Consider the sublimation of mothballs at 27 °C in a room having dimensions 8.0 ft ⨉ 10.0 ft ⨉ 8.0 ft. Assume that the mothballs are pure solid naphthalene (density 1.16 g/cm³) and that they are spheres with a diameter of 12.0 mm. The equilibrium constant K_c for the sublimation of naphthalene is 5.40⨉10^-6 at 27 °C. C₁₀H₈(s) ⇌ C₁₀H₈(g) (a) When excess mothballs are present, how many gaseous naphthalene molecules are in the room at equilibrium?

Video transcript

Hello. Everyone in this video we're trying to determine the number of gasses. Paradise, chloral benzine molecules present in the room at equilibrium. So let's first recognize that we're given this chemical equation here and also that the equilibrium constant equation is KFC equaling to a ratio. So on. The numerator is going to be the concentration of our products to its coefficient over the concentration of the reactant, to the power of its coefficient. Alright, so we can see from this equation here that we have one product and one reactant so only gashes and acquia solutions or substances are included in the equilibrium constant expression. So then we can basically just ignore the starting material here. So then our equilibrium constant equation will only consist of the concentration of C six H four cl two and because we have a coefficient of just one we won't add anything here And we're actually given the concentration of this and that's 2.7, 2 times 10 to the -13. So now knowing the equation um constant, we can go ahead and calculate for the volume of the room. So the rooms volume is calculated our dues in a different color will do in blue. So the rooms volume Is equal to five m times five m times another five m. And this gives us 100 and 25 m cubed. So converting these two leaders now so we'll do some dimension analysis. So again we're starting with 1 23 or 1 25. I apologize meters cute. Alright so I'm gonna first convert this into centimeters So I know the direct conversion from meters two centimeters. So for every 100 centimeters we have one m. We're gonna go ahead and cube this whole fraction here. And this gives us not only centimeter cubes but also meter cube to cancel out with this one. And then our next one here will be from one cm cubed. Let's write this a little bit better. 21 millimeter. And finally we're gonna go from milliliters to liters. So for every 1000 mL we have one leader. So you see now that the meter cubes will cancel and then we have our centimeter cube that will also cancel. And lastly the male leaders. So once you put everything into calculator you get the rooms volume and leaders is equal to 125000 units. Speak leaders. So now we can go ahead and find the number of molecules in the room. Starting off with the rooms volume again. So 125,000 L. We're gonna multiply this with the equilibrium constant. So 2.72 times 10 to the -13 for everyone. Leader. Then we're gonna go ahead and use avocados numbers so everyone more, We know that there are 6.00 or 0-2 times 10 to the 23 molecules. Go ahead and extend this like so move this to the middle. Alright so for the units and you can see that the leaders will cancel on top here should be moles. So then we can see that the malls were canceled, leaving us with just the units of molecules. So then once you put all these numbers into a calculator, we see the number equaling 22.4748 times 10 to the 16 Molecules. We're gonna go ahead and round this to three significant figures. And so that's the appropriate amount of sick fix. And the correct answer should be 2. five times 10 to the molecules. So this right here is going to be my final answer for this problem.