The following phase diagram shows part of the liquid–vapor phase-transition boundaries for pure ether and a solution of a nonvolatile solute in ether.

(b) What is the approximate mo#lal concentration of the sol-ute? [Kb for ether is 2.021°C kg2>mol.]

Video transcript

Hello. In this problem we are told that the phase diagram given below shows the relationship between vapor pressure and temperature for pure ethanol and a solution of ethanol with a non volatile salute. Were asked to use this diagram to determine the approximate alive of the solute in solution. Given that the boiling point elevation constant for ethanol is 1.2 degrees Celsius per allow. Let's begin by looking at our phase diagram. This dash line represents a vapor pressure of 760 tour. So this is where we will find the normal boiling point of the pure as in all. And the solution we call that when we add a non volatile salute to the solvent, it will lower vapor pressure. This is one of our negative properties. So that means then that the yellow line represents our pure solvent. So pure ethanol and the green line then where the vapor pressure is lowered, represents our solution. We can find then the boiling point for the pure Sullivan, so pure ethanol and that of the solution by the intersection of their lines with the dash line at 760 Tour. So beginning with the pure ethanol, you follow this down. It looks like that. The boiling point of pure ethanol then is about 78 degrees Celsius. If we follow Line down for our solution, it looks like that. The boiling point for our solution is about 83°C will now make use of our equation that describes the change in the boiling point for a solution. So we have our van top factor times our mobile boiling point elevation constant times the morality and this problem then I the Vantaa factor we will consider to be equal to one since the solute is unknown and we don't know whether or not it will associate. So we'll make the assumption that it is not were given the Low boiling point elevation constant is 1.2°C per mobile for ethanol. And our change in Pointing point then is equal to that of our solution. So 83 degrees Celsius minus that of our peer solvent. So 78 degrees Celsius. This works out to then five degrees Celsius. So taking our equation above and solving for morality, morality is going to be equal to the change in our boiling point Provided by the Van Hoff Factor divided by our boiling point elevation constant. So we have then 5°C divided by one, divided by 1.2 degrees Celsius per wow. Are units of degrees Celsius cancel and we're left with two units of morality. This works out then to four moles of our salyut per kilogram of That's an all. So the morality of our solution between pure ethanol and an unknown novel to salute is for um allow thanks for watching. Hope this helps