Help with chem homework

Question

A H2SO4 solution of unknown molarity is titrated with a 1.209 M NaOH solution. The titration requires 42.27 mL of the NaOH solution to reach the equivalent point with 25.00 mL of the H2SO4 solution. What is the molarity of the acid solution?

Answer 1

Short answer: the sulfuric acid is 1.022 M.

Everything here turns on one line you have to write before you touch a calculator, because sulfuric acid is diprotic and this titration is not 1:1:

H2SO4 + 2 NaOH -> Na2SO4 + 2 H2O

Step 1 - moles of base actually delivered. Volume in liters times molarity:

n(NaOH) = 0.04227 L x 1.209 mol/L
        = 0.051104 mol NaOH

Step 2 - convert to moles of acid using the coefficients. Each mole of H2SO4 consumes two moles of NaOH, so divide by 2:

n(H2SO4) = 0.051104 mol NaOH x (1 mol H2SO4 / 2 mol NaOH)
         = 0.025552 mol H2SO4

Step 3 - divide by the acid volume, not the base volume.

M = 0.025552 mol / 0.02500 L
  = 1.0221 mol/L
  = 1.022 M H2SO4

Four significant figures, since 1.209, 42.27 and 25.00 all carry four.

A second route that genuinely checks the first. Work in equivalents instead, which puts the factor of 2 in a different place, so agreement means something:

eq of H+ neutralized = 51.104 mmol
N(acid) = 51.104 meq / 25.00 mL = 2.0442 N
M(acid) = 2.0442 N / 2 eq per mol = 1.022 M

The three wrong answers this problem is built to produce.

• 2.044 M - the balanced equation was never written and the titration was treated as 1:1. This is the most common submission by a wide margin.
• 0.5110 M - the factor of 2 got applied twice, once as "it is diprotic" and again from the coefficient. The balanced equation has already absorbed the diprotic factor; that is exactly where the 2 in front of NaOH came from. Use the coefficients or use equivalents, never both.
• 0.6045 M - right moles of acid, then divided by the 42.27 mL of base. Molarity always wants the volume of the solution whose concentration you are naming.

A free direction check before any arithmetic. The base volume is 1.6908 times the acid volume. If the reaction were 1:1, the acid would have to be about 1.69 times more concentrated than the base. Because each mole of acid hands over two protons, halve that, and the acid should land a little below the base concentration of 1.209 M. 1.022 M does. 2.044 M does not, and you can see that before doing a single conversion.

Two small things worth knowing. The problem says "equivalent point" and means the equivalence point, the moment the moles delivered exactly satisfy the equation. And sulfuric acid gives up its second proton much more reluctantly than its first (Ka2 is about 1.2 x 10^-2), but a strong base still strips both off together, so you get one sharp endpoint rather than two visible steps. The salt left behind, Na2SO4, is neutral because sulfate is an extraordinarily weak base, which puts the equivalence point essentially at pH 7.