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Question: How do you find \(pOH\) given \(pH\)?...

How do you find pOHpOH given pHpH?

Explanation

Solution

‌As we all know that pHpH of a solution is basically the negative logarithm of hydrogen ion concentration and pOHpOH is calculated by knowing the hydroxide ion concentration in the solution and is given as the negative logarithm of hydroxide ions concentration.

Complete step by step solution:
As we have already discussed that pHpH and pOHpOH both are the negative logarithms of the concentrations of hydrogen ions and hydroxide ions respectively.
We know that, pHpH is expressed in terms of hydrogen ion concentration as shown below:
pH=−log⁡[H+]pH = - \log [{H^ + }]
We also know that, pOHpOH is expressed in terms of hydroxide ion concentration as shown below:
pOH=−log⁡[OH−]pOH = - \log [O{H^ - }]
Now, we know that water generally dissociates into hydrogen ions and hydroxide ions as shown:
H2O⇌H++OH−{H_2}O \rightleftharpoons {H^ + } + O{H^ - }
Then the equilibrium constant is given as ratio of the concentration of products to the concentration of the reactant. So it will be:
K=[H+][OH−][H2O]K = \dfrac{{[{H^ + }][O{H^ - }]}}{{[{H_2}O]}}
Now, in terms of ionic product of water we can write the above equation as:
K[H2O]=KWK[{H_2}O] = {K_W}
In other words, we can say that the ionic product of water is equivalent to the product of concentrations of hydrogen ion and hydroxide ion and it will be written as:
KW=[H+][OH−]{K_W} = [{H^ + }][O{H^ - }]
We are also aware with the fact that the hydrogen ion and hydroxide ion concentration are related as 1414 in the solution.
So we can write:
[H+][OH−]=14[{H^ + }][O{H^ - }] = 14
In terms of pHpH and pOHpOH we can write the above equation as:
pH+pOH=14pH + pOH = 14
Or
pOH=14−pHpOH = 14 - pH
Therefore, we can find the value of pOHpOH by simply subtracting the given value of pHpH from 1414.

Note: Remember that when the hydrogen ion concentration and hydroxide ion concentrations are equal then the solution is generally neutral and when the hydroxide ion concentration is more in the solution, then the solution is basic in nature and when the hydrogen ion concentration is more, then the solution is acidic in nature which can be identified with the help of the formula below: pH+pOH=14pH + pOH = 14.