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The enthalpy of combustion of benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)$ is commonly used as the standard for calibrating constant-volume bomb calorimeters; its value has been accurately determined to be $-3226.7 \mathrm{kJ} / \mathrm{mol} .$ When $1.9862 \mathrm{g}$ of benzoic acid are burned in a calorimeter, the temperature rises from $21.84^{\circ} \mathrm{C}$ to $25.67^{\circ} \mathrm{C} .$ What is the heat capacity of the bomb? (Assume that the quantity of water surrounding the bomb is exactly $2000 \mathrm{g}$.)

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$5.334 \mathrm{kJ} /^{\circ} \mathrm{C}$

Chemistry 101

Chapter 6

Thermochemistry

Drexel University

Brown University

University of Toronto

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.

02:29

The enthalpy of combustion…

05:34

02:37

01:56

01:26

02:22

Suppose you burn $1.500 \m…

01:21

The standard enthalpy of c…

06:23

High-purity benzoic acid $…

01:09

High-purity benzoic acid (…

07:17

Under constant-volume cond…

05:11

Suppose you burned $1.500 …

The combustion of 0.1584 g…

03:47

So for this problem, we're supposed to find heat capacity of a bomb kilometer. Given that some amount of Benzo Cassidy's combusted and some he is released. So this problem, of course, relates to the first law of thermodynamics, which says the heat in the system is always conserved and so we can express that through an equation. We know that whenever the benzo gas it is combusted. And since he was released, that same amount of heat is going to be absorbed by both the surrounding water in the Calumet ER, plus the Calera bitter itself. So we can write. That was directly. Is that the Q released by the Benzo Kassid going to equal heat, released or absorbed by the Calumet ER, plus the water. But algebraic lee. We know that they're going to be the exact opposite of what a negative sign, because one case it's being absorbed in the other case, it's being released, and so somehow we want to relate this expression to the heat capacity of the Calumet er. We know that the heat absorbed by the caliber motor can be expressed as the heat capacity of the calendar, with all right at sea times change in temperature of the kilometer and then we could just right huge 20 the negative que benzo gases on the left side. So when you want to isolate, see, you can write this expression as negative que benzo Gafford minus the queue mutual divided by the change in temperature that will give us the heat capacity of cholera. Better now, all we need to do is we need to find the cue of the Benzo casted, or how much heat is released by the middle passage. And then finally, we need to find how much heat is absorbed by the water. So what's first you calculation for the heat released by Benzo Kassid. Well, we know that for every mole of Ben's OIC acid that is combusted that there is 3226.7 killer jewels of heat released. So dealt eight of that reaction is I get 3000 226.7 killer jewels for one mole of Enzo gases. But we want to find that Ingram's so then we need to just divide by the more mass have been against ID, and when you do those calculations and you find the more massive Enzo Gas. Did you know that it is 122 point 12 grams? The last thing Meteo is just multiply by how many grams of benzo gases reacted which we know the problem to be one point nine 862 grams And so this will give us the queue of benzo gas it When you plug it all into the calculator, you get that? The cue of the benzo gutted is negative. 52 0.48 killer jewels. That's first part. Now we have to do same thing for water for water. The way that we're gonna do this is a different we're gonna use the equation that the heat absorbed is equal to the mass Tennessee. He come out specifically Kamathi times a change in temperature. So we know that from the problem the masses 2000 grams. We know that, as always, the specific heat capacity of water and 4.184 tools degree, Celsius grams and we know that the final and initial temperatures of the entire system so you can just use that for the change in temperature of the water final temperature is 25.67 From the initial temperature, I was 21.84 That expression will give us a que water, and we get that the Q over the water is equal to 32 point. Oh, for tools, however, we want to just keeping its consistent. So the first part of its collegial. So we'll just divide by 1000 here you'll just get 32 for That's the cue of the H 20 And so you can just use the first expression that we got, which is that the heat past calendar is negative. Q. Of benzo kassid minus the native que of water divided by the change in temperature. So we just saw for the Cube Negative, Cuba's or gas and the Native Cubans. Oh, gas. It is positive 52.4, and then the we have to subtract the cue of the each to O, which we just calculated with 32.49 kill jewels, and the last thing that we have is we need to find the change in temperature. But you know that the system of the temperature final temperature was 25.67 degrees sells. Yes, the initial temperature was 2124. You plug that all into your calculator, you'll get that. The heat capacity of the Calumet ER on the bomb five point 33 killing jewels, degree Celsius. And so, in this case, unlike the specific heat capacity, no mass is involved. It's just killed Jules Degree Centigrade, and 5.33 is the final answer.

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