In aqueous solution the ionization constants for carbonic acid are 7 1 x10 4.2K - = and 11 x104.82K - = Selection the correct statement for a saturated 0.034 M solution of the carbonic acid.

To analyze a saturated solution of carbonic acid (H₂CO₃) with a concentration of 0.034 M, we need to consider its ionization constants, K₁ and K₂, which are given as 4.2 x 10⁻⁴ and 4.8 x 10⁻¹¹, respectively. These constants represent the equilibrium constants for the two dissociation steps of carbonic acid in water.

Understanding Carbonic Acid Dissociation

Carbonic acid is a weak acid that can dissociate in two steps:

• First dissociation: H₂CO₃ ⇌ H⁺ + HCO₃⁻ (K₁ = 4.2 x 10⁻⁴)
• Second dissociation: HCO₃⁻ ⇌ H⁺ + CO₃²⁻ (K₂ = 4.8 x 10⁻¹¹)

The first dissociation is relatively strong for a weak acid, while the second dissociation is much weaker, indicating that the concentration of carbonate ions (CO₃²⁻) will be significantly lower than that of bicarbonate ions (HCO₃⁻) in a saturated solution.

Calculating Ion Concentrations

In a saturated solution of 0.034 M carbonic acid, we can assume that the concentration of H₂CO₃ is approximately equal to the initial concentration, as only a small fraction will dissociate. Let's denote the concentration of H⁺ ions produced from the first dissociation as x.

From the first dissociation, we can write the expression for K₁:

K₁ = [H⁺][HCO₃⁻] / [H₂CO₃]

Substituting the values, we have:

4.2 x 10⁻⁴ = (x)(x) / (0.034 - x)

For simplicity, since x will be small compared to 0.034, we can approximate this as:

4.2 x 10⁻⁴ ≈ (x²) / 0.034

Solving for x gives:

x² = 4.2 x 10⁻⁴ * 0.034

x² ≈ 1.428 x 10⁻⁵

x ≈ 0.00378 M

This means that the concentration of H⁺ ions is approximately 0.00378 M, and since HCO₃⁻ is produced in a 1:1 ratio with H⁺, the concentration of HCO₃⁻ will also be about 0.00378 M.

Considering the Second Dissociation

Now, we need to consider the second dissociation. The concentration of HCO₃⁻ is 0.00378 M, and we can denote the concentration of CO₃²⁻ produced as y. The expression for K₂ is:

K₂ = [H⁺][CO₃²⁻] / [HCO₃⁻]

Substituting the known values gives:

4.8 x 10⁻¹¹ = (0.00378)(y) / (0.00378 - y)

Again, since y will be small compared to 0.00378, we can approximate this as:

4.8 x 10⁻¹¹ ≈ (0.00378)(y) / 0.00378

Thus, we find:

y ≈ 4.8 x 10⁻¹¹

This indicates that the concentration of carbonate ions (CO₃²⁻) is very low, confirming that the second dissociation is not significant in this solution.

Final Thoughts on the Saturated Solution

In summary, for a saturated 0.034 M solution of carbonic acid:

• The concentration of H⁺ ions is approximately 0.00378 M.
• The concentration of HCO₃⁻ ions is also about 0.00378 M.
• The concentration of CO₃²⁻ ions is negligible at around 4.8 x 10⁻¹¹ M.

This analysis shows that in a saturated solution of carbonic acid, the predominant species are H⁺ and HCO₃⁻, while CO₃²⁻ is present in very small amounts. This behavior is characteristic of weak acids, where the first dissociation is more significant than the second.