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Use standard enthalpies of formation to calculate the standard change in enthalpy for the melting of ice. (The Hf for H2O(s) is -291.8 kJ>mol.) Use this value to calculate the mass of ice required to cool 355 mL of a beverage from room temperature (25.0 C) to 0.0 C. Assume that the specific heat capacity anddensity of the beverage are the same as those of water.

$$111.35 \mathrm{g}$$

05:31

Kevin C.

Chemistry 102

Chemistry 101

Chapter 9

Thermochemistry

Thermodynamics

Chemical reactions and Stoichiometry

Rice University

University of Maryland - University College

University of Toronto

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in this question, we are doing a calorie mitory problem. Um We want to know the mass of ice required to melt uh to change the temperature of a beverage By 25°C. So remember when you're doing kalorama tree, there are a few things that we need to keep in mind. Q. Equals M. C. Delta T. Where Q. Is your heat either gained or lost? Emma's your mass C. Is your specific heat and the delta T. Is the change in temperature. When you're dealing with two different substances that are changing temperatures, you are also going to be using Q. Lost equals negative Q. Gained. It doesn't really matter which side of the equation here that you make negative. Remember one side is going to gain energy that's going to be taking in, it's gonna be positive. The other side is losing the energy. So it's going to be negative. So in order to get them to be equal, you've got to Change one of the signs for either side. All right. So in this problem we are dealing with water as a solid. Changing into water is a liquid. The reason I'm starting with this is we need to calculate the delta H of formation for that reaction. Remember that's the some of our products minus the sum of our reactant. They gave us the value for the solid water. You had to look up the value for the liquid water in the tables. So our delta H of formation is going to equal a negative to 85.83 killer jewels, which is the value for the liquid. You're gonna subtract from that a negative 2 91 .8 Killer Jewels which is the value from the solid right products minus reactant. This gives us 5.97 with Sig figs. You're going to run that to 6.0. Kill a jewels for the amount of energy that you have to put into the system in order to melt that ice. We're also going to calculate the delta T. They told us that this started at 25 degrees Celsius and ended at zero. Remember this is T final minus T. Initial zero minus 25 Is a -25 C. That is my delta T. Mm hmm. No when you are doing this we have Q. Lost equals negative Q. Gained. But the Q lost is not going to be calculated by doing M. C. Delta T. Because this is a change of state. Whenever you change state you have to take your um number of moles times your delta H. Of in this case fusion. So we calculated what that value is. That's why they gave us the numbers to begin with. So here we have some number of moles Times 6000 jewels I need to convert my six killer jewels into jewels is going to equal the negative. I'm going to make this side negative and you'll see why in a second the mass of our beverage they gave it to him to us in milliliters. But remember They also told us that the density was one g per million later. So milliliters here equal grams. So I just substituted that Times 4.18 Jewels Program Degree C. Times Our Delta T. of -25. All right. In this case we have when we do this math, we just need 3 55 times 4, 18 Times 25. The negative signs are gonna cancel each other out. And we're calculating moles. So moles here are going to equal 6.18. And this is really moles of our ice or solid water. So I'm gonna just multiply that by its molar mass, that'll get me into grams. This is going to round 210 g of ice. If we go back and I didn't market here, this only had two sig figs. So this zero was significant that the others were not. Um And if we carry that through the calculation, We are going to end up with 110 grams of ice. Yeah. Mhm

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