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Question: If \( {K_w} = {10^{ - 16}} \) at a certain temperature. pH of 0.01 M NaOH at the same temperature co...

If Kw=10−16{K_w} = {10^{ - 16}} at a certain temperature. pH of 0.01 M NaOH at the same temperature could be:

A. 14

B. 12

C. 2

D. 16

Explanation

Solution

Here Kw{K_w} mentioned in the reaction is equilibrium constant. It is also known as a dissociation constant or ionization constant of water. In pure water [H+][{H^ + }] = [OH−][O{H^ - }] is equal to 1.00×10−71.00\times{10^{ - 7}} M. We can define pH as the power of hydrogen ions in a given solution. We can calculate pH of the solution using a formula,

pH=−log⁡10[H+]pH = - \log 10\left[ {{H^ + }} \right]

If the pH of the solution is 0 then the solution is highly acidic, 1414 means the solution is highly basic. The pH value of 7 shows as neutral as water.

Complete step by step answer:

We know that Kw{K_w} is equilibrium constant. It can be represented in two forms:

When it's fully equilibrium then:

Kw=[H3O+][OH−]{K_w} = [{H_3}{O^ + }][O{H^ - }]

And in a simplified equilibrium it is:

Kw=[H+][OH−]{K_w} = [{H^ + }][O{H^ - }]

Also, we know that water gets ionized at any one time that its concentration remains virtually unchanged. It is defined to avoid making the expression unnecessarily complicated by including another constant in it.

For calculating pH, we need to note that pH is the negative base 10 logarithm of the hydrogen ion concentration of a solution. For calculating it, we take the log of a given hydrogen ion concentration and reverse the sign.

In the above question, [OH−]=0.01M[O{H^ - }] = 0.01M

We can substitute the known values we get,

Then, [H+]=Kco[OH−]=10−160.01=10−16+2=10−14[{H^ + }] = \dfrac{{{K_{co}}}}{{[O{H^ - }]}} = \dfrac{{{{10}^{ - 16}}}}{{0.01}} = {10^{ - 16 + 2}} = {10^{ - 14}}

Therefore, pH=−log⁡[H+]pH = - \log [{H^ + }]

−log⁡[10−14]=14- \log [{10^{ - 14}}] = 14

pH+ pOH =14

So, pH of 0.01 M NaOH at the same temperature could be 14.

So, the correct answer is Option (A).

Note: We need to keep in mind that for calculating the pH value of a solution of a weak base it is similar to that of the weak acid. However, the variable x in the solution will represent the concentration of the hydroxide ion. For finding the pH we have to take the negative logarithm for getting the pOH value followed by subtracting from 14 to get the pH i.e. pH = 14 -1 =13.