Chloroacetic acid, ClCH2COOH, has a pKa of 2.87. What are [H3O+], pH, [ClCH2COO−], and [ClCH2COOH] in 1.55 M ClCH2COOH?

See explanation below

Explanation:

first to all, this is an acid base reaction where the chloroacetic acid is being dissociated in water. Therefore, is an equilibrium reaction.

ClCH₂COOH has a pKa of 2.87 so, the Ka would be:

pKa = -logKa ---> Ka = antlog(-pka)

Ka = antlog(-2.87)

Ka = 1.35x10⁻³

Now that we know the Ka, we need to write the chemical reaction and then, an ICE chart:

      ClCH₂COOH + H₂O <----------> ClCH₂COO⁻ + H₃O⁺    Ka = 1.35x10⁻³

i)            1.55                                             0                0

c)             -x                                             +x               +x

e)         1.55-x                                            x                 x

Writting now the equilibrium reaction:

Ka = [H₃O⁺] [ClCH₂COO⁻] / [ClCH₂COOH]

Replacing the values of the chart:

1.35x10⁻³ = x² / 1.55-x

1.35x10⁻³(1.55-x) = x²

2.0925x10⁻³ - 1.35x10⁻³x = x²

x² + 1.35x10⁻³x - 2.0925x10⁻³ = 0  --> a = 1; b = 1.35x10⁻³x; c = 2.0925x10⁻³

From here we use the general equation for solve x in a quadratic equation which is:

x = -b±√(b² - 4ac) / 2a

Replacing the values we have:

x = -1.35x10⁻³ ±√(1.35x10⁻³)² - 4*1*(-2.0925x10⁻³) / 2

x = -1.35x10⁻³ ±√(8.37x10⁻³) / 2

x = -1.35x10⁻³ ± 0.091 / 2

x1 = -1.35x10⁻³ + 0.091 / 2 = 0.045 M

x2 = -1.35x10⁻³ - 0.091 / 2 = -0.046 M

In this case, we will take the positive value of x, in this case, x1.

With this value, the equilibrium concentrations are the following:

[H₃O⁺] = [ClCH₂COO⁻] = 0.045 M

[ClCH₂COOH] = 1.55 - 0.045 = 1.505 M

Finally the pH:

pH = -log[H₃O⁺]

pH = -log(0.045)

pH = 1.35

just did the assignment and the answer was #1 +2 n