In which of the following cases is the acid strength highest?

Options

A. `K_(a)=10^(-6)`
B. `pK_(a)=5`
C. `pK_(b)=10`
D. `K_(b)=10^(-11)`

Answer

To determine which case has the highest acid strength, we need to analyze the given values of \( K_a \) and \( K_b \) and convert them into \( pK_a \) values. Here’s a step-by-step solution:

### Step 1: Understand the relationship between \( K_a \) and \( pK_a \)
The strength of an acid is often expressed in terms of its dissociation constant \( K_a \). The relationship between \( K_a \) and \( pK_a \) is given by:
\[ pK_a = -\log(K_a) \]
A lower \( pK_a \) value indicates a stronger acid.

### Step 2: Calculate \( pK_a \) for the given cases
1. **Case 1**: \( K_a = 10^6 \)
\[ pK_a = -\log(10^6) = -6 \]

2. **Case 2**: \( pK_a = 5 \) (given directly)

3. **Case 3**: \( pK_b = 10 \)
To find \( pK_a \), we use the relationship:
\[ pK_a + pK_b = 14 \implies pK_a = 14 - 10 = 4 \]

4. **Case 4**: \( K_b = 10^{11} \)
First, calculate \( pK_b \):
\[ pK_b = -\log(10^{11}) = -11 \]
Now, find \( pK_a \):
\[ pK_a = 14 - (-11) = 14 + 11 = 25 \]

### Step 3: Compare the \( pK_a \) values
Now we have the following \( pK_a \) values:
- Case 1: \( pK_a = -6 \)
- Case 2: \( pK_a = 5 \)
- Case 3: \( pK_a = 4 \)
- Case 4: \( pK_a = 25 \)

### Step 4: Determine the highest acid strength
The strongest acid corresponds to the lowest \( pK_a \). From our calculations:
- The lowest \( pK_a \) is \( -6 \) from Case 1.

### Conclusion
Thus, the case with the highest acid strength is **Case 1** with \( K_a = 10^6 \).

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