A 50.0 g sample of solid CO2 (dry ice) is added at -100 °C to an evacuated (all of the gas removed) container with a volume of 5.0 L. If the container is sealed and then allowed to warm to room temperature 125 °C2 so that the entire solid CO2 is converted to a gas, what is the pressure inside the container?

Video transcript

Hi everyone for this problem we're told a mothball weighing 130 g was placed inside a 10 liter vacuum container. The container was then slowly heated to 80°C. After it reached the temperature, the mothball fully sublime is to gas, calculate the pressure inside the container. Alright, so here we need to calculate pressure and we are dealing with a gas here. So we need the ideal gas law. So the ideal gas law is P. V. Is equal to N. R. T. And we're solving for pressure. So we need to isolate pressure by dividing both sides by V. When we do that, we get pressure is equal to N. R. T. Over V. Okay, so let's go ahead and see what we have and solve for what we may not have and represents moles. So we need to figure out how many moles Is our Mothball. Alright, they tell us we have 130 g. So we have 100 and 30 g of C 10 H eight. We need to convert these grams to moles. And we can do that by using molar mass. So in one mole of naps. Selene. So C 10 H eight. Which is our mothball. How many g do we have using our periodic table? We have a 128.18 g. Okay, so our units of grams cancel and we're left with moles. So when we solve this we get 1.014 malls of C 10 H eight. This is our nap feeling so we have our most perfect. Our next thing is are our is our gas constant And this is a value. We should know r. is equal to 0. leaders time A. T. M. Over more times kelvin. Okay so we have our T. Is our temperature. So they tell us our temperature is 80°C. But if we take a look at our our constant our temperature is in the unit of Kelvin. So we need to convert this C to Kelvin and we do that by adding 273.15. So we get a temperature of 353. Kelvin. So we have our temperature and the last thing is volume we're told that We have a volume of leaders and this is in the correct unit. If you look at our gas constant R volume is and leaders so we have everything that we need to plug in to solve for pressure. So let's go ahead and do that. So n is 1. more. R is 0. leaders times atmosphere over more times kelvin. T is 353. Kelvin. And our volume is 10 leaders. So we need to make sure our units cancel here and because we're looking for pressure, our unit leftovers should be a T. M. So let's just verify that our moles cancel, Calvin cancel and leaders cancel. And if you take a look, our unit that we're left with is a Tm. Which is perfect. Alright. So once we solve this, we're going to get a final pressure of 2.938 a. T. M. And this is our final answer. This is going to be the pressure inside the container. That's the end of this problem. I hope this was helpful.