What volume of 0.100 M #"HCl"# solution is needed to neutralize 50.0 mL of 0.350 M #"KOH"#?

Question

Noah Aldrich · Accepted Answer

#"175 mL"# Hydrochloric acid, #"HCl"#, and potassium hydroxide, #"KOH"#, react in a #1:1# mole ratio to produce aqueous potassium chloride, #"KCl"#, and water. #"HCl"_ ((aq)) + "KOH"_ ((aq)) -> "KCl"_ ((aq)) + "H"_ 2"O"_ ((l))# This means that a complete neutralization requires equal numbers of moles of hydrochloric acid, i.e. of hydronium cations, #"H"_3"O"^(+)#, and of potassium hydroxide, i.e. of hydroxide anions, #"OH"^(-)#. As you know,m molarity is defined as the number of moles of solute present in #"1 L"# of solution. Now, notice that the potassium hydroxide solution, which has a molarity of #"0.350 M"#, is #(0.350 color(red)(cancel(color(black)("M"))))/(0.100color(red)(cancel(color(black)("M")))) = color(red)(3.5)# times more concentrated than the hydrochloric acid solution, which has a molarity of #"0.100 M"#. In other words, for the same volume of both solutions, the potassium hydroxide solution contains #color(red)(3.5)# times more moles of solute than the hydrochloric acid solution. This means that in order to have equal numbers of moles of both solutes, you need to have a volume of hydrochloric acid solution that is #color(red)(3.5)# times bigger than the volume of the sodium hydroixde solution. Since the sodium hydroixde solution has a volume of #"50.0 mL"#, it follows that the volume of hydrochloric acid needed will be #V_"HCl" = color(red)(3.5) xx "50.0 mL" = color(green)(|bar(ul(color(white)(a/a)color(black)("175 mL")color(white)(a/a)|)))-># to three sig figs

Luna Chen · Answer

undefined $V_{\text{HCl}} = \frac{(\text{Molarity}_{\text{KOH}}) \times (\text{Volume}_{\text{KOH}})}{\text{Molarity}_{\text{HCl}}}$

$V_{\text{HCl}} = \frac{(0.350 \, \text{M}) \times (0.050 \, \text{L})}{0.100 \, \text{M}}$

$V_{\text{HCl}} = 0.175 \, \text{L} $ or $175 \, \text{mL}$.