The dissociation constant of monobasic acids `A, B,C` and `D` are `6 xx 10^(-4),5xx10^(-5), 3.6 xx 10^(-6)`, and `7 xx 10^(-10)`, respectively. The `pH` values of their `0.1M` aqueous solutions are in the order.

Options

A. `D gt C gt B gt A`
B. `A gt B gt C gt D`
C. `A =B = C = D`
D. None

Explanation

To determine the order of pH values for the given monobasic acids A, B, C, and D based on their dissociation constants (Ka), we can follow these steps:

### Step 1: Identify the given dissociation constants
The dissociation constants (Ka) for the acids are as follows:
- Acid A: \( K_a = 6 \times 10^{-4} \)
- Acid B: \( K_a = 5 \times 10^{-5} \)
- Acid C: \( K_a = 3.6 \times 10^{-6} \)
- Acid D: \( K_a = 7 \times 10^{-10} \)

### Step 2: Understand the relationship between Ka and pH
The higher the dissociation constant (Ka), the stronger the acid. A stronger acid will dissociate more in solution, producing more \( H^+ \) ions, which leads to a lower pH value.

### Step 3: Calculate the concentration of \( H^+ \) ions for each acid
For a weak acid, the dissociation can be represented as:
\[ HA \rightleftharpoons H^+ + A^- \]
The dissociation constant expression is:
\[ K_a = \frac{[H^+][A^-]}{[HA]} \]

Assuming \( x \) is the concentration of \( H^+ \) produced, we can approximate for a 0.1 M solution:
\[ K_a \approx \frac{x^2}{0.1 - x} \]
Since \( x \) is small compared to 0.1, we can simplify this to:
\[ K_a \approx \frac{x^2}{0.1} \]
Thus, we can solve for \( x \):
\[ x^2 = K_a \times 0.1 \]
\[ x = \sqrt{K_a \times 0.1} \]

### Step 4: Calculate \( H^+ \) concentration for each acid
1. For Acid A:
\[ x_A = \sqrt{6 \times 10^{-4} \times 0.1} = \sqrt{6 \times 10^{-5}} \approx 7.75 \times 10^{-3} \, M \]

2. For Acid B:
\[ x_B = \sqrt{5 \times 10^{-5} \times 0.1} = \sqrt{5 \times 10^{-6}} \approx 2.24 \times 10^{-3} \, M \]

3. For Acid C:
\[ x_C = \sqrt{3.6 \times 10^{-6} \times 0.1} = \sqrt{3.6 \times 10^{-7}} \approx 1.89 \times 10^{-3} \, M \]

4. For Acid D:
\[ x_D = \sqrt{7 \times 10^{-10} \times 0.1} = \sqrt{7 \times 10^{-11}} \approx 8.37 \times 10^{-6} \, M \]

### Step 5: Determine the order of pH values
The order of \( H^+ \) concentrations is:
- \( x_A > x_C > x_B > x_D \)

Since pH is inversely related to \( H^+ \) concentration:
- Lower \( H^+ \) concentration means higher pH.

Thus, the order of pH values from highest to lowest is:
- \( \text{pH}_D > \text{pH}_B > \text{pH}_C > \text{pH}_A \)

### Final Answer
The order of pH values of their 0.1M aqueous solutions is:
\[ \text{pH}_D > \text{pH}_B > \text{pH}_C > \text{pH}_A \]