ACT Science: Perform Titration Calculations Using Molarity and Mole Ratios

Titration: A technique to determine the concentration of an unknown solution. Procedure: Add a known solution (titrant) drop by drop until the reaction reaches equivalence (the point where moles of titrant equal moles of analyte, accounting for stoichiometry). Formula: M₁V₁=M₂V₂ only works when the balanced equation has a 1:1 mole ratio. Example: Titrating HCl with NaOH (1:1 ratio). If 25 mL of 0.1 M HCl is titrated with NaOH, and 20 mL of NaOH is used at equivalence, then (0.1)(25)=M_NaOH(20), so M_NaOH=0.125 M. When the ratio isn't 1:1, multiply by the stoichiometric coefficients before simplifying.

On ACT Science, passages describe titration experiments and ask you to calculate unknown molarity or volume using this formula.

Error 1: Using the formula when the mole ratio isn't 1:1. If the balanced equation is 2HCl+Ca(OH)₂→..., you must account for the 2:1 ratio. Error 2: Confusing which solution is M₁ and V₁. Typically, M₁V₁ is the unknown concentration and volume; M₂V₂ is the titrant (known). Error 3: Using incorrect units. Ensure all volumes are in the same units (mL to mL, L to L). Write out the balanced equation first and identify the mole ratio.

Verification: After calculating, ask: Does the answer make sense? If you're titrating a weak acid with a strong base, you expect the base concentration to be lower (you need more base). Check your logic.

Problem 1 (1:1 ratio): 20 mL of 0.5 M HCl is titrated with NaOH. At equivalence, 25 mL of NaOH is used. M_NaOH=(0.5×20)/25=0.4 M. Problem 2 (2:1 ratio): H₂SO₄ (20 mL, 0.1 M) is titrated with NaOH. Balanced: H₂SO₄+2NaOH→... If 50 mL of NaOH reaches equivalence, find M_NaOH. Moles H₂SO₄=(0.1)(20)=2 mmol. Moles NaOH at equivalence=2×2=4 mmol (2:1 ratio). M_NaOH=4/(50)=0.08 M. Complete both problems; verify the second by noting that NaOH concentration is lower (1:2 ratio requires more NaOH by concentration).

Challenge: A 30 mL sample of Ca(OH)₂ is titrated with 0.2 M HCl. At equivalence, 60 mL of HCl is used. Balanced: Ca(OH)₂+2HCl→... Find M_Ca(OH)₂. Moles HCl=(0.2)(60)=12 mmol. Moles Ca(OH)₂=12/2=6 mmol. M_Ca(OH)₂=6/30=0.2 M.

ACT Science includes titration because it's a fundamental laboratory technique. Understanding titration tests your grasp of molarity, stoichiometry, and experimental design. Expect 1-2 titration questions per Science section, often as calculations requiring the formula and stoichiometric adjustment.

Spend 20 minutes this week solving 5-6 titration problems with different mole ratios. By test day, you'll quickly identify the balanced equation, determine the mole ratio, and calculate unknown molarity or volume without hesitation.