Molarity, #"M"#, is a measure of concentration of a solution, and represents #"mol solute"/"1L solution"#. Milliliters need to be converted to liters. The following is the equation needed to answer this question:
#C_1V_1=C_2V_2#
where concentration is #C# and volume is #V#.
Given/Known Information
#C_1="4.2 M KOH"="4.2 mol KOH"/"L"#
#V_1="45.0 mL"xx"1 L"/"1000 mL"="0.0450 L"#
#V_2="250 mL+45.0 mL"="295 mL"xx"1 L"/"1000 mL"="0.295 L"#
Unknown: #C_2#
Solution
Rearrange the equation to isolate #C_2#. Insert the known values and solve.
#C_2=(C_1V_1)/V_2#
#C_2=(4.2"mol KOH"/"L"xx0.0450color(red)cancel(color(black)("L")))/(0.295color(red)cancel(color(black)("L")))="64 mol KOH"/"L"="64 M KOH"# rounded to two significant figures
