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Chloroacetic acid (ClCH2COOH) is a weak acid with Ka = 1.4 x 10-3. Calculate the pHof a 0.010 M solution of this acid in aqueous solution.

Question

Chloroacetic acid (ClCH₂COOH) is a weak acid with K<sub>a</sub> = 1.4 x 10<sup>-3</sup>. Calculate the pH of a 0.010 M solution of this acid in aqueous solution.

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Solution

To calculate the pH of a 0.010 M solution of chloroacetic acid, we can use the formula for the ionization constant of a weak acid (Ka) and the definition of pH. Here are the steps:

  1. Write the ionization equation for the weak acid: ClCH2COOH ⇌ ClCH2COO- + H+

  2. Write the expression for the ionization constant (Ka): Ka = [ClCH2COO-][H+] / [ClCH2COOH]

  3. Assume that the acid ionizes to a small extent, so the concentration of the acid at equilibrium is approximately equal to the initial concentration. Also, the concentrations of the ions are equal because for every one molecule of acid that ionizes, one ClCH2COO- ion and one H+ ion are produced. So, let x be the concentration of H+ ions: Ka = x^2 / (0.010 - x)

  4. Because the acid ionizes to a small extent, we can assume that x is much smaller than 0.010, so the equation simplifies to: Ka = x^2 / 0.010

  5. Solve for x, which is the concentration of H+ ions: x = sqrt(Ka * 0.010) = sqrt(1.4 x 10^-3 * 0.010) = 3.74 x 10^-3 M

  6. Use the definition of pH to calculate the pH of the solution: pH = -log[H+] = -log(3.74 x 10^-3) = 2.43

So, the pH of a 0.010 M solution of chloroacetic acid is approximately 2.43.

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