The pH of `0.1` M monobasic acid is `4.50`. The acidity constant `(K_(a))` of the monobasic acid is

Options

A. `1.0xx10^(-7)`
B. `1.0xx10^(-5)`
C. `1.0xx10^(-4)`
D. `1.0xx10^(-8)`

Explanation

To find the acidity constant \( K_a \) of the monobasic acid given the pH, we can follow these steps:

### Step 1: Calculate the concentration of hydrogen ions \([H^+]\)

Given that the pH of the solution is 4.50, we can use the formula:

\[ pH = -\log[H^+] \]

To find \([H^+]\), we can rearrange this equation:

\[ [H^+] = 10^{-pH} \]

Substituting the given pH value:

\[ [H^+] = 10^{-4.50} \]

### Step 2: Calculate the value of \([H^+]\)

Calculating \( 10^{-4.50} \):

\[ [H^+] = 10^{-4.50} = 3.16 \times 10^{-5} \, \text{M} \]

### Step 3: Set up the equilibrium expression for the dissociation of the acid

For a monobasic acid \( HA \) that dissociates as follows:

\[ HA \rightleftharpoons H^+ + A^- \]

Let \( x \) be the concentration of \( H^+ \) produced at equilibrium. Therefore, at equilibrium:

- The concentration of \( H^+ \) is \( x = 3.16 \times 10^{-5} \, \text{M} \)
- The concentration of \( A^- \) will also be \( x \)
- The concentration of the undissociated acid \( HA \) will be \( 0.1 - x \)

### Step 4: Write the expression for the acidity constant \( K_a \)

The expression for the acidity constant \( K_a \) is given by:

\[ K_a = \frac{[H^+][A^-]}{[HA]} \]

Substituting the equilibrium concentrations into this expression:

\[ K_a = \frac{(3.16 \times 10^{-5})(3.16 \times 10^{-5})}{0.1 - 3.16 \times 10^{-5}} \]

### Step 5: Simplify the expression

Since \( x \) is much smaller than 0.1, we can approximate:

\[ 0.1 - 3.16 \times 10^{-5} \approx 0.1 \]

Thus, we can simplify \( K_a \):

\[ K_a \approx \frac{(3.16 \times 10^{-5})^2}{0.1} \]

### Step 6: Calculate \( K_a \)

Calculating \( K_a \):

\[ K_a \approx \frac{(3.16 \times 10^{-5})^2}{0.1} = \frac{10^{-10}}{0.1} = 10^{-9} \]

### Step 7: Final Result

Thus, the acidity constant \( K_a \) of the monobasic acid is approximately:

\[ K_a \approx 1 \times 10^{-9} \]