Accepted Answer

Hi everyone. This problem reads, air is enclosed in a container and exerts a total pressure of two atmospheres. Find the concentration of carbon dioxide in parts per million. If it's partial pressure is 2.7 times 10 to the negative four atmospheres, assuming that the average molar mass of air is 29 g per mole. So the question that we want to answer here is the concentration of carbon dioxide in parts per million. What we can do to solve this problem is use our partial pressure equation and in this case we're interested in carbon dioxide. So what this will look like is the partial pressure of carbon dioxide is equal to the mole fraction of carbon dioxide times the total pressure. Now, because we're interested in finding the concentration of carbon dioxide. What we want to do is we'll want to isolate the mole fraction of carbon dioxide to solve for that. So let's go ahead and isolate that by dividing both sides of our equation by the total pressure. So now what we have is the mole fraction of carbon dioxide is going to equal the partial pressure of carbon dioxide over the total pressure and we can plug in these values. Okay, so in the problem, we're told the partial pressure of carbon dioxide is 2.7 Times to the -4 atmospheres, and this is over the total pressure, which we're told in the problem is two atmospheres. So when we solve this, what we're going to get for the mole fraction Is 1.3, 5 times 10 to the -4. So this is the mole fraction. What we're going to do is we're going to assume one mole of air. We're not told this, but we're going to assume that there's one mole of air. With that assumption. What we can say is our moles of carbon dioxide is going to equal this 1.35 times 10 to the negative four that we just calculated. And we're going to multiply it by one mole. So then what we get is we have 1.35 times 10 to the negative four moles of carbon dioxide. Okay, So now remember, we want to answer the question of concentration of carbon dioxide in parts per million. So for concentration we're going to need the mass. Okay, so, for the mass of carbon dioxide, we're gonna take our moles of carbon dioxide. So, this 1.35 times 10 to the negative four moles of carbon dioxide. And we want to go from moles of carbon dioxide, two g of carbon dioxide. And we'll find that by using the molecular weight of carbon dioxide, which is 44.1. So, in one mole of carbon dioxide, There is 44.01 g of carbon dioxide. Okay, So now, once we saw for this, we have 0. 41 g of carbon dioxide. All right, So now all we have left to do is calculate this in parts per million. Okay, So parts per million of carbon dioxide. We're gonna take Our massive carbon dioxide. So the 0.005941g. And we're going to divide it by the massive air which were told in the problem is 29 g. Okay. And then we're going to multiply this by 10 to the sixth. That's the parts per million. Okay? So once we do this, the answer that we get is 204.9 parts per million. So our final answer here That will highlight is 204.9 parts per million of carbon dioxide. And this is our final answer. That is it for this problem. I hope this was helpful.

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