Problem

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Problem 69 Hard Difficulty

Zinc metal reacts with hydrochloric acid according to the balanced equation:

When 0.103 g of Zn(s) is combined with enough HCl to make 50.0 mL of solution in a coffee-cup calorimeter, all of the zinc reacts, raising the temperature of the solution from 22.5 C to 23.7 C. Find Hrxn for this reaction as written. (Use 1.0 g/mL for the density of the solution and 4.18 J/g # C as the specific heat capacity.)

Answer

$$
-1.6 \times 10^{2} \mathrm{kJ} / \mathrm{mol} \mathrm{Zn} \text { or } 1.6 \times 10^{5} \mathrm{J}
$$

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Video Transcript

So this problem is a kalorama tree problem. And when we're dealing with kalorama tree um we need the formula, whoops, hang on a second would help if I could write and talk at the same time. So we're trying to find heat. Right heat is equal to M. C. Delta T. You might use that as Q. Right? Most books will use specific heat as the sea here. Some of them will use an S. Depends on the author. The amateur mass in grams. Um Generally as long as your specific he is given in jewels program degree C. And the delta T. Is the change in temperature also in Celsius. So in this problem we are told that zinc is going to react with hydrochloric acid. You don't really need this equation. But what's happening here is reforming the NCL too and hydrogen gas. I'm not gonna worry about balancing it because we don't need it balanced to do this problem. They told us that we had .103g of zinc and that we have um 50 mL of hcl. If you've ever done this reaction is an exotic thermic reaction, you'll actually feel the Test two or beaker that you're doing this reaction in getting hot. Um but we're gonna show that mathematically a little while. Now when we do these questions, I already told you we need a mass. We don't have a mass here for the solution and we need to get there. So they did give us along with the volume identity. They told us to use 1.0 grams per million er we can use this as a conversion factor to get the grounds. So We have 50 g of our hcl solution now we can plug in to M. C. Delta T. We have our mass of 50 g. We have a specific heat A 4.18 jules program degree Celsius. And they gave us The two values for temperature. So delta T. Is equal to T final minus T. Initial. They told us that the temperature changes From 22.5 to 23.7 23.7 -22.5 Gives me a delta t of 1.2°C. I'm going to plug that into this formula. This will allow me to solve for my heat. The unit that we should be left with his jewels. So grams will cancel. Degrees C. Will cancel. Will be left with jewels. When I solve this, Whoops We get 250 0.8 jewels. We're not done though. That's the heat. For the one point. Sorry for the .103g of zinc that reacted in order to find a delta age for the reaction I need to take the number of moles. I need to find the number of moles. Sorry of zinc. In order to get this unit to be jewels per mole. That's what I need to get delta age for a reaction. So we need moles of zinc. We were given .103 g of zinc. So this isn't difficult. We're really just dividing by the molar mass And that's from the periodic table 65.39. This gives me zero 158 moles of zinc. Now that I have that, I'm going to just divide these two numbers, Take the 250.8 jules. I'm going to divide that by .00158 and that's in moles. When I do that, I am going to get 159 jules per mole. And that is our delta age for the reaction. Yeah.

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