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Want to know what is the ph of a point three molar hypochlorous acid solution. Solution. Okay the ka for hypochlorous acid is three point five times ten to the eight all right so for any problem.

Like this. Where you are given a weak acid and you want to know about the ph given its ka. We can always write the equilibrium equation for the weak acid right so if you take that weak acid and you put it in water.

Okay. Hcl o. Plus.

H2o and then thats an equilibrium. With the proton transfers to the water. And you get h2so4 is hypochlorite.

Or rather hypochlorite ions. All right and we have the the given ka. Okay so were starting out in order to find the ph.

Thats the negative log of the hydronium ion concentration. We need to find the equilibrium concentrations and we know that the the equilibrium. Constant is this so.

What we can do is an ice table. Okay ice being the acronym for the initial. Change an equilibrium.

Condition so were starting out with 03. Molar. That was given to us in the problem.

We dont care about the water. Were not going to include that it doesnt show up in our ka. So were not concerned about the liquid water.

We dont have any ions to begin with okay our initial conditions are just the point three molar acid all right so now the change as we move from here to equilibrium. Theres a gonna be a small shift toward the right we obviously cant shift toward the left. Because we dont have anything here to remove.

So there has to be a loss of reactants and a gain of the products. Okay so and and all the coefficients are 1. So those are just minus.

X and plus x ok so at. Equilibrium we all have 03. 0.

Molar minus x. For our acid concentration and then x and x. For the hydronium ion.

And the hypo chloride ion ok so now were going to put this in our expression. For the ka and if we write that expression out its the product of the product concentrations divided by the product of the reactant concentrations. Okay.

So here. Were gonna have h3o plus times. Cl.

O. Divided by and again. We dont put.

The water. So.

Itll just be the hcl. Oh right now i havent explicitly shown it but these three are all in aqueous solution and the water is liquid. Okay so here we have our equation we can put in the equilibrium concentrations from here.

And what well end up. With is x squared on top from the two concentrations. Here each one being.

X divided by the hcl of. Concentration which is 03. X.

Okay. So thats equal to 3 point. 5 times.

10. To the minus 8. Okay.

So we we could use the quadratic equation with this if we reformatted this in that form. But i think its simpler. We can just assume that because this value is very small.

Were going to have a very small number for x okay. And since that would be very small in comparison to this point three. We can assume that this difference okay.

If we remove just a tiny little bit from here. Its not going to make any significant difference. Okay so we can just ignore that all right and then now this becomes.

We can reduce this down to x equals itll be three. Point five times ten to the minus eight. Times 03 so times.

03. 02. What we end up here.

With is we have three point five times ten to the minus eight times zero point 3 take the square root of that and we have x equals. 00 02 okay thats giving more significant figures than i need but thats fine all right now. We should always verify our our assumption.

Oh point zero zero zero. One you can see thats pretty much less. If we subtract that from point three zero and well end up with point two nine nine nine nine.

So its not going to make a significant. Difference there at two significant. Figures its still gonna be 03 0.

K. So this is our concentration of the hydronium ions as well as the hypo chloride ions. So if we want the ph from this well just take the negative log of this value and im just going to write that as 10.

2. Times. 10 to the minus fourth.

And what we get here is itll be about three point nine nine okay so that is the ph and that makes sense very slightly more than one times. Ten to the minus fourth. So that should be around four okay.

So thats the ph of a point three molar solution of hypochlorous acid. .

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