Question

For many weak acid or weak base calculations, you can use a simplifying assumption to avoid solving quadratic equations.

$$ K_{\mathrm{a}}=\frac{x^{2}}{[\mathrm{HA}]-x} \approx \frac{x^{2}}{[\mathrm{HA}]} $$

Classify these situations by whether the assumption is valid or the quadratic formula is required.

Answer 1

let us calculate % dissociation in each solution

If it is equal to or less than 5%, the approximation is valid

when,

a) [HA] = 0.01 M

Ka = 1 x 10^-5 = x^2/0.01

x = 3.16 x 10^-4 M

% dissociation = 3.16 x 10^-4 x 100/0.01 = 3.2%

valid approximation

b) [HA] = 0.1 M

Ka = 1 x 10^-3 = x^2/0.1

x = 0.01 M

% dissociation = 0.01 x 100/0.1 = 10%

in-valid approximation

c) [HA] = 1 M

Ka = 1 x 10^-3 = x^2/0.

x = 0.0316 M

% dissociation = 0.0316 x 100/1 = 3.2%

valid approximation

d) [HA] = 0.001 M

Ka = 1 x 10^-5 = x^2/0.001

x = 1 x 10^-4 M

% dissociation = 1 x 10^-4 x 100/0.001 = 10%

in-valid approximation

e) [HA] = 0.01 M

Ka = 1 x 10^-4 = x^2/0.01

x = 1 x 10^-3 M

% dissociation = 1 x 10^-3 x 100/0.01 = 10%

in-valid approximation

So we get a) and c) have valid approximation and b, d, and e) need quadratic equation

--

Assumption valid

a) [HA] = 0.01 M

Ka = 1 x 10^-5

c) [HA] = 1 M

Ka = 1 x 10^-3

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Quadratic equation is required

b) [HA] = 0.1 M

Ka = 1 x 10^-3

d) [HA] = 0.001 M

Ka = 1 x 10^-5

e) [HA] = 0.01 M

Ka = 1 x 10^-4