The pressure of a gas at the triple point of water is 1.35 atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO2 solidifies?

Video transcript

Hey everyone welcome back in this problem. We're told that the triple point for carbon dioxide occurs at negative 57 degrees Celsius and 5.2 atmospheres. Okay, We're told that the pressure of a gas sample at this point is 3.8 atmospheres. If the volume does not change, we are asked to determine the pressure of the gas sample at the boiling point of nitrogen. Yeah. All right. We're told that the volume does not change. And we have information about pressure and temperature. Okay? So let's recall Gay lucic's law. Okay, This is a version of the ideal gas equation. Okay. Where we have constant volume and we have and the number of moles constant because we have no exchange of matter. Okay? So this is going to say that the initial or the first pressure and temperature it is equal to the ratio of the final pressure and temperature. Okay, So P. I over T. I. Is equal to P. F over T. F. Now, what we're looking for is we're looking for pressure at a particular temperature. So, we're looking for this P. F. Quantity. We know p. I. The initial pressure we're told is 3. atmospheres and we're at the triple point of carbon dioxide. Okay, You'll notice that we have a different pressure. So we're gonna go ahead and use the pressure we've been given and then use the um temperature of that triple point okay, for our initial temperature. So that's gonna be negative 57 degrees Celsius. So we're gonna take negative 57 plus 273. Okay. So that we can write this in terms of Calvin on the right hand side, we have pf the final pressure we're looking for in the final pressure. We're looking for what we want to find the pressure at the boiling point of nitrogen. Okay. And same thing as before we're looking for the pressure. So we're going to take the Temperature of the boiling point of nitrogen which is negative 196°C. Okay. And we're going to add 273 so that we can write this again in terms of Calvin. Alright, rearranging, we're gonna get p. f. is equal to 3. atmospheres Times Calvin Divided by 216 Calvin Calvin is going to cancel we're going to be left with 1.35 Atmospheres. Okay, so that's gonna be the pressure of that gas at the boiling point of nitrogen. That's going to correspond with answer a 1.35 atmospheres. That's it for this question. I hope that helps you in the next video