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A gas company in Massachusetts charges $\$ 1.30$ for$15 \mathrm{ft}^{3}$ of natural gas $\left(\mathrm{CH}_{4}\right)$ measured at $20^{\circ} \mathrm{C}$ and 1.0 atm. Calculate the cost of heating $200 \mathrm{mL}$ of water (enough to make a cup of coffee or tea) from $20^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C} .$ Assume that only 50 percent of the heat generated by the combustion is used to heat the water; the rest of the heat is lost to the surroundings.

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$x=\$ 0.011$

Chemistry 101

Chapter 6

Thermochemistry

University of Maryland - University College

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.

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Okay, We are going to do some calculations regarding heating up a cup of coffee and what it costs. Here's the information we're given. I'm This is sort of superfluous, but there's a gas company in Massachusetts and in charges $1 and 30 cents per cubic foot for methane. And this methane will be at 20 degrees Celsius and one atmosphere pressure. Okay, we are going to calculate how many dollars to heat up 200 milliliters of coffee, and it's gonna be the water to make the copy. Coffee. Now, what we need to know is up, and we're gonna heat this from 20 degrees Celsius to 100 degrees Celsius. So our delta T is going to be 80 degrees Celsius. And we're not wearing too much said about Sig figs on this one. Um, and Onley 50% of the heat from combusting from combustion from the CH four. Will, I'm going to say make it to heating the water. We're gonna lose that. We're gonna you lose 50%. So we're losing 50%. Okay, Our plan. Let's make a plan Number one. We're going to use Q equals. Gotta wait for that to disappear M c Delta t and that will give us the queue for the 200 mils of water. How much he we need Then we're going to double that number one answer, because we are Because we lose 50% of the heat. So we're gonna do that for number two. Number three, we're going to find the Delta Age for the combustion of methane. And four, we're going, Teoh, use the killer jewels per mole that we found from number three and the killer jewels from number to to find moles of ch four. That's four for number five. We're used. PV equals nrt to find v six. I think we're converting. Yeah, we're going to convert dollars per cubic foot to dollars per leader and seven find the dollars for the couple water. Okay, so that's the plan. Let us begin. Okay. So number one we said we were going to use Q equals M times, C times, delta T. And this is gonna be the queue for water. So I should have written up there. Now I m the mass of water is the same as the volume of water because we know the density of water is one. So we've got 200 grams of water. Water specific heat is 4.184 J over GC degrees, and we calculated Delta T is being 80 degrees c. Beautiful. So when we do our math on this one, we get our q of our water is equal to 6.7 times 10 to the fourth jewels. And in case we're interested, that will be 6.7 times. Tend to the first killer jewels. So now we can use that whatever way we'd like. Okay, now, number two. He said we were going to double that. So we're gonna take 6.7 times, tend to the first killer. Jules, we're gonna double that cause we're losing half, and we're going to get 1.3 times 10 to the second killer jewels. That's the number we're going to use again later. And then after that, we're using standard M Phil Pease. I'm gonna switch colors here, and I'm I forgot to do something, so I'm gonna writer chemical equation C H four plus o two yields C 02 plus h +20 and I've got a quick go. Look up the heat of feud, um, formation for methane. My problem. I forgot to look that one up. It is 74.8 killer jewels per mole, and I happen to just know Waters is to negative to 85.8 killer jewels per mole. And this one's negative 3 83.5 killer jobs per mall. Remember that? Its products minus react, it's products first, and we have to have a balanced chemical equation. Imagine I forgot to balance that. There we go. So we're going to have our delta h for this reaction is negative. 3 83.5 And that's just time One times one. So I'm gonna leave that off these air all killing joules per mole. Plus two times this is 16 1 carry the one 5 71.6 That's plus a negative. And then from that, we're going to subtract one times 74.8. And after I'm done with my math on this, I believe if I've got these numbers written down correctly, I'm 8 90 point three might be 90.2, but you'll get the general idea, okay? And that's how maney killer jewels per mole. That's how many killer jewels per mole for this reaction. Okay, so now let's go to our next. But I think I got room here for number four. We're going to find the malls. And moles are equal to kill a jewels from I'm gonna put a number two divided by the killer jewels per mall from number three. So answer for number two, divided by answer for number three. Number two is 1.3 times 10 to the minus. Or attended a to Kila jewels divided by negative 890.3 killed Jules per mole. I don't really care what the sign is because I'm just after moles here. Um, so this will be 0.0, that very nice zero 0.15 moles, and we'll be in that number later as well. Now, if you'll recall for number five, we're going to use PV equals NRT to find V. So v will equal n r t overpay and And we just calculated a 0.15 moles. Um, we're using atmospheres, 1.0 atmospheres. So we've got, um 0.8 to 1. L A t m overcame all. And my temperature was 20 degrees. So it'll be 2 93 k. OK, excellent. Do the math on this one and we'll get 3.6 leaders almost there. Easy stuff left. Next, let's convert our dollar 30 per cubic foot into leaders. So first let's go to I will have to go two inches because I don't know how to do that. There's foot and inches. Now We need to cube this whole thing. Don't forget to quote Cube 12 as well. You've got a cute cube, the 12 and then our next one will be one inch is 2.54 centimeters. Again, we're cubing the whole thing. So don't forget to Q both of those. And then let's turn that Centimeters Cube into leaders. There's 1000 centimeters cubed in one leader and we're done. We're going to get well, let's see here. I better put this in scientific notation cause it's pretty little 3.1 times 10 to the minus, third dollars per one leader of ch four. Okay, now from this problem are last step. We have 3.6 leaders of ch four to heat our water and it costs this much money to heat it up her leader door math, and we get, um, 0.11 dollars, which is about less just over a penny. 1.1 cent. So there's the answer. Good work.

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