10 g of dry ice (solid CO₂) is placed in a 10,000 cm³

Question

10 g of dry ice (solid CO₂) is placed in a 10,000 cm³ container, then all the air is quickly pumped out and the container sealed. The container is warmed to 0°C, a temperature at which CO₂ is a gas. What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.0 atm, immediately followed by an isobaric compression until the volume is 1000 cm³.

Accepted Answer

Hey, everyone. Let's go through this practice problem. A sample of solid iodine weighing 20 g is placed in a sealed container with a volume of 500 mL at 25 degrees Celsius. The container is then heated to 80 degrees Celsius causing the solid iodine to sublime into a gas. What is the gas pressure inside the container at 80 degrees Celsius? Assuming all of the solid iodine sublimates and the container remains sealed. Consider the molar mass of solid iodine is 254 g per mole. You have four options to choose from. Option a 4.56 atmospheres, option B 5.62 atmospheres, option C 6.45 atmospheres and option D 5.26 atmospheres. Now, because we're looking for a gas pressure from other variables including its volume, temperature and the amount of a substance. This is a good opportunity to use the ideal gas law which states that the pressure of a gas multiplied by its volume is equal to its number of moles multiplied by the ideal gas constant multiplied by the temperature. Since we're looking for pressure, let's solve this equation for P by dividing both sides of the equation by the volume. So we find that the pressure is equal to N RT divided by the volume. So now let's go through each of the variables and make sure that we have everything that we're going to need to plug into a calculator. First, the end for the number of moles of the gas, we're not actually given the number of moles of the gas, but we do have the mass of the material that was converted into the gas that sublimated. And we're told that it was 20 g. Now, the problem also tells us the molar mass of the material, the molar mass of solid iodine. And we're told that it's 254 g per mole. That means that we can use the molar mass essentially as a conversion factor to convert from the mass. We've been given to the number of moles. So N is going to be equal to the 20 g. And then we're going to apply the molar mass as a conversion factor. That's 254 g for one mole. I'm gonna multiply this by one mole divided by g. And if we put that into a calculator, then we find a number of moles of about 0.787 moles. Now let's talk about the temperature and note the problem mentions two different temperatures. We're given the temperature of the iodine before the sublimation. And the temperature after the iodine. So this is where it's important that you read the problem carefully because the problem is specifically asking us for the pressure inside the container at 80 degrees Celsius after the sublimation has taken place. So the relevant temperature for us is the 80 degrees Celsius. Though, of course, in order to get it to work with the ideal gas law, we have to convert it into Kelvins by adding 273. So if we do that, we find that the temperature that's important to us is Kelvins. Finally, the last variable we have to worry about is the volume. So the volume is not gonna change because everything's located inside the same sealed container. And we're told that the volume of that container is 500 mL. But once again, we're gonna have to do a unit conversion. If you want to get this quantity to work with the Ideal gas law, we need to convert it from milliliters to cubic meters. And it's helpful to know that one cubic meter is equivalent to one million or one multiplied by 10 to the power of six mL. So that conversion factor is all we need. So this is equal to 0.5 cubic meters. And now we have all the variables that we're gonna need. We have all the numbers that we need to plug into the pressure equation into a calculator. So now let's start plugging things in. So the pressure is going to be equal to 0.787 moles multiplied by the ideal gas constant. And recall that the ideal gas constant has a value of 8. jewels per mole. Kelvins. This is being multiplied by the temperature which we established is 353 Kelvins and everything is being divided by the volume, 0.5 cubic meters. And if we put all this into a calculator, then we find a pressure of about 461, pascals. But if we look at the options, we were given the multiple choice options are all written with the units of atmospheres. So in order to actually solve this problem, we're going to need to convert from pascals into atmospheres and recall that one atmosphere is equal to 1.13, multiplied by 10 to the power of five pascals. And so if we put this into a calculator, then we find that this pressure is equal to about 4. atmospheres. And so with that is the answer to this problem. And if we look at our options, we can see that option A says this 4.56 atmospheres. So option A is the answer to the problem. And that's all for this video. I hope this video helped you out. If you think you need more practice please check out some of our other tutoring videos which will give you more experience with these types of problems, but that's all for now and I hope you all have a lovely day. Bye bye.

Key Concepts

Ideal Gas Law

Isothermal Process

Isobaric Process

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