Michael S. answered • 13d
B.S. in Chemistry, Indiana University; Organic Chem Teaching Intern
Base: 2.42 × 10−3 mol | HCl: 4.83 × 10−3 mol | [HCl] = 0.193 M
The balanced equation is the whole problem
Ca(OH)2(aq) + 2 HCl(aq) → CaCl2(aq) + 2 H2O(l)
Calcium hydroxide supplies two hydroxide ions per formula unit, so it neutralises two HCl. That factor of 2 is what this question is really checking — skip it and every answer after part 1 is off by half.
Part 1 — moles of base
n = MV = (0.206 mol/L)(0.01173 L) = 2.42 × 10−3 mol Ca(OH)2
Note it is the titrant volume, 11.73 mL, that goes here — that is the quantity the burette measured.
Part 2 — moles of acid
n(HCl) = 2 × 2.42 × 10−3 = 4.83 × 10−3 mol
At the endpoint all the acid has been consumed, so this is exactly how much HCl was in the flask to begin with.
Part 3 — molarity of the acid
Now switch to the analyte volume, the 25.00 mL that was in the flask:
M = n/V = 4.83 × 10−3 mol / 0.02500 L = 0.193 M
Swapping the two volumes is the most common error here. The rule: moles of titrant come from the burette reading; molarity of the unknown comes from the pipetted sample volume.
Does the answer make sense?
It took only 11.73 mL of base to neutralise 25.00 mL of acid — less than half the volume — yet the acid is still less concentrated than the base (0.193 vs 0.206 M). That is not a contradiction: each mole of Ca(OH)2 does double duty. Run the check the other way and it confirms itself: 0.193 M × 25.00 mL = 4.83 mmol of acid, needing 2.42 mmol of base, which at 0.206 M is 11.73 mL ✓
Same problem with NaOH instead: the ratio would be 1:1 and the acid would come out at 0.0967 M — exactly half. That comparison is worth doing once, because it makes the role of the coefficient concrete rather than something you remember to look for.
