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A $0.0560-\mathrm{g}$ quantity of acetic acid is dissolved in enough water to make $50.0 \mathrm{mL}$ of solution. Calculate the concentrations of $\mathrm{H}^{+}, \mathrm{CH}_{3} \mathrm{COO}^{-},$ and $\mathrm{CH}_{3} \mathrm{COOH}$ at equilibrium. ($K_{\mathrm{a}}$ for acetic acid $=1.8 \times 10^{-5}$).

$$0.00058 \mathrm{mol} / \mathrm{dm}^{3}$$[CH3COOH] = 0.0181 M

Chemistry 102

Chapter 15

Acids and Bases

Liquids

University of Central Florida

Rice University

Lectures

03:07

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, a liquid is one of the four fundamental states of matter (the others being solid, gas and plasma). A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Water is, by far, the most common liquid on Earth. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena.

04:38

A liquid is a state of matter in which a substance changes its shape easily and takes the form of its container, and in which the substance retains a constant volume independent of pressure. As a result of this, a liquid does not maintain a definite shape, and its volume is variable. The characteristic properties of a liquid are surface tension, viscosity, and capillarity. The liquid state has a definite volume, but it also has a definite surface. The volume is uniform throughout the whole of the liquid. Solids have a fixed shape and a definite volume, but they do not have a definite surface. The volume of a solid does not vary, but the volume of a liquid may vary.

02:45

A 0.0560-g quantity of ace…

03:44

01:49

The dissociation of acetic…

05:12

A solution is made by addi…

05:36

04:42

Calculate the equilibrium …

01:02

What are the equilibrium c…

So we have acetic acid here, and if it goes, could reaches equilibrium in solution with water. It's going to give off protons and the contract it base in ions. Um, so we have an initial grams and Mel, leaders of water we have to know is the final. You want to know the final, our equilibrium, concentrations of that, that and that. So we got quite a lot of work to do. First of all, let's figure out the polarity, the initial polarity or concentration off acetic acid. We're gonna have to take convert grams two moles first, and then we were given milliliters of solution, which will have to convert to leaders. So the grams given to us where a 0.0 560 grams of acetic acid. So now we're gonna have to find the, um, muller mass of acetic acid. So if you have a periodic table, you would have toe look up. Um, the mass for carbon. There's two carbons. There's to oxygen's and for hydrogen. So you should find 24 32 for, so your total is going to be 60 grams. Um, so then we get rid of our grams that'll leave us with moles. And when we get a small number of moles. 0.0 93 three and I'm rounding into 36 figures. Significant figures. It goes on beyond that. Um, so that's our moles. Now we just gotta cover Mill Leader's a leader. So we had 50 Mel leaders. Just remember every leader as 1000 little leaders by dividing this by 1000 were we get rid of male leaders in her left with leaders, which will be 0.0 five leaders. Now we can get our concentration. So let's take our acetic acid. The concentration of acetic acid then, is 0.933 moles per 0.5 leaders. So you divide those together and your goods zero point 01 eight 66 moles per liter. Okay, so now we have an initial concentration that'll give us We can actually use that. Um, because what we're gonna do next is the we want the we're gonna use the acid ionization constant, and that's gonna be your proton concentration times. The an ion concentration divided by the remaining, um, acetic acid concentration. Now we know for acetic acid that the acid organization constant is one point eight times 10 to the negative five. Um, the ah acetic acid concentration. We can actually use the this number because it will lose such a insignificant amount, that is, should it be much, it won't be much smaller than that. So we'll just use that number. It's close enough, which will give us, um Rh plus, which we don't know. Then we can plug in and X, and we can plug in an X for the and I on the concentration, which we won't know, but we do know they'll both be the same. So they can eat to be X and ah, I'm going to go ahead and plug in the zero point 01866 down here, and we know that it'll equal 1.8 times attending the negative five. So, um, we can rewrite that is X squared. And actually, if you multiply, multiply this number by this number that will give us an X squared equals, um three point three five. And I got this. I put it in scientific notation cause it's very small number. So, um, now we're down to this. So now if we take the square roots of both sides, we will get a value for X, which is equal to five 0.80 times. 10 the negative four Moller. No, this will work for the, um, Proton concentration. On what Did I do it in green? Because this is part of our final answer. Um, is equal to the acid Tate ion concentration, which are both equal to that answer. We got five for NATO times 10 to the negative four moller. But we still had one more thing to solve. It was the concentration of the, uh, acetic acid. Once it reaches equilibrium, we knew the initial. Um So how do we find that we'll take your initial zero point 01 eight 66 and subtract the 5.8 times 10 to the negative four, and that will give you what's remaining, and it's ah, you get something like 0.0 1804 You should round that 23 significant figures are final answer than ah, put in scientific notation 1.81 three significant figures. Times 10 to the negative, too. So that's part of it. And then, um, this is the other part of your answer. Okay, So hydrogen ion concentration and and I and concentration are 5.8 times in the negative for Mueller. And then the remaining acid concentration is 1.81 times 10 of the negative, too. Okay, There you go.

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