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Henry's law constant for $\mathrm{CO}_{2}$ at $38^{\circ} \mathrm{C}$ is $2.28 \times 10^{-3}$ $\mathrm{mol} / \mathrm{L} \cdot$ atm. Calculate the $\mathrm{pH}$ of a solution of $\mathrm{CO}_{2}$ at $38^{\circ} \mathrm{C}$ in equilibrium with the gas at a partial pressure of 3.20 atm.

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$$4 \cdot 26$$

Chemistry 102

Chapter 15

Acids and Bases

Liquids

Carleton College

Drexel University

Brown 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.

04:57

Henry's law constant…

01:10

The solubility of $\mathrm…

01:24

The Henry's law const…

02:57

What is the $\mathrm{pH}$ …

okay for this problem. We're going to look at Henry's law and use that to help us find pH. And here's what we are given for this problem. Okay, We have CO two carbon dioxide gas, and it is at 38 degrees Celsius. Um, Henry's lock constant. And these laws, constant is 2.28 times 10 to the minus three. That's a three. Let's we make that nicer. So we don't get mixed up minus three, and that will be bulls per L A T M. And we're gonna find we're looking for pH. This is our unknown. And what else are we given here? The gas as a partial pressure. The partial pressure is 3.20 atmospheres. Okay, we're looking for pH. So we have to eventually get Teoh Um, the concentration of H plus. We'll have to write an equilibrium constant. So first of all, let's write our chemical equation. And shall we make that this color? Sure. So we've got co two. That'll be a gas plus water, and that is going to be an equilibrium with the hydrogen ion que and bicarbonate. Okay, there's my chemical equation. Now that's our chemical equations all balanced. Um, I'm also gonna Ray Takeyh expression here. Maybe I'll write that a little later, but right now we're going to find Armel Arat e. We're gonna find Omar literally polarity of this by taking 2.28 times 10 to the minus three balls per leader Atmosphere. That's my Henry's law, Constant. And if I multiply this by my partial pressure, I will get my concentration of seven point 30 times 10 to the minus three Moller. Okay, so now let's just go to a purple here. This concentration is the concentration of my CO two. That's the concentration of CO two. And I can look up my k a. I'm gonna go to my next page 7.30 My co two concentration is seven point. What did I say? That was 30 times 10 to the minus three. And I've got Theo too. Plus h +20 I'm not gonna put my states on this one. So if we do a little ice here, I'm starting out with 7.30 times 10 to the minus three zero and zero plus x plus x. These will both be X this will go down by X. Okay, so those are my equilibrium concentrations and I can look up my K A and my K is given as 4.2 times 10 to the minus seven. That's a very low number, which means that we can consider this. Since this is a very, very low number, Weiqing, this is going to be for all practical purposes, 7.30 So just get to put that in there. And now let's write the K expression and substitute que a equals h plus hcl three minus and go to got those right there. So then let's go ahead and substitute our values in. Um, I'll do that right here. 4.2 times 10 to the minus seventh equals That will be X squared over 7.30 times, 10 to the minus three solving for X. We get 5.5 times 10 to the minus five. Now our last step and let's do as heads are red to find the pH. We're gonna take the negative log of that concentration that we just figured out here. So we're going to take the negative log of 5.5 times 10 to the minus five and our Ph will be 4.26 Remember to sig figs, two decimal plates. Places. There it is. Thanks for listening.

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