5 answers

Calculate the molar concentration and the concentration expressed in mg / L of oxygen in water at 25ºC for a

Question:

Calculate the molar concentration and the concentration expressed in mg / L of oxygen in water at 25ºC for a partial pressure of 0.22 atm (Kh = 1.3*10^-3 mol/L/atm)


Answers

Fish generally need an $\mathrm{O}_{2}$ concentration in water of at least 4 $\mathrm{mg} / \mathrm{L}$ for survival. What partial pressure of oxygen above the water in atmospheres at $0^{\circ} \mathrm{C}$ is needed to obtain this concentration? The solubility of $\mathrm{O}_{2}$ in water at $0^{\circ} \mathrm{C}$ and 1 atm partial pressure is $2.21 \times 10^{-3} \mathrm{mol} / \mathrm{L} .$

.

So here we have another Henry's little problem where we have a gas in this case oxygen being dissolved as a part of a solution. And so the way Henry's Law is written is soy ability of that gas is based on all the Henrys long, constant K times the pressure And so we're going to do first is since we're working with oxygen is we're going to determine the K specific to that substance that we can go ahead and use that and different problems. And so the way we want to do that is by the last bit of information that they've given us about the song ability of oxygen at that desired 37 degrees Celsius. So they tell us that the soy ability at that temperature is 1.93 times 10 to the negative third moles per liter, and they tell us it In this case, the pressure is one atmosphere. Okay, But now what you want to do is a kind of looked ahead in our problem, and it's asked me.

Poor has given May for the second part of the problem a pressure in millimeters of mercury and so what I need to realize is that here, when I'm solving for my K, it'll be an atmosphere. So later on, in the second part of the problem, I'll need to convert that millimeters of Mercury toe atmospheres. So just come a heads up on that poor. So what we'll do when we're solving for que is will divide both sides by one. And yep, you guessed it him.

The K or the constant is just going to be equal to the soy ability at that particular temperature. And the units are moles by the violators times at speakers. And so now we're going to be able to use this value in the remainder of our calculation. So we've been asked you is kind of find the Souljah bility or the concentration when the pressure is 68 millimeters of mercury. So what we know now as we know RK from our previous work is 1.93 times 10 to the negative third.

But again, because this unit is in atmospheres, I need to make sure that my pressure isn't atmospheres as well. So I'm going to come to the side and do a quick conversion from millimeters of mercury toe atmospheres. The conversion factor tells me that there are 760 millimeters of mercury for every one atmosphere. So to convert, I'll be taking 68 dividing by 760. That tells me that I have point 0895 atmospheres, right? And I'll go ahead on around that 2.98 just first big sake if we give all right.

So let's go ahead and multiple. I am. See what we get. 1.93 times to the negative. Third time's points here or not, that gets up.

Say, Souljah Bility, Uh, I'm going to put this in scientific notation 1.74 times tend to the negative fourth, and our units at this point are moles per liter or polarity. And so the last cash the problem is we're not quite finished yet because instead of expressing the concentration in moles per leader, they would like us to express it in MiGs per later or milligrams per liter. So we're gonna do just a little bit of work here. So you've got 1.74 times 10 to the negative fourth moles per liter. So first, let's go ahead and convert from moles to grams than our last step will be to go from grams to milligrams.

This is oxygen, which normally has a molar mass of 16 grams from all. But since it's die atomic, go to then the total mass will be 32 grams per mole. Then I'll be able to convert from grams to milligram spun doing that. There are 1000 milligrams per one gram. So no, my units will be the desired milligrams per liter.

So when I do that 1.74 times 10 to the negative. Fourth times 32 times 1000 What That gets me ISS five point 57 milligrams per litre for my concentration of oxygen or Saudi ability at.

For this problem. We're told that the partial pressure of oxygen in the air sea level is 0.21 a. T. M. And were asked to use the table from the textbook.

Together with Henry's law calculate, calculate the Moler concentration of oxygen in the surface. Water off the mountain like saturated with air at 20 to be Celsius and an atmosphere pressure of 650 tour. First thing we want to do is we want to actually convert this tour into a T M. So we're going to do 6 50 divided by 7 60 to convert from tour to E. T.

M. And we get that that 0.855 a t m. Then when we look at the table, we find that the saturation of oxygen is 1.38 times 10 to the negative third. So using our equation of S 02 it's been equal are a constant plus times the pressure of +02 We can go ahead and start substituting some of this stuff in, So we have 1.38 times 10 to the negative. Third equals our constant times 0.21 a t m.

Which gives us a K of 6.57 times 10 to the negative third moles per leader. A t m. From that, we can now plug this value back into our equation for that pressure to find out what the soluble ity will be under those conditions. And so we end up with arse. Eligibility of 02 is going to equal 6.57 times 10 to the negative Third time's our pressure, which is 0.855 a.

T. M. And we have a soluble ity of 5.6 ju times 10 to the negative third..

It has been from 58 of Chapter 11. So casually saw the ability of oh, tune water had a partial pressure of 02 is 120 tour so pressure is 1 20 Tour Remember? One a. T m is equal to 7 60 tour so we can rewrite. We can rewrite this as 1 25 basis 7 60 So this is zero point you're a 0.16 a. T.

M. Now the Henry's Law constant is 1.3 times sent to negative third multiplayer leader peridot a T M. So Henry's laws that C is equal to K p were seized. Gas concentration. Asian K is Henry's law a constant and P s pressure So 1.3 times 10 to the negative.

Three malls per leader, a t m and then zero point 168 a. M. Then that means see is going to be equal to 1.3 times and nick 3rd 0.16 That's gonna be two points zero eight times tend to be negative for it. Moeller. It's gonna be moved for leader, which just as the unit for Moeller.

Let's calculate the, uh, gas concentration, which is the soluble ity of 02 Sees equal there k times p on. So are, um, Henry's law constant here, um, is way. Call the 1.3 times 10 to the negative. Three moles. Ah, uh, leader atmosphere.

So there's a constant The pressure were given as, uh, 120 tour. Well, let's convert that to atmosphere which there is 760 tour in one atmosphere And here we get tor canceling atmosphere is canceling. We're left with units of most for leader which will give us a gas concentration of the soy ability for oxygen is 2.1 time to tend to the negative four moles per leader..

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