Question

Question: which solution has the higher pH ? Explain.

(a) A 0.1 M solution of an acid with ${\mathit{K}}_{\mathbf{a}}\mathbf{=}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$ or one with${\mathit{K}}_{\mathbf{a}}\mathbf{=}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}$

(b) A 0.1 Msolution of an acid with ${\mathbf{\text{pK}}}_{\mathbf{\text{a}}}\mathbf{\text{= 3.0}}$or one with${\mathbf{\text{pK}}}_{\mathbf{\text{a}}}\mathbf{\text{= 3.5}}$

(c) A 0.1 M solution or a 0.01 M solution of a weak acid

(d) A 0.01 M solution of a weak acid or a 0.01Msolution of a strong acid

(e) A 0.01 Msolution of an acid or a 0.01 m solution of a base

(f) A solution of pOH 6.0 or one of pOH 8.0

Short answer

(a) A 0.1 M solution with $K_a=4.5\times {10}^{-5}$ has higher pH.

(b) A 0.1 M solution with ${\text{pK}}_{\text{a}}\text{= 3.5}$ has higher pH .

(c) A 0.01 M solution of weak acid has higher pH .

(d) A 0.01 M solution of weak acid has higher pH .

(e) A 0.01 M solution of base has higher pH .

(f) A pOH 6.0 solution has higher pH .

Step-by-step solution

Definition of  pH

The negative logarithm of ${\mathbf{\text{H}}}^{\mathbf{\text{+}}}$ ion concentration is used to calculatepH. As a result, the meaning ofpHis justified as hydrogen power.

(a) Greater pH

A higher pH indicates that the substance is less acidic. A lower$K_a$indicates a lower acidity. When comparing the two$K_a=1\times {10}^{-4}$is higher than$4\times {10}^{-5}$ .

Therefore, the pH of the $K_a$ with a lower value,$4\times {10}^{-5}$ , is higher.

(b) Greater pH  

A lower $K_a$ indicates a lower acidity. ${\text{pK}}_{\text{a}}\text{=}{\text{- logK}}_a$Is the inverse relationship between $p{K}_a$and $K_a$. As a result, the greater the role="math" localid="1663306991792" $p{K}_a$value, the lower the $K_a$ value.

Therefore, ${\text{pK}}_{\text{a}}\text{= 3.5}$ is less acidic and has a higher pH than ${\text{pK}}_{\text{a}}\text{= 3.0}$.

(c) Greater pH

The $\left[{\text{H}}^{\text{+}}\right]$ is directly proportional to the Solution's concentration. As a result, smaller concentration has a lower $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$. Because the connection between pH and $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$ is inverse, the lower concentration will have a higher pH

$\text{pH}\text{=}\text{- log}\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$.

Therefore, pH of 0.01 M of weak acid is higher than 0.01 M of weak acid.

Step 5: (d) Greater  pH

Strong acids totally dissociate, whereas weak acids only partially dissociate. As a result, weak acid will produce fewer $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$. As stated in (c), the smaller the concentration, the greater the pH . Therefore, the pH of 0.1 M weak acid is greater than that of 0.1 M strong acid.

Therefore, solution is 0.1 M of weak acid.

(e) Greater pH 

Base will have less $\left[{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\right]$since it will increase the amount of $\left[{\text{OH}}^{\text{-}}\right]$. As a result, it will have a higher pH than acids.

Therefore, a base with a 0.01 M has a greater pH than an acid with a 0.1 M.

(f) Greater  pH

There is a connection between pH and pOH .

$$\begin{gathered} \text{pH + pOH =}\text{14} \\ \text{pH =}\text{14 - pOH} \end{gathered}$$

Therefore, pOH has a higher pH value than pOH = 8.0.