answer
we first need to determine the balanced chemical reaction. which is :
Ca(OH)₂ + 2HCl > CaCl₂ + 2H₂O
now that we have the balanced reaction we can find the number of mols of HCl using the equation
C = n/v
and when we rearange the equation, we get:
n = CxV
= 0.0300M x 0.0782 L
= 0.0023 mols
we know from the balanced equation that the mol ratio of Ca(OH)₂ : HCl is 1 :2
therefor 1/2 x 0.0023 = 0.0012 mols of Ca(OH)₂ will be required
the volume then becomes:
v = n/C
= 0.0012/0.0200 M
= 0.0586L
= 58.6 mL
58.6 mL will be required to neutralize the acid