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Calculate the $mathrm{pH}$ of each solution given the following $left[mathrm{H}_{3} mathrm{O}^{+}ight]$ or $left[mathrm{OH}^{-}ight]$ values:a. $left[mathrm{H}_{3} ...

Question

Calculate the $mathrm{pH}$ of each solution given the following $left[mathrm{H}_{3} mathrm{O}^{+}ight]$ or $left[mathrm{OH}^{-}ight]$ values:a. $left[mathrm{H}_{3} mathrm{O}^{+}ight]=1 imes 10^{-8} mathrm{M}$b. $left[mathrm{H}_{3} mathrm{O}^{+}ight]=5 imes 10^{-6} mathrm{M}$c. $[mathrm{OH}]=4 imes 10^{-2} mathrm{M}$d. $[mathrm{OH}]=8 imes 10^{-3} mathrm{M}$e. $left[mathrm{H}_{3} mathrm{O}^{+}ight]=4.7 imes 10^{-2} mathrm{M}$f. $left[mathrm{OH}^{-}ight]=3.9 imes 10^{-6} mathrm{M}$

Calculate the $mathrm{pH}$ of each solution given the following $left[mathrm{H}_{3} mathrm{O}^{+} ight]$ or $left[mathrm{OH}^{-} ight]$ values: a. $left[mathrm{H}_{3} mathrm{O}^{+} ight]=1 imes 10^{-8} mathrm{M}$ b. $left[mathrm{H}_{3} mathrm{O}^{+} ight]=5 imes 10^{-6} mathrm{M}$ c. $[mathrm{OH}]=4 imes 10^{-2} mathrm{M}$ d. $[mathrm{OH}]=8 imes 10^{-3} mathrm{M}$ e. $left[mathrm{H}_{3} mathrm{O}^{+} ight]=4.7 imes 10^{-2} mathrm{M}$ f. $left[mathrm{OH}^{-} ight]=3.9 imes 10^{-6} mathrm{M}$



Answers

Autoionization of Water and pH
Calculate $\left[\mathrm{OH}^{-}\right]$ in each aqueous solution at $25^{\circ} \mathrm{C},$ and classify the solution as acidic or basic.
$$\begin{array}{l}{\text { a. }\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.2 \times 10^{-8} \mathrm{M}} \\ {\text { b. }\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=8.5 \times 10^{-5} \mathrm{M}} \\ {\text { c. }\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.5 \times 10^{-2} \mathrm{M}}\end{array}$$

So in this question were given a concentration of O. H minus. We are asked to find the concentration H 30 plus. And then, since we're asked to figure out if this is acidic or basic, we're really being asked them to find the pH. So the way this happens is to do this step. This first step, it's the second step. The first step. We're gonna use the fact that the 25 degrees Celsius, like it's told to us the concentration of O. H minus times a concentration H 20 plus equals tense. The negative 14th this is from the auto Organization of Water. This is really important fact to know. And so, since we have the consolation village minus the plug that in, we can find the concentration age, your plus the next step. If we want to find the pH. Just remember that the P H is equal to the negative log of the concentration of HBO. Plus, this is by definition of what pH is and so we can plug in right here and plug pump out of Ph is. So for the first part, we have a concentration of O. H. minus, which is equal to 1.1 times tense, a negative knife and so plugging that in above where we had right here that tends the negative 14. We'll divide that by our value of O H minus, which is 1.1 times 10 saying of ninth and we'll find the concentration of a studio. Plus is 9.9 times tense, a negative six. Now, if you want to find the pH, we'll take it. The negative log of this value right here and that is equal to 5.4 which is less than seven meeting. This is an acidic solution for the next one. Our concentration of O. H. Minus is equal to 2.9 times 10 to the negative second, so it's pretty big right there. And so we can expect this will be a basic solution. We can find the concentration of H 20 plus again by taking 10th the negative 14th dividing, uh, that by 2.9 times 10 scenarios second and you get 3.4 times 10 to the negative 13. I should know that these air Moeller, uh, should not be creators in its my apologies. And so if we want to find the pH, we'll take the negative log of this number right here. It will pump out a number. We should expect it to be pretty high up. Yeah, 12.46 That's much greater than seven. This is a basic solution. Last one. Here we have a concentration of O. H. Minus. That is 6.9 times 10 tonight of 12th. Again, we plug in using the fact that the product of this and that should be tense. Negative. 14 and we'll get that. The answer is 1.4 times 10. So native third and Mohler fridge. These cases the pH then is he goes to the negative log of, Ah, this value right here and the values 2.83 which is less than seven being This is an acidic solution. Remember, small values of pH. Our basic

After 15 problem. 12. Ask us to determine the pH of various solutions when we're given the concentration of hydrogen ions in that solution. So to do these will need to remember the formula that pH is equivalent to the negative log of your hydrogen ion concentration. So all we need to do here is plug in the given concentration into this formula. So let's sit with a for any working in a concentration of two times 10 to the negative five Moeller. So we'll plug it in negative log of 2.0 times 10 to the negative five Moeller and calculating that in your calculator you'll find that the pH there is 4.70 We'll do the same thing for fee. So will have negative log of the given concentration 4.7 times 10 to the negative seven Moeller and that is 6.33 Finally, for see, we have negative log of are given concentration of 3.8 times 10 to the negative. Three more, which is 2.42

So in this problem, we're given a bunch of hydroxide ion concentrations. And from there we have to calculate the hydrogen ion concentration, the pH and the P O. H. And so what we can do is basically go from hydroxide to H plus knowing the relationship where concentration of H plus times the concentration of O. H minus is 1.0 times 10 to the minus 14. So using that relationship, that means one times 10 to the minus 14 divided by the hydroxide ion concentration would give us the hydrogen ion concentration. So that gets us from this column in my table to the next column. Now I need to get th How did I get pH from hydroxide? I mean, from hydrogen ion concentrations, th is going to be equal to negative log of the concentration of H plus. I can take thes values that we just calculated. Take the negative log, and that gives us the pH. Now I need to get to the P. O. H. Is actually two ways I can get there. The first thing I can do is say pH plus P o. H always equals 14. So that's one way to do it. I could take 14 minus the pH. And that gives us our P O H. Eli's. Or you could say P. O. H is equal to negative log of the hydroxide ion concentrations, and that will give you the same answers.

In this problem were asked to calculate the pH corresponding to the given hydroxide. Ion concentrations were also asked to tell whether each solution is acidic, basic or neutral. We can solve this problem by first getting our p o. H from using this formula here. P. O. H is related to pH by this formula, where we see that their total must equal 14 so we can calculate or p o. H subtracted from 14 to find our Ph and then based on this scale, here, we can figure out the identity of our solution with her first hydroxide ion concentration. When we plug in and sell for a P. O. H refined that it is equal to seven. So when we subtract from 14 we find that our pH is also equal to seven. As a result, we can say that the solution is neutral. We can repeat this for part B, and when we plug in, we find that our P O. H is equal to 12 0.34 Subtracting from 14 r p H is equal to 1.66 which means we have an acidic solution. Moving on to part C or P O. H here is equal to 3.98 Subtracting from 14 r p h is equal to 10.2 This means that we have a basic solution and finally looking at Part D when we plug in or P. O. H is equal 2.15 when that means we have a corresponding Ph. Equal to 13 0.85 and this is a basic solution.


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