A solution of a nonvolatile solute in water has a boiling point of 375.3 K. Calculate the vapor pressure of water above this solution at 338 K. The vapor pressure of pure water at this temperature is 0.2467 atm.

Video transcript

Welcome back everyone to another video, a solution of a non volatile solid which is also non electrolyte in water has a boiling point of 375.3. Kelvin calculate the vapor pressure of water above the solution at 338. Kelvin. The vapor pressure of pure water at this temperature is 0.2467 atmospheres. The four answer choices given to us are a 0.928 B 0.437 C 0.229 ND 0.464. All of them are given in atmospheres. Let's understand the logic behind this problem. We can essentially find the vapor pressure as false. Using the Rails law. The vapor pressure of water will simply be equal to the mole fraction of water in our solution multiplied by the standard V pressure of water or basically pure water right at the given temperature. So now we can essentially use this formula, but we need to find a lot of things. And first of all, if we're given the boiling point of the solution, we can use the boiling point elevation law which tells us that delta TB is equal to I multiplied by KB multiplied by Mity B. And from here we see that morality is equal to the change in the boiling point divided by the van Hog factor and divided by morality. I'm sorry, divided by the boiling point constant KB. Now, what is the change in the boiling point? Well, essentially we need to, first of all convert our file boiling point into Celsius. So we're going to say 375.3 minus 273.15 Kelvin, right? This will give us the final boiling point in degrees Celsius. And we are subtracting the normal boiling point of water, which is 100 °C. And we are dividing by the van ho factor, which is one because we have a non electrolyte and also on the bottom of the fraction, we're taking 0.512 °C per mole, which is the boiling point constant KB. And in this case, if we calculate the result, we end up with four point 2968 ML, which is also given to us as moles per kilogram of solvent. Now let's assume that we have 1 kg of our solvent. OK. For the simplicity, meaning number two, we can easily find the number of moles of solid. The number of moles of solid would simply be equal to 4.29 68 moles. Why? Well, essentially we have 1 kg of our solvent, right. So if we multiply by 1 kg, we get moles of solid. Number three, we can find the number of moles of solvent which is water. And we take 1 kg which is equivalent to 1000 g and dividing by the molar mass of water, which is 18.015 g per mole. And this gives us 55.6 moles. Now, we can finish our problem, the vapor pressure of water will be equal to the mole fraction. So we're taking 55.6 moles and dividing by the sum of moles are basically the total number of moles. So this includes the number of moles of water and the number of moles of our solid. So we're taking four point 2968 moles. So this first expression tells us the mole fraction and we're multiplying by the vapor pressure of 0.2467 atmospheres, which gives us our final answer. That'd be 0.229 atmospheres. And we can solve that based on our answer, the correct answer choice. So this problem would be option C that would be it for today. And thank you for watching.