Answer
$V=68.7\ mL$
Work Step by Step
By the Henderson-Hasselbach Equation:
$pH=pKa+\log([A^-]/[HA])$
$[A^-]=[OH^-]=1.00\ M\times V/(V+250.0)$
$[HA]\approx0.5\ M\times 250.0\ mL/(V+250.0)\ mL$
$4.5=4.76+\log(V/125)$
$V=68.7\ mL$
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