At standard temperature and pressure, the molar volumes of Cl2 and NH3 gases are 22.06 and 22.40 L, respectively. (c) The densities of crystalline Cl2 and NH3 at 160 K are 2.02 and 0.84 g/cm3, respectively. Calculate their molar volumes.

Video transcript

hi everyone for this problem we're told to consider CH four and N two which have molar volumes of 24.4 liters at standard temperature and pressure. If the densities of CH four and N two at negative 160 degrees Celsius are the following, calculate the molar volume at this temperature. So our goal here is to calculate molar volume and molar volume is going to be leaders over more. So what we can do here is use the densities that were given and go from the densities to moller volume. So let's go ahead and start with our densities were given to which are these here? So for the molar volume of CH four, let's start off with our density with the volume and the numerator. So we have one centimeter cubed over 0. g of CH four. Okay, so we need to go from g to moles and we can do this using the molar mass of CH four. So in one mole of CH four We have 16.05 g of CH four. So looking at our units, our grams is going to cancel and now we have moles in the denominator. So the next thing we need to go is going from centimeters cubed two leaders. Okay, so the conversions for that is in one centimeter cubed or in one cc we have 0. leaders. Okay, so making sure units cancel our centimeters cube cancels here. So when we do this calculation we will get 9.17 leaders per mole of c H four. So this is going to be our moller volume for CH four. Okay, so let's go ahead and do the same thing for end to. So our molar volume four and two, We're going to have we're going to use our density same thing as we just did. So in one cc we have 0. g of end to so we'll go from grams to moles by using the molar mass of end to so and one more of end to We have 28.02 g of end to. Okay, so making sure our units cancel our grams cancel and we're left with moles. So now we need to go from cubic centimeter to leaders. Okay, so in one cc There is 0. leaders our cubic centimeters cancel. And we're left with leaders. Okay, so when we do this calculation will get an answer of 9.19 leaders per mole of N two. Okay, so this is going to be our final answer for N two and that is the end of this problem. I hope this was helpful