Answer :
To find the pH of the buffer after adding H+, convert the given mass of the weak base to moles, adjust concentrations for the reaction with H+, and apply the Henderson-Hasselbalch equation using the pKa value calculated from the given pKb.
To calculate the pH of the buffer after adding 0.300 mol of H+, we need to consider the reaction of H+ with the weak base ((CH3)2NH). (CH3)2NH will react with H+ to form its conjugate acid (CH3)2NH2+, decreasing its concentration and increasing the concentration of the conjugate acid.
First, we convert the mass of (CH3)2NH2 to moles. The molar mass of (CH3)2NH2 is 45.08 g/mol, so 59.1 g corresponds to 59.1 g / 45.08 g/mol = 1.310 moles of (CH3)2NH2. In the reaction, 0.300 moles of H+ will be consumed, and the same amount of (CH3)2NH2+ will be formed.
The Henderson-Hasselbalch equation is used to calculate the pH of a buffer solution:
pH = pKa + log([base]/[acid])
Where pKb of (CH3)2NH is given, and the pKa can be found using the relation pKa + pKb = 14. Solving this we get pKa = 14 - pKb. After using the equilibrium concentrations in the formula, we can calculate the pH of the buffer.
