You'd need #"41.7 mL"# of citric acid for this particular buffer.

You need to find two equations that you can use to determine the volume of the citric acid solution. The first one will be

#V_("buffer") = V_1 + V_2 = "125 mL" = "0.125 L"# **(1)**

The total volume of the buffer solution will be equal to the sum of the two solutions mixed together - #V_1# is the volume of the citric acid solution, while #V_2# is the volume of the sodium citrate solution.

Next, use the **Henderson-Hasselbalch equation**

#pH_("solution") = pKa + log(([C_6H_5O_7^(3-)])/([C_6H_8O_7]))#

#3.45 = 3.15 + log(([C_6H_5O_7^(3-)])/([C_6H_8O_7])) => ([C_6H_5O_7^(3-)])/([C_6H_8O_7]) = 2.0# **(2)**

Now, the concentration of the citric acid in the buffer is equal to

#C_("citric") = n_("citric")/(V_1+V_2)#

The number of moles of citric acid can be determined from the initial concentration

#n_("citric") = C * V_1 = "0.150 M" * V_1 = 0.150 * V_1#

Likewise, the concentration of the citrate is

#C_("citrate") = n_("citrate")/(V_1 + V_2)#, and

#n_("citrate") = C * V_2 = "0.150 M" * V_2 = 0.150 * V_2#

Plug all of this into equation **(2)** and you'll get

#(0.150 * V_2)/(V_1 + V_2) * (V_1 + V_2)/(0.150 * V_1) = 2.0#, or

#V_2/V_1 = 2 => V_2 = 2 * V_1#. Plug this into equation **(1)**

#V_1 + 2 * V_1 = 0.125 => V_1 = 0.125/3 = 0.0417#, which means that

#V_2 = 0.125 - 0.0417 = 0.0833#

Therefore, the volume for the citric acid solution will need to be

#V_1 = "0.0417 L" = "41.7 mL"#