Problem

The heat of vaporization of water at 373 K is 40.…

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Problem 126 Hard Difficulty

Find H, E, q, and w for the freezing of water at -10.0 C. The specific heat capacity of ice is 2.04 J/g # C and its heat of fusion (the quantity of heat associated with melting) is -332 J/g.

Answer

-310.5692

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Chemistry 102

Chemistry 101

Chemistry: Structure and Properties

Chapter 9

Thermochemistry

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Video Transcript

So this problem wants us to find Delta H Delta E Q and W for water freezing at negative ten point zero degrees Celsius. And so first we'LL write down What we do know. So we know that the heat capacity of ice is two point zero four Jules Program degree Celsius. We know that the Delta H of fusion, which is associating with melting at zero degrees Celsius, is negative three thirty two jewels program, and we know that the heat capacity of water is four point one eight four Jules per gram degrees Celsius. And so now we can use this information in order to find the delta H of fusion at negative ten degrees Celsius. And so how we do that is we take the Delta H of fusion at zero degrees Celsius, and that is equal to Delta H of liquid water from zero to negative ten point zero degrees Celsius, plus the delta H of fusion for water at negative ten point zero degrees Celsius, plus the delta H of ice from negative ten point zero degree Celsius, two zero degrees Celsius. And so we can rearrange this to solve for the Delta H of fusion at negative ten point zero degrees Celsius, which is what we want on so that will be equal to Delta H effusion at zero degrees Celsius, minus delta H of the liquid water from zero to negative ten point zero degree Celsius. Ah, minus the delta H of ice from negative ten two zero degrees Celsius. And so we can plug in all these values. And so the Delta Age of Fusion, at zero degrees Celsius, is negative. Three three two jewels program. The Delta H of liquid will be the heat capacity of liquid water. Four point one eight four Jules program degree Celsius times negative ten point zero degrees Celsius is that is our delta T minus the delta h of ice. So we'LL use our he capacity for ice to point zero four Jules program degrees Celsius and multiply that by ten point zero degrees Celsius Is that is our delta T. And so doing all this gives us adult H effusion of negative three ten point five six Jules program. So this is our Delta H, and we also know that this equals Q because for a constant pressure, which we are assuming Delta H equals. Q. So we have our Delta h and we have our cue. Okay, now we can go about finding r. W. And so first we confined Delta V. So for one gram of water, which is this going to be the easiest to calculate? Delta V equals one, divided by zero point nine one six seven centimetres cubed program minus one point zero centimeters Cube program. And that gives us a zero point zero nine one centimeters Cube program, or nine point one times ten to the negative Fifth Leaders programme. So now we confined our p delta V so pressure times the change in volume are pressures one point zero atmospheres and are changing volume. We just found to be nine point one times ten to the minus fifth Leaders programme. And now this is the change in volume that the water is undergoing while it moves from liquid with ice. And so that gives us nine point one times ten to the negative Fifth Leader atmospheres per gram which is equal to zero point zero zero nine two jewels program. So now that we have that r w is negative. P. Delta v. R work and so that's just going to be negative. Zero point zero zero nine two jewels program. So we have our W. We have our Q and we have our Delta H. So now to find our Delta E. That is just equal to Delta H minus P. Delta V. And so it's just our Q minus. R w. And so we take our cue three ten point five six minus R W zero point zero zero nine two and therefore our Delta is equal to negative three ten point five six nine two jewels program, and that is our final answer. Since there is no mass given, we have to determine all of these energies on a per gram basis, and so that is our final answer.

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