Question

A mixture of Na2CO3 and NaHCO3 has a mass of 82.0 g . It is dissolved in 1.00 L of water and the pH is found to be 9.92. Find the mass of NaHCO3 in the mixture.

Answer 1

Where negative sign signifies spontaneous process.

Buffer solutions are the solutions which can resist the change in the pH up to some extent.

The Henderson-Haasselbalch equation for the reaction can be written as:

The system of sodium carbonate and sodium bicarbonate will behave as buffer in which the acid will be Bicarbonate ion and carbonate is the conjugate base.

Given:

Total mass of mixture of sodium carbonate and sodium bicarbonate = 82.0 g

Let the mass of sodium carbonate = x g

The mass of sodium bicarbonate = (82.0 – x) g

Calculation of concentration of Sodium carbonate:

Molar mass of sodium carbonate = 106 g/mol

Mass taken = x g

Volume of the solution = 1L

Concentration:

[Na₂CO₃] = [CO₃^2-]

So,

Similarly,

Calculation of concentration of Sodium bicarbonate:

Molar mass of sodium carbonate = 84 g/mol

Mass taken = (82.0 – x) g

Volume of the solution = 1L

Concentration:

Also,

[NaHCO₃] = [HCO₃^-]

So,

Ka of Bicarbonate ion (Ka₂ of carbonic acid) = 5.61*10^-11

Also, pKa is the negative of the logarithm of Ka value.

Given,

pH= 9.92

The mass of sodium bicarbonate = (82.0 – 30.4339) g = 51.566 g