For many years drinking water has been cooled in hot climates by evaporating it from the surfaces of canvas bags or porous clay pots. How many grams of water can be cooled from 35 to 20 °C by the evaporation of 60 g of water? (The heat of vaporization of water in this temperature range is 2.4 kJ/g. The specific heat of water is 4.18 J/g-K).

Video transcript

Hello everyone today we are being asked to calculate the mass in grams of ethanol. That can be called from 45 degrees Celsius to 30 degrees Celsius by the evaporation of 1 g of ethanol. We also have some useful data. We may be able to use the first thing we wanna do is calculate the number of jewels of heat energy we have. So we're gonna say that Q. Is equal to the mass that we have which is 1 50 g. We're going to use a conversion factor of R. We're going to use the delta H. The heat of vaporization of ethanol which is 0.8 to six K. Illegals programs to get rid of the grams. And then we're going to go ahead and convert that killer jewels to regular jules by saying that for every one kg jewel that we have. We have 10 to the third regular jules. And so our units are going to cancel out. We're gonna be left with 123,900 jewels. Of course. We're going to take our heat equation which is the mass times the specific heat times the change in temperature. Notice that heat is being released because it says the ethanol can be cooled so he can be released. So our heat is going to be negative Q. Our temperature that we have in the question stem is in Celsius. So we're going to have to convert that to kelvin and in doing so we have 45 degrees Celsius, we're going to add 273 To that value. And we're also going to do the same with our 30°C. And so when we add to 73 to our 45°C, we get 308, Kelvin. And when we do the same for our 30°C we get a value of 303° Kelvin. When we denote the difference, We can see that we're gonna actually do 303 subtracted by 318 to get us negative 15 kelvin and we do this because We're essentially losing 15° Kelvin not gaining. And so we plug these values in remember we said our Q is going to be negative. So we have negative 123,900 is equal to the mass, which we don't know yet Times the specific heat which is 2.46 jewels. Poor g Kelvin. We're gonna multiply that by our temperature which is 15° Kelvin. We're gonna have some units canceled out. And the jewels on both sides will cancel out as well. We're gonna get a final mass of 33,577 g. Of course we want our answer in kilograms. So we're going to go ahead and use a conversion factor that one kg is equal to to the third grams. Once these units cancel out, we're then going to be left with a mass of 3.36 kg as our final answer, I hope this helped, and until next time.