A 2.0-L container of liquid nitrogen is kept in a closet measuring 1.0 m by 1.0 m by 2.0 m. Assuming that the container is completely full, that the temperature is 25.0°C, and that the atmospheric pressure is 1.0 atm, calculate the percent (by volume) of air that is displaced if all of the liquid nitrogen evaporates. (Liquid nitrogen has a density of 0.807 g/mL.)

Video transcript

Hello everyone today. We have been given a problem and asked to solve for the percent by volume of air. So it says a 57 liter canister full of liquid oxygen is placed into a 570.75 m times 1.3 m times 0. m box At 30°C and . atmospheres. What is the percent by volume of air displaced? If all of the oxygen gas evaporates, right? All of the oxygen gas evaporates. And we are to assume that the density of oxygen gas is 1.43 g per liters. The first thing we want to do is find malls of oxygen gas and we can do that by taking our leaders. We were 57 L and using the density To cancel out the number of leaders. So we have 1.43 g over one leader. Our leaders cancel out And we're left with 81.51 g. We then want to take that grams That amount of grams that 81.51 g and multiply it by the molar mass of oxygen gas. Notice we are dealing with 02 so we're dealing with two oxygen molecules. So its molar mass will be 32 g per one mole arguments. Once again canceled out. And we're left with 2.5 for 72 moles of 02. We'll keep that number to the side for now. Our second step is to find the volume over oxygen gas and we can do that by utilizing the ideal gas law which says that pressure times volume is it was the number of moles times the gas constant times our temperature Rearranging this equation. We can solve for our volume. We can say we can use our Molds which is 2.5472. We can multiply that by a gas constant which is 0.08-1. Then we multiply that by our temperature which noticed how we were given and Celsius. So we simply just need to add 2 .15 Kelvin to that value. And we place this all over our pressure, which is 0.97 atmospheres. This gives us our volume of .3567 L. We'll keep that number to the side. Now we want to find the volume that occupies a specific room. This .75 times .13 times 1. times .4 m Box. So we're going to multiply those values. We'll take .75 m. multiply that 1.3 m By .4 m And we get 0.39 meters cubed To find the leaders. However, we must take this value of .39 m cubed and convert that into leaders. So we'll use the conversion factor that one m cubed is equal to 1000 liters. Our units for m cubed, cancel out and we were left with 390 leaders. Lastly To find the% 65. L. And we divide it by the total leaders of the box, which is 390 leaders. And we multiply that by 100 arguments of leader canceled out And we're left with a final answer of 16.76%. I hope this helped. And until next time.