Question

Complete the following table by calculating the missing entries and indicating whether the solution is acidic or basic. $$ \begin{array}{lllll} \hline & & & \text { Acidic or } \\ {\left[\mathrm{H}^{+}\right]} & \mathrm{OH}^{-}(a q) & \mathrm{pH} & \text { pOH } & \text { basic? } \\ \hline 7.5 \times 10^{-3} \mathrm{M} & & & & \\ & 3.6 \times 10^{-10} \mathrm{M} & & & \\ & & & & \\ & & 8.25 & & \\ & & & 5.70 & \\ \hline \end{array} $$

Short answer

} \\\ \hline 7.5 \times 10^{-3} \mathrm{M} & 1.33 \times 10^{-12} \mathrm{M} & 2.12 & 11.88 & \text { Acidic } \\\ & 3.6 \times 10^{-10} \mathrm{M} & 11.44 & 9.44 & \text { Basic } \\\ 10^{-8.25} \mathrm{M} & 10^{-5.75} \mathrm{M} & 8.25 & 5.75 & \text { Basic } \\\ 10^{-8.30} \mathrm{M} & 10^{-5.70} \mathrm{M} & 8.30 & 5.70 & \text { Basic } \\\ \hline \end{array} $$

Step-by-step solution

Find the missing OH- concentration for the given H+ concentration

Using the relationship between H+ and OH- concentrations, we can calculate the OH- concentration: \[ [\mathrm{OH}^{-}] = \frac{K_w}{[\mathrm{H}^{+}]}\] For the given H+ concentration: \[ [\mathrm{OH}^{-}] = \frac{1.0 \times 10^{-14}}{7.5 \times 10^{-3}}\]

Calculate pH and pOH for the given H+ and OH- concentrations

Using the definitions of pH and pOH, we can calculate the pH and pOH of the given solutions: For the given H+ concentration: \[pH = -\log (7.5 \times 10^{-3})\] For the given OH- concentration: \[pOH = -\log (3.6 \times 10^{-10})\]

Determine the missing H+ and OH- concentrations for the given pH and pOH values

Using the inverse of the definitions of pH and pOH, we can determine the H+ and OH- concentrations: For the given pH value: \[ [\mathrm{H}^{+}] = 10^{-8.25}\] For the given pOH value: \[ [\mathrm{OH}^{-}] = 10^{-5.70}\]

Find the complementary value of pH or pOH for the given pH and pOH values

Use the relation of pH and pOH to find the complementary value: For the given pH value (8.25): \[ pOH = 14 - 8.25\] For the given pOH value (5.70): \[ pH = 14 - 5.70\]

Classify each solution as acidic or basic

Use the classification rules to determine whether the solution is acidic or basic: 1. pH < 7: Acidic 2. pH > 7: Basic 3. pH = 7: Neutral Apply these rules to the calculated pH values to classify each solution. Here is the completed table: $$ \begin{array}{lllll} \hline & & & \text { Acidic or } \\\ {\left[\mathrm{H}^{+}\right]} & \mathrm{OH}^{-}(a q) & \mathrm{pH} & \text { pOH } & \text { basic? } \\\ \hline 7.5 \times 10^{-3} \mathrm{M} & 1.33 \times 10^{-12} \mathrm{M} & 2.12 & 11.88 & \text { Acidic } \\\ & 3.6 \times 10^{-10} \mathrm{M} & 11.44 & 9.44 & \text { Basic } \\\ 10^{-8.25} \mathrm{M} & 10^{-5.75} \mathrm{M} & 8.25 & 5.75 & \text { Basic } \\\ 10^{-8.30} \mathrm{M} & 10^{-5.70} \mathrm{M} & 8.30 & 5.70 & \text { Basic } \\\ \hline \end{array} $$