If you know the [OH⁻ ], how can you determine the pH of a solutio...

Question

If you know the [OH⁻ ], how can you determine the pH of a solution?

Accepted Answer

Welcome back everyone under normal conditions. How can the P H of A solution be calculated? Given the concentration of hydroxide and the solution we have choices A through D which differ in how to calculate the P H. Where choice choices A and C are similar because they both state to utilize the P O H formula equal to the negative log of the concentration of hydroxide. However, choice A differs because it states that under normal conditions, the P H plus the P O H should equal 14 and you would rearrange that formula to sulfur P H. And choice C states that under normal conditions, the P H is equal to the P O H. We also have choices B and D where choice B states to substitute the concentration of hydroxide in the P H formula for the negative log of the concentration of hydroxide. And choice D states to determine the concentration of hydro h +30 plus in the solution by using the formula where hydro's concentration is equal to divided by the concentration of hydroxide. And to then substitute the value of the concentration of hydro by taking the P H formula and the difference from 14. So we would begin by recalling that under normal conditions. If we assume that we have normal conditions for the solution, our dissociation constant for water or K W of water is equal to the concentration of hydro H 30 plus multiplied by the concentration of hydroxide. And we recognize that this occurs from water reacting with itself as both an acid and a base where the acidic water is going to donate a proton to the second reactant. And as a result, we would form the conjugate base hydroxide of water. And we would also form our second product hydro H 30 plus which is the conjugate acid of water. So these two products form our K W equation. And we also want to recall that R K W is equal to the value of the result from our products of hydro num multiplied by hydroxide concentrations which would equal one point oh times 10 to the negative 14th power. So now with this outlined, we're going to want to derive three different equations using our concentrations of our products hydro and hydroxide in order to ultimately derive 1/4 equation where we can solve for P H. So we're going to need to simplify by taking the logarithm of both sides of the above equation. So we would have in our next step, the log of the concentration of hydro num multiplied by the log of the concentration of hydroxide equal to the log of 1. times 10 to the negative 14th power. So now we're going to then recall our rule of logarithm. So our law where, because we on the left hand side of our equation are taking the log of the product of two different terms, we would then just change that by taking the log of the sum of our two terms. So we would have the log of the concentration of hydro num which is then added to the log of the concentration of hydroxide. So that is for our log rule on the left hand side of our equation. And for the log rule or rather for the power rule on the right hand side of our equation, we would set the right hand side so that we have our equal sign and then the exponent of negative 14 will now become a coefficient so that we would have negative 14 as a coefficient which is then multiplied by the log of 10, which is the base to the exponent negative 14. So that is the application of our log rule and power rule. And now with this rule applied, we're going to then recall that the log of 10 is equal to one. So we can simplify. So that in our next line, we have the log of the concentration of hydro plus the log of the concentration of hydroxide equal to negative 14. So so far what we have simplified to we can state will be our first equation. We'll say equation one. So now we're going to come up with a second equation where we can incorporate P H. We're going to recall that P can be calculated by taking or setting it equal to the negative log of the concentration of hydro. As well as I'm sorry, this should say hydro num H 30 plus. And we can also recall that secondly, we can calculate P H by taking the negative log of the concentration. I'm sorry. That would be P O H. So the second equation is going to be P O H which is found from taking the negative log of the concentration of hydroxide. Now we're next going to want to make the log terms be positive for both of these equations. So we're going to multiply both sides of these equations by negative one. So as a result that would allow to simplify so that we have negative P H equal to the positive log of the concentration of hydro num, this would be equation two. And then for equation three, we would have the negative P O H equal to the log of hydroxide. This is equation three. So if the log of hydroxide and the log of hydro num equaled a negative P O H and negative P H, we can go back to equation one and substitute equation three and two into equation one. And so therefore, as a result, we would have the negative P H plus the negative P O H equal to negative 14. And let's recall that under standard conditions, this equation should be positive. So we should ultimately multiply everything in the equation by a factor of negative one. So that thus in our next line, we can have positive P H plus positive P O H equal to positive 14. And now in order to solve for P H because according to the prompts, we are given the concentration of hydroxide, we would be able to get the P O H by utilizing our equation that we cited where we stated that that is equal to the negative log of the concentration of hydroxide. And thus, in order to solve for P H, we would just reformat this equation so that we would say that the P H is equal to 14 subtracted from the calculated P O H that we would find. And ultimately, this would be our fourth and final equation on how to solve for Ph. So going back to the multiple choice, we can rule out choice B since it says to only substitute the concentration of hydroxide so that the P H is equal to the negative log of hydroxide. However, that fails to utilize the setup that we had where we took 14 minus the P O H. So B is too simple. We can also rule out choice D because it says to determine the concentration of hydro num by taking 14 over the concentration of hydroxide and then substitute by taking 14 minus the log of hydro to get the P H which is not the format that we determined. And we would also rule out choice C because under normal conditions, the P H will not equal the P O H, we would have to determine the P O H by using the concentration of hydroxide by taking its negative log. So that leaves us with choice A as the only correct choice which states to determine the P O H of the solution. By first using the P O H times the concentration or sorry, taking the P O H equal to the negative log of the concentration of hydroxide. And then under normal conditions, the P H plus the P O H will equal 14. And then to ultimately calculate the P H, we will rearrange the formula so that the P H is found from taking 14 minus our calculated P O H. So choice A is the only correct and final answer to complete this example. I hope this made sense and let us know if you have any questions.

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If you know the [OH⁻ ], how can you determine the pH of a solution?

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