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A 4.1 17-g impure sample of glucose ( $\mathrm{C}…

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Lime is a term that includes calcium oxide (CaO, also called quicklime) and calcium hydroxide $[\mathrm{Ca}(\mathrm{OH})_{2},$ also called slaked lime]. It is used in the \right. steel industry to remove acidic impurities, in airpollution control to remove acidic oxides such as $\mathrm{SO}_{2},$ and in water treatment. Quicklime is made industrially by heating limestone $\left(\mathrm{CaCO}_{3}\right)$ above $2000^{\circ} \mathrm{C}:$ $$\begin{aligned}\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) & \\\Delta H^{\circ}=& 177.8 \mathrm{kJ} / \mathrm{mol}\end{aligned}$$
Slaked lime is produced by treating quicklime with water: $$\begin{aligned}
\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s) & \\\Delta H^{\circ}=&-65.2 \mathrm{kJ} / \mathrm{mol}\end{aligned}$$
The exothermic reaction of quicklime with water and the rather small specific heats of both quicklime $\left(0.946 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\right)$ and slaked lime $\left(1.20 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\right)$ make it
hazardous to store and transport lime in vessels made of wood. Wooden sailing ships carrying lime would occasionally catch fire when water leaked into the hold. (a) If a $500 -g $ sample of water reacts with an equimolar amount of $\mathrm{CaO}$ (both at an initial temperature of $25^{\circ} \mathrm{C}$ ), what is the final temperature of the product, $\mathrm{Ca}(\mathrm{OH})_{2} ?$ Assume that the product absorbs all of the heat released in the reaction. (b) Given that the standard enthalpies of formation of $\mathrm{CaO}$ and $\mathrm{H}_{2} \mathrm{O}$ are $-635.6 \mathrm{kJ} / \mathrm{mol}$ and $-285.8 \mathrm{kJ} / \mathrm{mol},$ respectively, calculate the standard enthalpy of formation of $\mathrm{Ca}(\mathrm{OH})_{2}.$

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Video Transcript

Okay, Let us prepare for a very, very long and challenging problem. So for this problem, we're dealing with line, that's an L line. In line is a term that includes calcium oxide. CEO, also called quick Line, and it includes calcium hydroxide, also known as slate line. Okay, masons use this. It's used in the steel industry also to remove impurities. It's used to improve our remove acidic oxides from air, and it's used in water treatment. Okay, so I've got some more information down here. The specific heat of quicklime is zero 0.946 J over G C degrees and the specific heat of the quake lie or the slate line is 1.20 J over juicy degrees. Okay, what else do we have here? I've got two reactions. The first reaction is how to make quick line and we make quicklime. We heat limestone. So to make quick line, we'll take limestone, which is C A C l three and will heat it super high. He to greater than 2000 degrees C and that will give us calcium oxide. That's my quick line and CO two and my delta age for this reaction is positive. 1 77 0.8. Kill a Jules per mole. Okay? And then the slate line is made by treating the quicklime with water, and that will produce my calcium hydroxide. And my dealt age for this reaction is negative. 65 0.2. Kill a Jules per mall. Okay, so we'll notice that the second reaction, the quicklime with water. This reaction is excellent. Thermic. And it's got a pretty low specific heat. Pretty low specific. He was right up here. We'll take a look at that specific heat. And that means that, um if you had a wooden sailing ship, they could catch fire if water leaked into the hold. Okay, So for this problem, I'm gonna switch colors. Sort of this one. Sort of. If 500 grams of water reacted with an equal Moeller same number of moles of calcium oxide. Find the final temperature. If the initial tamp is 25 degrees Celsius, I think that's everything we need to know. Let's begin. Okay, there's a second part for this Probable, but we'll talk about that later. So for this problem, first we're going to find moles of H two all and then what do we know? We know that moles of H 20 said it was equal Moeller with c a O and it will be equal Moeller with C a o. H two and let's go back for a moment because you'll notice I've got 11111 So one more one more. We're equal Bowler with that. Okay, so next I'm gonna leave a little room here to find that than are second order of business will be to find the heat generated by however many moles X moles from Celtic one. I can't read my own writing that one's pretty easy to do. And then for three, we're going to use Q equals M c Delta t to find Delta T. That's a very simple calculation. And then after that, will from Delta T we'll find TF. Okay, let's begin. This first calculation is ultra simple. We were given 500 grams of water and simply divide that by the molar mass of water 18.2 grams per mole. We're going to carry some extra sig figs here because Sig figs were sort of poorly given in this problem. 27.75 moles of age to out and 27.75 moles of age duo that equals 27.75 bulls of CEO. And that will equal 27.75 bulls of CEO H Okay, quit. That's part one. Done. Next question says, find the heat generated from from the number of moles and killed one. What? We're looking for the C a o h. So we're gonna take Let me switch colors 27.75 goals of calcium hydroxide times. We're going to use this number right here. Negative 65.2 killing joules per mole to find negative 1.809 times 10 to the third kilo jewels. Okay, next, we're going to use Q equals M c Delta T to find our delta t que We were just given. But now look, this isn't killer jewels, so I need to add three zeros. Let me rearrange my equation. Delta T equals Q over em times. See? Q is 1.809 times 10 to the sixth jewels. Make sure you understand where I got jewels there. Times are mass. I should have done this earlier I'm gonna have to erase this part and do it on the next page. Okay, so down over here and orange, I'll find the, um, mass of CIA. Oh, Wage too. So I have 27.75 moles of C a O age too. And I'm going to divide that by the molar mass, which is 74.10 actually. Gonna multiply that 74.10 grams per more. So I have grams of I haven't done that yet. Hang on. I put it all in one equation in mind. Whoopsy I just got 74 hang on. 27 points. 75 times 74.1. Enter is 2056.3 grams. So I've got 2056.3 grams and my C was 1.2 1.20 j over G C. Degrees. Okay. Good sakes. So we got for an answer of this 733 degrees C. That's my change in temperature. That's my delta t. Now, if my Delta T equals 7 33 that means my increase. This is my temp increase. So I started a 25 degrees C and I went up by 7 33 degrees C. My final temperature is 700 58 degrees c. Very good. That is the first part. Now the next part we are asked, Let me see where my problem is. Now be, assume the product and given the standard anthill P of C and O. H. Let me write down this equation again. C a o plus H +20 You'll see a O. H to and my delta age for this, for this reaction was negative. 65.2 killer jewels promote. My unknown right now is What is this in killer jewels? Promote? What's my heat of formation? My Delta h for this And we are given some information to help us out on that were given that the Delta the heat of formation for Kelsey Amok site is negative. Negative 6 35 0.6. Water is negative to 85 point eight and again, this is X. Okay, so we know that to find our Delta h its products, what's here's my products minus reactive. So I've got my delta H is 65.2 killed, Jules. Per mole equals X minus And now all my coefficients, Air one. So I've got a negative 6 35 0.6 plus my negative to 85.8. And if you're careful here up, I'll bracket this one to make it a little easier to see if you're careful and keep your signs where they're supposed to be. I got negative. Nine 86 0.6 Killer jewels promote. And that's the Delta H A fusion for calcium hydroxide. You made it to the end.

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