In an aqueous solution the ionisation constants for carbonic acid are `K_(1)=4.2xx10^(-7)andK_(2) =4.8xx10^(-11)`. Select the correct statement for a saturated 0.034 M solution of the carbonic acid.

Options

A. The concentration of `CO_(3)^(2-)` is 0.034 M
B. The concentration of `CO_(3)^(2-)` is greater than that of `HCO_(3)^(-)`
C. The concentration of `H^(+)andHCO_(3)^(-)` are approximately equal
D. The concentration of `H^(+)` is double that of `CO_(3)^(2-)`

Explanation

To solve the problem regarding the ionization of carbonic acid in a saturated solution, we will follow these steps:

### Step 1: Understand the Ionization of Carbonic Acid
Carbonic acid (H₂CO₃) undergoes two ionization steps:
1. The first ionization:
\[ \text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^- \]
with an ionization constant \( K_1 = 4.2 \times 10^{-7} \).

2. The second ionization:
\[ \text{HCO}_3^- \rightleftharpoons \text{H}^+ + \text{CO}_3^{2-} \]
with an ionization constant \( K_2 = 4.8 \times 10^{-11} \).

### Step 2: Analyze the Ionization Constants
Since \( K_1 \) is significantly larger than \( K_2 \), it indicates that the first ionization step is much more favorable than the second. Therefore, in a saturated solution of carbonic acid, most of the hydrogen ions (H⁺) will come from the first ionization.

### Step 3: Concentration of Ions
In a 0.034 M solution of carbonic acid, we can assume that the concentration of hydrogen ions produced from the first ionization will be approximately equal to the concentration of bicarbonate ions (HCO₃⁻) produced. This is because for every molecule of carbonic acid that ionizes, one hydrogen ion and one bicarbonate ion are produced.

Let’s denote:
- \([H^+] \approx [HCO_3^-]\)

### Step 4: Calculate the Concentration of Ions
Since the solution is saturated and the concentration of carbonic acid is 0.034 M, we can conclude:
- \([H^+] \approx [HCO_3^-] \approx x\)

From the first ionization step:
\[ x \approx 0.034 \, \text{M} \]

### Step 5: Evaluate the Contribution of the Second Ionization
The contribution of the second ionization (producing carbonate ions, CO₃²⁻) will be negligible due to the very small value of \( K_2 \). Thus, we can ignore it for practical purposes.

### Conclusion
The correct statement regarding the saturated 0.034 M solution of carbonic acid is that the concentration of hydrogen ions is approximately equal to the concentration of bicarbonate ions, and the contribution from the carbonate ions is negligible.

### Final Answer
The correct statement is: The concentration of hydrogen ions \([H^+]\) is approximately equal to the concentration of bicarbonate ions \([HCO_3^-]\) in the solution.

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