For the vaporization of benzene, ∆H_vap = 30.7 kJ/mol and ∆S_vap = 87.0 J/(K*mol). Does benzene boil at 70 °C and 1 atm pressure? Calculate the normal boiling point of benzene.

Video transcript

well, everyone's in this video, we're given the delta age of vaporization and the delta S. A vaporization for acetone. With these values here. So at 40 degrees Celsius. And at one a team of pressure. We're being asked if acetone boils and it does not boil then what is the normal boiling point here? All right. So what we know is that acetone boils when Our Delta S. A total value is equal to zero. We can calculate T. So the boiling point value when delta as total Is equal to zero. We know that the formula for delta S. Total physical to the adult as of system plus the delta S of its surroundings. We know that my delta S. Of the system is equal to the delta S. Of vaporization and we know that the delta S. Of surroundings. This formula is also equal to negative delta H. Of vaporization over T. For temperature. Alright, so we can now begin our calculations. So again, zero is what our delta s of total is. And then we have our 95 jewels for kelvin times small value here. And we're adding that with the delta s of vaporization. Or the delta system value. Same thing that's negative 31.3 killer jewels per mole. Gonna convert this killer jewels unit into jewels. So we're gonna go ahead and say for every 1000 jewels we get one kill a jewel and of course it's all going to be over. R. T. Temperature. We'll go ahead and simplify this here. So we get the 95 which is 95 jewels per kelvin times mom is equal to 3.13 times 10 to the four power jewels per mole again. All this over T. For temperature, we want to now isolate our tea so T. Is equal to 3.13 times 10 to the four power jewels per mole. Over 95 jewels per kelvin times mold. We can see here for their units sake that the jewels will cancel and the molds were canceled. So once I put that into a calculator I get that T. Is equal to 329.47 calvins. We will convert the kelvin into Celsius. How we do this is by subtracting 273.15. Then we can get our normal normal boiling points to be equal to 56.32 degrees Celsius. So earlier we're seeing that at four degrees Celsius and at 1 18 minute pressure we're being asked if the acetone boils. But this value which reaches calculated for is when acetone boils. So to answer a question then, is that at 40 degrees Celsius, acetone does not spoil, but rather the boiling point of us too and it's actually equal to 56°C. So this right here is going to be my final answer for this problem