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When backpacking in the wilderness, hikers often boil water to sterilize it for drinking. Suppose that you are planning a backpacking trip and will need to boil 35 L of water for your group. What volume of fuel should you bring? Assume that the fuel has an average formula of C7H16; 15% of the heat generated from combustion goes to heat the water (the rest is lost to the surroundings); the density of the fuel is 0.78 g>mL; the initial temperature of the water is 25.0 C; and the standard enthalpy of formation of C7H16 is -224.4 kJ>mol.

2.1L

Chemistry 102

Chemistry 101

Chapter 9

Thermochemistry

Thermodynamics

Chemical reactions and Stoichiometry

University of Central Florida

Rice University

University of Kentucky

Lectures

00:42

In thermodynamics, the zer…

01:47

A spontaneous process is o…

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When backpacking in the wi…

00:54

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04:30

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01:08

(II) In a hot day's r…

00:23

Solve each application.

So in this problem, we want to boil thirty five litres of water and we need to know how much fuel Specifically C seven h sixteen. How much of that fuel we will need. And so the first thing we do is calculate the heat required. So that's just em. See, Delta T. And so our M is going to be our thirty five leaders times one thousand grams per leader. In order to get that into grams, then our ah specific heat of water four point one eight four Jules per gram degrees Celsius and then our delta T, which is a hundred degrees Celcius minus twenty five degrees Celsius. Since the boiling point of water is one hundred and we start at twenty five and then we'LL divide this whole thing by zero point one five. Since we're since our fuel is producing fifteen percent efficiency than ah, we need to divide this by point one five in order to get the total Q. And so when we do this, our cue is equal to seven, three two two zero zero zero zero Jewels or seven three two, two zero Killer. Jules. So this is our required heat now, the next thing we need to do is determine the amount of heat that is generated from the reaction of our fuel. And so to do this, we write down the equations, the chemical equations that we know of. So seven see solid plus eight h two gas form C seven h sixteen liquid. And we're given in the problem that the Delta H for this is negative two to four point four killer Jules promote. Then are we can also take see solid plus O two gas to form Seo to gas and that has adult H of formation of negative three nine, three point five Killer Jules Permal. And then finally we can take a TSH to gas plus one half o to gas and form a tch tuo gas which has adult age of negative two for one point eight to kill a Jules Permal. And so are the three of these air Simply dealt h o formation of these were just devising them in this in this in this way so we can compare them and find a total equation which I'll do now and so we take the first equation and we flip it we have C seven h sixteen, liquid forming seven. See solid plus eight h two gas. And so we flipped the sign of our Delta H two positive two to four point four. Killa Jules. Now we take our second equation and multiply it by seven in order to get the seven C solids that we have in our previous equation. So seven see solid Plus seven oh two gas formed seven co two gas and that has a delta h of negative. Two seven five four point five Killer. Jules, We just multiplied by seven and then we take our third equation and multiplied by eight in order to cancel out the eight h two gas That's over here. So we have eight h two gas plus for oh to gas form's eight h two o gas and that has adult age of negative. One nine three four point five six. Kill it, Jules. So now we can sum all these equations together, and so we end up with C seven h sixteen liquid plus eleven o to gas form seven co two gas plus eight h two o gas and then we some are adults ages to get our new Delta H two B negative. Four four six. Four point six six. Kill it, Jules. And so now that we have that, we can take the heat required to heat up our water. Seven, three, two, two, zero Killer, Jules. And divide that by the heat per mall that we just found. Four, four, six, four point six one Too many sixes. Four, four, six, four point six six Killa Jules Permal And that'LL give us moulds of gas And so we can take the Moler Mass of C seven eight sixteen, one hundred point two zero one nine grams per mole. And then divide that by the density zero point seven eight grams per mil leader. And the density is given in the problem. And so that gives us that we will need twenty one o six point eight zero millilitres or two point one leaders of fuel. And that is our final answer.

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