 ### Can you use an approach similar to Hess's law to …

00:52 Manhattan College

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Problem 60

Under constant-volume conditions, the heat of combustion of benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}$ ) is 26.38 $\mathrm{kJ} / \mathrm{g} .$ A 2.760 -g sample of \right.
benzoic acid is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.60 to $29.93^{\circ} \mathrm{C}$ (a) What is the total heat capacity of the calorimeter? $\mathrm{b}$ ) $\mathrm{A} 1.440$ -g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 22.14 to $27.09^{\circ} \mathrm{C} .$ What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

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## Video Transcript

All right, guys. We're getting problem number sixty in chapter five. Chemistry Central science. So, under constant volume conditions, you combustion of Ben's OIC acid, which is gonna be our C seven h six. Oh two is twenty six point three killed. Jules, program A two point seven six grant from sample of benzo gases burned in a bomb kill a reminder temperature of the earth of the camera. Motor increases from twenty one point six to twenty nine point nine three degrees Celsius was the total he capacity of the calorie meter. Now let me change this. I'm gonna Q over m go. Thank the Acura Ram is fine. So? So we're going to be using the formula. Q is equal to see Delta t so we have keep. So where you have Q Here we go, eh? So we're going to multiply this by our mass us, which is two point seven years, two point seven six zero. That gives her heat. So cue is equal to twenty six three eight. I was two point seven six zero. Equal toe, seventy two point eight killed. Jules. So we're going to rearrange. That's our cue. We're going to rearrange this that there's going to be Q over Delta T is equal to C. So seventy two point eight eight divided by a point three during which is equal to eight point seven for killer Jules per per degree Celsius. Which is it equal to our see value now for Part B, we have a at one point four four zero gram sample. Hell of a new organic substance is conducting the same calorie meter. The temperature of the calorie Mary increases from from twenty two point one four two twenty seven point zero nine degrees Celsius. It was the heat of combustion program of the new substance. So we're going to put as so cue over m is going to equal. See Delta t em took you over em is equal to to our killer, though he capacity calorie meter point eight seven four Kill Jules Perm as kill a Jules print degree Celsius and our temperature. That's going to be four point nine five degree Celsius, and we're going to divide that by one point four for zero grams. Yeah, that means Q over M is going to be equal to this equation. Eight point seven four times four point nine five, divided by one point for for it's a Q over M. In this case, that's going, but that's going to be thirty point zero four. Kill a Jules program. So now, for part. See, they wanted us to know. Suppose that in changing samples a portion of the warming killer and was lost in what way, if any, would this change that he capacity of the calorie matar? So if you have so and you sorry, the water from the calorie manners loss, so there's less water to heat. So you. So if there's less water to heat, then it's gonna be easier to raise your temperature. So so is your Producing the same amount of energy from this reaction is going to cause a larger increase in your calorie meter temperature. So we're going to look. So remember this formula Q is equal to see Delta t. So, if you so if Q is constant and let's take uh, if you's constant and tempt, lt is increasing. Delta Psi has to decrease in order to keep this comp constante que so that means that the water is lost and see is going to he's going to decrease as delta T increases. Yes, and we all understand your produced a mount of heat, so you're as for less water. So that's going to cause a higher increasing, increasing the temperature. So you're going to have have a smaller he capacity because it's sickening. It's getting is it's easier to reach that same temperature.