the balanced equation for the reaction is
Ca(OH)₂ + 2HNO₃ ---> Ca(NO₃)₂ + 2H₂O
Molar ratio of Ca(OH)₂ to HNO₃ is 1:2
Number of moles of Ca(OH)₂ reacted - 0.5 moldm⁻³ x 50.0 x 10⁻³ dm³
number of Ca(OH)₂ moles - 0.025 mol
according to the molar ratio
1 mol of Ca(OH)₂ reacts with 2 mol of HNO₃
therefore 0.025 mol of Ca(OH)₂ reacts with - 2 x 0.025 = 0.05 mol of HNO₃
there are 0.05 mol of HNO₃ in 125 mL
and concentration = number of moles / volume in 1 dm³
concentration = 0.05 mol / 125 x 10⁻³ dm
concentration of HNO₃ = 0.4 mol/dm³