We're asked to find the volume (in "mL") of a 0.45M "HCl soln" that will neutralize 25.0 "mL" of a 1.00M "KOH soln".
To do this, let's first write the chemical equation for the reaction:
"HCl"(aq) + "KOH"(aq) rarr "KCl"(aq) + "H"_2"O"(l)
What we can do is use the molarity equation to find the number of moles of "KOH" that are present:
"molarity" = "mol solute"/"L soln"
"mol solute" = ("molarity")("L soln")
"mol KOH" = (1.00"mol"/(cancel("L")))overbrace((0.0250cancel("L")))^"converted to liters" = color(red)(0.0250 color(red)("mol KOH"
Now, we can use the coefficients of the chemical equation to find the relative number of moles of "HCl":
color(red)(0.0250)cancel(color(red)("mol KOH"))((1color(white)(l)"mol HCl")/(1cancel("mol KOH"))) = color(red)(0.0250 color(red)("mol HCl"
Lastly, we can use the molarity equation again to find the volume of "HCl" solution:
"molarity" = "mol solute"/"L soln"
"L soln" = "mol solute"/"molarity"
"L HCl soln" = (color(red)(0.0250)cancel(color(red)("mol HCl")))/(0.45(cancel("mol"))/"L") = color(blue)(0.056 color(blue)("L" = color(blue)(ul(56color(white)(l)"mL"
