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At $28^{\circ} \mathrm{C}$ and 0.982 atm, gaseous compound HA has a density of $1.16 \mathrm{g} / \mathrm{L} .$ A quantity of $2.03 \mathrm{g}$ of this compound is dissolved in water and diluted to exactly 1 L. If the pH of the solution is 5.22 (due to the ionization of $\mathrm{HA}$ ) at $25^{\circ} \mathrm{C},$ calculate the $K_{\mathrm{a}}$ of the acid.

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Chemistry 102

Chapter 15

Acids and Bases

Liquids

University of Central Florida

Drexel 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.

03:48

A certain acid, HA, has a …

03:19

An aqueous solution of a $…

02:58

05:46

A $0.185 \mathrm{M}$ solut…

03:40

A 0.185 M solution of a we…

02:14

Acid Solutions.A 0.185…

02:51

A 0.115 M solution of a we…

04:51

Let's find K A and in this problem, we're going to be using PV equals NRT. First, we have quite a few givens. Let's get him written down. Our temperature is given as 28 degrees Celsius, which we will need later as 301 k We have a pressure given at 0.982 atmospheres. Um, the asset H A has a density of 1.1 grams per leader. We have a mass of 2.3 grams of h A is going to be dissolved in exactly one leader of solution and a resulting solution has a ph of 5.22 those air givens. So we're to find a k A. This is our unknown. Okay, let's make a plan of how we're going to do this. I'm not too bad here. It's really not too bad of a problem. It takes little time, but to find K A, we need to know polarities. So we're going to use PV equals NRT to find malls. And then once we have moles, we're going to use the density, which is exactly a leader, and end to find Moeller Mass and then we'll use are given mass and molar mass. And the fact that we have exactly one leader that should be a one leader to find polarity that will give us our mill arat e will use after we've got similarity will use ice and we confined values for the ice. You know, things that we're gonna put in for Ph. And once we have all that will be able to substitute into R K equation. Let's get started. Okay. First, to find malls, we're gonna use n equals P B over our teeth and let me get my paper. Here we have 0.9 0.982 atmospheres times exactly one leader I'm saying exactly, cause that won't affect our sig figs. And we're going to use for R 0.8 to 1. L A t m overcame all and 301. Kelvin. When we're done doing our math, we will have for moles. 0.397 moles of H A. Okay, now we're going to figure out our molar mass because we have exactly one leader. So, um, I know that I have 1.16 grams in one leader and I know I have zero point 0397 malls in one later. So I do my math here and I get a molar mass of 29.2 grams per mole. Now, let's use our knowledge that polarity equals moles per leader. And how am I gonna get malls? I know that I had was given 2.3 grams and we'll convert that to malls by using the molar mass. And we have exactly one leader. This will give it 0.695 polarity and that similarity of h A. This is the polarity of H A. Let's do a nice table and we've got a H plus and a So this is zero and zero and this was 0.695 This will increase by negative X plus X plus x leave a little bit more room here and you'll figure out why in a little bit this will be 0.695 minus x X and X. Okay, Now I'm gonna put these values my equilibrium values into my K expression. But I get a lot of excess there, so this isn't going to work too well for me. Do I have a low battery? Let me plugging quick. There we go. So I'm going to use my knowledge that the Ph was 5.22 So if I take 10 to the minus 5.22 I get an H plus concentration of 6.3 times 10 to the minus six Mohler and that value is the value for this X this X and this X. Now we're ready to put R K a equation together. K equals and in my numerator, actually, let me make this a little smaller here, get this on one page. Que is going to be hpe plus and a minus. And those values air the same. They're both acts divided by age A. So we know that we're gonna put an accent. We're gonna put this in for X, So I'm going to have 6.3 times 10 to the minus six squared, divided by 0.695 minus 6.3 times 10 to the minus six. Do the math on this, and your final answer will be 5.2 times 10 to the minus temp. Which means I probably could have ignored that. You can check that if you'd like

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