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Understanding the Calculation of H+ Concentration in 0.006 M Benzoic Acid Solution

When considering the H+ concentration of a 0.006 M benzoic acid solution, it's important to delve into the chemistry behind weak acids, their dissociation in water, and how this impacts the H+ concentration. Benzoic acid (C₆H₅COOH) is a weak acid, which means it does not fully dissociate in aqueous solutions. This characteristic makes the calculation of the hydrogen ion (H+) concentration a bit more involved compared to strong acids.

Dissociation of Benzoic Acid in Water

Benzoic acid partially ionizes in water according to the following equation:

[ \text{C}6\text{H}5\text{COOH} \rightleftharpoons \text{C}6\text{H}5\text{COO}^- + \text{H}^+ ]

The extent of this dissociation is governed by the acid dissociation constant, ( Ka ). For benzoic acid, the ( Ka ) value is approximately ( 6.3 \times 10^{-5} ) at room temperature. Given the weak nature of benzoic acid, not all the molecules dissociate, which is why we must use the ( K_a ) expression to calculate the H+ concentration.

Setting Up the ICE Table

To calculate the H+ concentration of 0.006 M benzoic acid, we employ an ICE (Initial, Change, Equilibrium) table. The initial concentration of benzoic acid is 0.006 M, and we assume the initial concentrations of C₆H₅COO⁻ and H+ are 0 M:

• Initial: [C₆H₅COOH] = 0.006 M, [C₆H₅COO⁻] = 0, [H+] = 0
• Change: [C₆H₅COOH] decreases by x, [C₆H₅COO⁻] increases by x, [H+] increases by x
• Equilibrium: [C₆H₅COOH] = 0.006 - x, [C₆H₅COO⁻] = x, [H+] = x

Calculating H+ Concentration Using ( K_a )

The equilibrium expression based on ( K_a ) is:

[ Ka = \frac{[\text{C}6\text{H}5\text{COO}^-][\text{H}^+]}{[\text{C}6\text{H}_5\text{COOH}]} = \frac{x \times x}{0.006 - x} ]

Given that ( K_a ) is quite small, the dissociation is minimal, allowing us to approximate ( 0.006 - x \approx 0.006 ). This simplifies the equation to:

[ 6.3 \times 10^{-5} = \frac{x^2}{0.006} ]

Solving for x (which is the concentration of H+):

[ x^2 = 6.3 \times 10^{-5} \times 0.006 ]

[ x^2 = 3.78 \times 10^{-7} ]

[ x = \sqrt{3.78 \times 10^{-7}} ]

[ x \approx 6.15 \times 10^{-4} \text{ M} ]

Thus, the H+ concentration of a 0.006 M benzoic acid solution is approximately ( 6.15 \times 10^{-4} ) M.

Conclusion

The calculation of the H+ concentration in a 0.006 M benzoic acid solution illustrates the principles of weak acid dissociation. By using the ICE table method and simplifying the dissociation constant expression, we find that the hydrogen ion concentration is significantly lower than the initial concentration of benzoic acid, underscoring the weak nature of benzoic acid in aqueous solutions. Understanding this process is crucial for accurately predicting the pH of weak acid solutions, which is a fundamental concept in chemistry.