Calculate [H+] & [CHCl2COO-] in a solution of 0.01M HCl and 0.01M of CHCl2COOH. Take (Ka = 2.55 * 10^-2

To find the concentrations of hydrogen ions \([H^+]\) and the chloroacetate ion \([CHCl_2COO^-]\) in a solution containing 0.01 M HCl and 0.01 M chloroacetic acid (CHCl2COOH), we need to consider the dissociation of both the strong acid (HCl) and the weak acid (CHCl2COOH). Let's break this down step by step.

Step 1: Understanding the Contributions of HCl

HCl is a strong acid, which means it completely dissociates in solution. Therefore, the concentration of hydrogen ions from HCl can be calculated directly:

• [H⁺] from HCl = 0.01 M

Step 2: Analyzing the Weak Acid CHCl2COOH

Chloroacetic acid (CHCl2COOH) is a weak acid that partially dissociates in solution. The dissociation can be represented as follows:

CHCl2COOH ⇌ H⁺ + CHCl2COO^-

The acid dissociation constant \(K_a\) for chloroacetic acid is given as \(2.55 \times 10^{-2}\). We can set up an expression for \(K_a\):

Step 3: Setting Up the Equilibrium Expression

The equilibrium expression for the dissociation of CHCl2COOH is:

K_a = \frac{[H⁺][CHCl₂COO^-2COOH]}

Let \(x\) be the concentration of \(H^+\) and \(CHCl_2COO^-\) produced from the dissociation of CHCl2COOH. At equilibrium, we have:

• [H⁺] = 0.01 + x
• [CHCl₂COO^-] = x
• [CHCl₂COOH] = 0.01 - x

Step 4: Plugging into the Ka Expression

Substituting these values into the \(K_a\) expression gives:

2.55 \times 10^{-2} = \frac{(0.01 + x)(x)}{(0.01 - x)}

Since \(x\) is expected to be small compared to 0.01 M, we can simplify the equation by assuming \(0.01 + x \approx 0.01\) and \(0.01 - x \approx 0.01\). This leads to:

2.55 \times 10^{-2} = \frac{(0.01)(x)}{0.01}

Thus, we can simplify further:

2.55 \times 10^{-2} = x

Step 5: Calculating [H⁺] and [CHCl₂COO^-]

From our calculations, we find:

• [CHCl₂COO^-] = x = 2.55 \times 10^{-2} M
• [H⁺] = 0.01 + 2.55 \times 10^{-2} = 0.01 + 0.0255 = 0.0355 M

Final Results

In summary, the concentrations in the solution are:

• [H⁺] = 0.0355 M
• [CHCl₂COO^-] = 2.55 \times 10^{-2} M

This analysis shows how the strong acid contributes significantly to the hydrogen ion concentration, while the weak acid's dissociation adds a smaller amount to the total hydrogen ion concentration.