Questions: Complete the following table, which lists information about the measured acid dissociation constants of three unknown weak acids. Note: be sure each number you put in the table has the correct number of significant digits. acid Ka pKa relative strength ---- --- --- ---------------- A 5.8 x 10^-9 B 7.36 x 10^-2 C 9.9

Complete the following table, which lists information about the measured acid dissociation constants of three unknown weak acids. Note: be sure each number you put in the table has the correct number of significant digits.

acid Ka pKa relative strength
---- --- --- ----------------
A 5.8 x 10^-9
B 7.36 x 10^-2
C 9.9

Transcript text: Complete the following table, which lists information about the measured acid dissociation constants of three unknown weak acids. Note: be sure each number you put in the table has the correct number of significant digits. \begin{tabular}{|c|c|c|c|} \hline acid & $K_{a}$ & $\mathbf{p} K_{a}$ & relative strength \\ \hline A & $5.8 \times 10^{-9}$ & $\square$ & $\square$ \\ \hline B & $7.36 \times 10^{-2}$ & $\square$ & $\square$ \\ \hline C & $\square$ & 9.9 & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Calculate $\mathbf{p}K_a$ for Acid A

The $\mathbf{p}K_a$ is calculated using the formula:

\[ \mathbf{p}K_a = -\log_{10}(K_a) \]

For Acid A, $K_a = 5.8 \times 10^{-9}$:

\[ \mathbf{p}K_a = -\log_{10}(5.8 \times 10^{-9}) \approx 8.2366 \]

Step 2: Determine the Relative Strength for Acid A

The relative strength of an acid is inversely related to its $\mathbf{p}K_a$. A smaller $\mathbf{p}K_a$ indicates a stronger acid. Since $\mathbf{p}K_a = 8.2366$ is relatively high, Acid A is a weak acid.

Step 3: Calculate $\mathbf{p}K_a$ for Acid B

For Acid B, $K_a = 7.36 \times 10^{-2}$:

\[ \mathbf{p}K_a = -\log_{10}(7.36 \times 10^{-2}) \approx 1.1335 \]

Step 4: Determine the Relative Strength for Acid B

Since $\mathbf{p}K_a = 1.1335$ is relatively low, Acid B is a stronger acid compared to Acid A.

Step 5: Calculate $K_a$ for Acid C

Given $\mathbf{p}K_a = 9.9$ for Acid C, we can find $K_a$ using:

\[ K_a = 10^{-\mathbf{p}K_a} = 10^{-9.9} \approx 1.2589 \times 10^{-10} \]

Step 6: Determine the Relative Strength for Acid C

With a high $\mathbf{p}K_a$ of 9.9, Acid C is a weak acid, weaker than both Acid A and Acid B.

Final Answer

\[ \begin{tabular}{|c|c|c|c|} \hline acid & $K_{a}$ & \mathbf{p}K_{a} & relative strength \\ \hline A & $5.8 \times 10^{-9}$ & \boxed{8.2366} & \boxed{\text{weak}} \\ \hline B & $7.36 \times 10^{-2}$ & \boxed{1.1335} & \boxed{\text{strong}} \\ \hline C & \boxed{1.2589 \times 10^{-10}} & 9.9 & \boxed{\text{weak}} \\ \hline \end{tabular} \]

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