Calculate the ph of a 0.200 m nach3co2 solution. ka for acetic acid, ch3co2h, is 1.8 * 10-5.

Annswer : The correct answer is : pH = 9.03

To calculating pH of NaCH₃CO₂, we need to do following steps:

Step 1 : Find kb for NaCH₃CO₂

Since NaCH₃CO₂ and CH₃CO₂H are conjugates base - acid pair, we can calculate kb for NaCH₃CO₂ from ka of CH₃CO₂H using relation:

Kw = ka x kb,

Where Kw = ionic product of water = 1 x 10 ⁻¹⁴

ka = dissociation constant of acid = 1.8 x 10⁻⁵

kb = dissociation constant of base

Plugging value of kw and ka in formula:

1 x 10 ⁻¹⁴ = 1.8 x 10⁻⁵ x kb

Dividing both side by 1.8 x 10⁻⁵

1 x 10⁻¹⁴ / 1.8 x 10⁻⁵ = 1.8 x 10⁻⁵ / 1.8 x 10⁻⁵ x kb

kb = 5.6 x 10 ⁻¹⁰

Step 2 : Setting ICE (Initial, change and equilibrium concentration) Table.

NaCH₃CO₂is strong base, so its ion CH₃CO₂⁻ undergoes hydrolysis and gives OH⁻ as follows:

CH₃CO₂⁻ + H₂O → CH₃CO₂H + OH⁻.

Initial (M) 0.200 - 0 0

Change (M) - x - + x + x

Equilibrium (M) 0.200 - x x x

Step 3: Writing kb for reaction

kb = [CH₃CO₂H] [OH⁻] / [CH₃CO₂⁻ ]

Plugging equilibrium concentrations in above equation

5.6 x 10 ⁻¹⁰ = [ x] [x] / [0.200 - x ]

Neglecting x from 0.200 - x

5.6 x 10 ⁻¹⁰ = [ x²] / [0.200 ]

Multiplying both side by 0.200

5.6 x 10 ⁻¹⁰ x 0.200 = [ x²] [0.200 ] / [0.200 ]

x² = 1.12 x 10⁻10

x = 1.06 x 10⁻⁵

[CH₃CO₂H] = [OH⁻] = x = 1.06 x 10⁻⁵

Step 4 : Calculating pOH

pOH = - log [OH-]

pOH = - log [ 1.06 x 10⁻⁵ ]

pOH = 4.97

Step 5: Calculating pH

Relation between pH and pOH : pH + pOH = 14

pH = 14 - pOH = 14 - 4.97

pH = 9.03