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) (mathbfp Ka) relative strength A ПI 9.006 B 10.4 C 4.50

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) (mathbfp Ka) relative strength
A ПI 9.006
B 10.4
C 4.50

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 & ПI & 9.006 & $\square$ \\ \hline B & $\square$ & 10,4 & $\square$ \\ \hline C & $\square$ & 4.50 & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Understanding the Relationship Between $ K_a $ and $ \mathbf{p}K_a $

The acid dissociation constant $ K_a $ and its logarithmic form $ \mathbf{p}K_a $ are related by the equation: \[ \mathbf{p}K_a = -\log_{10}(K_a) \] To find $ K_a $ from $ \mathbf{p}K_a $, we use the inverse: \[ K_a = 10^{-\mathbf{p}K_a} \]

Step 2: Calculating $ K_a $ for Acid A

Given $ \mathbf{p}K_a = 9.006 $ for Acid A, we calculate $ K_a $ as follows: \[ K_a = 10^{-9.006} \approx 9.860 \times 10^{-10} \]

Step 3: Calculating $ K_a $ for Acid B

Given $ \mathbf{p}K_a = 10.4 $ for Acid B, we calculate $ K_a $ as follows: \[ K_a = 10^{-10.4} \approx 3.981 \times 10^{-11} \]

Step 4: Calculating $ K_a $ for Acid C

Given $ \mathbf{p}K_a = 4.50 $ for Acid C, we calculate $ K_a $ as follows: \[ K_a = 10^{-4.50} \approx 3.162 \times 10^{-5} \]

Step 5: Determining Relative Strength

The relative strength of an acid is inversely related to its $ \mathbf{p}K_a $ value. Lower $ \mathbf{p}K_a $ values indicate stronger acids.

Acid A: $ \mathbf{p}K_a = 9.006 $ (weaker)
Acid B: $ \mathbf{p}K_a = 10.4 $ (weakest)
Acid C: $ \mathbf{p}K_a = 4.50 $ (strongest)

Final Answer

\[ \begin{array}{|c|c|c|c|} \hline \text{acid} & K_{a} & \mathbf{p}K_{a} & \text{relative strength} \\ \hline \text{A} & \boxed{9.860 \times 10^{-10}} & 9.006 & \text{weaker} \\ \hline \text{B} & \boxed{3.981 \times 10^{-11}} & 10.4 & \text{weakest} \\ \hline \text{C} & \boxed{3.162 \times 10^{-5}} & 4.50 & \text{strongest} \\ \hline \end{array} \]

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