The pH of a buffer solution is given by:

pH = pKa + log [(A-)/(HA)], where (A-) is the concentration of the conjugate base and (HA) is the concentration of the acid.And pKa is the acid dissociation constant which is given as 4.74.

We have to produce a buffer solution with a pH of 5.05. The acid solution given has 10 mmol of acetic acid. So, we have (HA) = 10 mmol. The required number of milimoles of acetate to be added to this solution can be found using the equation:

5.05 = 4.74 + log(10) [ (A-)/ 10]

=> 5.05 - 4.74 = log(10) [(A-)/10]

=> 0.31 = log(10) [ (A-)/10]

=> [(A-)/ 10] = 10^0.31

=> (A-) = 10*10^0.31

=> (A-) = 10^1.31

=> (A-) = 20.417

**The number of milimoles of acetate to be added is 20.417.**