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A quantity of $2.00 \times 10^{2} \mathrm{mL}$ of $0.862 \mathrm{M} \mathrm{HCl}$ is mixed with an equal volume of $0.431 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}$ in a constant-pressure calorimeter of negligible heat capacity. The initial temperature of the $\mathrm{HCl}$ and $\mathrm{Ba}(\mathrm{OH})_{2}$ solutions is the same at $20.48^{\circ} \mathrm{C}$, For the process $$\mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)$$ the heat of neutralization is $-56.2 \mathrm{kJ} / \mathrm{mol} .$ What is the final temperature of the mixed solution?

Chemistry 101

Chapter 6

Thermochemistry

University of Central Florida

University of Maryland - University College

Lectures

05:27

In chemistry, a chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Both reactants and products are involved in the chemical reactions.

06:42

In chemistry, energy is what is required to bring about a chemical reaction. The total energy of a system is the sum of the potential energy of its constituent particles and the kinetic energy of these particles. Chemical energy, also called bond energy, is the potential energy stored in the chemical bonds of a substance. Chemical energy is released when a bond is broken during chemical reactions.

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for this problem. We're going to be looking at Kalorama Tree and we're going to be looking specifically at an acid base. Reactions itself were given quite a few things here. Make sure if you're watching this when you write this down so you don't have toe keep coming back and forth were given HCL and we have 2.0 times 10 to the to 200 milliliters of a zero point 862 Moller solution. And my initial temperature for both my solutions is 20.48 degrees c. Okay. And we also have a barium hydroxide solution and I've got the same amount. So I also have 200 milliliters and this is at a concentration of zero 0.431 Moeller and its initial temperature is also 20 point for eight degrees c. Okay, and we're put these in a constant pressure Calorie Madjer, we've got a negligible heat capacities. You don't have to worry about this and were also given that this reaction, which is the result of our neutralization, obviously has a delta H A heated neutralization of negative 56.2 killer jewels per mole. What is T f what is the final temperature? So this is what we're going to solve. Okay, so our plan for working this problem, we're going to first. I will write the equation will, right, The balanced equal equation. And we're gonna also right the balanced net Ionic equation. Both of those. We're going to figure out how many malls of HCL and moles a barium hydroxide, Um, and we'll know what we need to do with those we get to those after we've got all that. Then we are going to, um, figure out the energy Ah, the enter total energy, the energy for the neutralization. And when once you've got that will use Q equals M c, Delta T, and we'll solve for the final temperature. So that's our plan. Let's begin. Okay. Our first thing that we said we were going to do is write a balanced chemical equation. So we've got HCL, and this is easy to balance. All just do. It is we go here. Plus, Berry, um, hydroxide produces barium chloride. Also a quiz and a couple of water molecules. If we recall everything we know about, um, let me get to this. If we call everything we recall everything we know about writing completed Net Ionic equations here is my a quiz product. So I've got a barium. This is going to be crossed out. And my chloride this is going to be crossed out. Everything that I've highlighted there is going to be crossed out. Okay? Just to make sure my cameras it is so I'm going to rewrite this to H C H plus a Q plus two o h minus a que produces two h 20 There's my equation. And if you'll, um recall let me go back. This is this equation right here, so we can just see what we've got here. Whoops. I'm in the wrong spot. Okay? So I can get rid of my twos. And I know that my I felt the age for this reaction. Waas What was it? 50 negative. 56.2. Killer jewels promote. Okay, now let's figure out how many moles of HCL we have. In order to do that, I'm going to take my mill leaders. And I had 2.0 times 10 to the second Mill leaders which is equal to 2.0 me 2.0 times 10 to the minus one leaders times my mill Arat e was 0.8 something 862 That's moles per leader. I want to do my math on this I get 0.172 moles of hcl Perfect. Now how about we figure out how many moles of barium hydroxide we had the same amount So I'm just gonna go ahead and start with 2.0 times 10 to the minus one leaders times Ah point, Where is that 0.0.43? One means that I've got zero point zero eight 08 six to moles of barium hydroxide. They make a little more room for that. Now I need to know my age plus and my oh, age concentrations So I can see from my, um hcl moles. My moles of hcl were equal to 0.172 which means I also have 0.172 moles of age plus Okay, now if I've got 0.862 moles of barium hydroxide I'm going to have to There's two moles of O h minus per one mole of barium hydroxide. Oh, a miracle I get 0.172 moles of O H minus so we can see on my balanced chemical equation right here that this also means that I have 0.172 moles of water. Let's put this on her next page. I have 0.172 moles of H. 20 and we were given that it's a negative. I believe it was negative. 56.2 56 point to kill a Jules per mole, which will give me I did this. I just don't remember where I did this. 9667 9000 600 or nine point 667 killer jewels our own later. Okay, Next, you will recall that we were going to use Q equals M C, Delta T, and this will be far water solution. And I know Q is nine 1006 167 jewels because this is my cue mass. What is the mass of my solution? Well, I had 200 and 200 mill leaders, So, um, I have 400 milliliters of solution which equals 400 grams of solution. So I have 400 I put a decimal point right there. Grams of solution. I know that the specific heat capacity for Waters 4.184 j over G c degrees, and I know that my this is a negative number. So it's Excell terming. So my final temperature is greater than my initial temperature and my initial temperature instead of writing mad, and they're all just put my initial temperature head and the initial temperature is 20 0.48 degrees C. Let me see if I can question it in there. Just a little bit better. T f minus 20.48 degrees C. There we go. Okay. And now we're already do her math. This isn't the easiest problem in the world to solve. I would suggest multiplying these two numbers and then we'll distribute. So multiply the TF, times this product, this buy this product, then it gets pretty easy to do. Um, anyway, when you're finished on this, your final temperature will be 26.26 degrees c. Okay, Good enough

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