Question

A chemistry student weighs out 0.0634g of formic acid HCHO2 into a 250.mL volumetric flask and dilutes to the mark with distilled water. He plans to titrate the acid with 0.1800M NaOH solution. Calculate the volume of NaOH solution the student will need to add to reach the equivalence point. Be sure your answer has the correct number of significant digits.

Answer 1

7.65 × 10⁻³ L.

3 sig. fig. as in the mass of formic acid.

Explanation

How many moles of formic acid?

Relative atomic mass from a modern periodic table:

• H- 1.008,
• C- 12.011, and
• O- 15.999.

Molar mass of formic acid $\text{HCOOH}$:

$1.008 + 12.011 + 2\times 15.999 + 1.008 = 46.025\;\text{g}\cdot \text{mol}^{-1}$.

Number of moles of formic acid molecules in the 0.0634 gram sample:

$\displaystyle n = \frac{m}{M} = \frac{0.0634}{46.025} = 1.37751\times 10^{-3}\;\text{mol}$.

Keep at least one extra sig. fig. to avoid rounding errors.

How many moles of NaOH?

It takes one $\text{OH}^{-}$ ion to neutralize each carbonyl group $-\text{COOH}$.

There's one carbonyl group in each formic acid $\text{H-}\text{COOH}$ molecule. Each formula unit of NaOH supplies one $\text{OH}^{-}$ ion. As a result, it takes one mole formula units of NaOH to neutralize one mole formic acid molecules.

There are $1.37751\times 10^{-3}\;\text{mol}$ of formic acid in the volumetric flask. It will take the same number of NaOH formula units to reach the equivalence point.

How many liters of NaOH?

$\displaystyle V = \frac{n}{c} = \frac{1.37751\times 10^{-3}\;\text{mol}}{0.1800\;\text{M}}= \frac{1.37751\times 10^{-3}\;\text{mol}}{0.1800\;\text{mol}\cdot\text{L}^{-1}} = 7.65\times 10^{-3}\;\text{L}$.

How many significant figures?

Number of sig. fig. in data involved in the calculation:

• 3 in the mass of the formic acid,
• 4 in the concentration of NaOH.

Take the least number of sig. fig. as the number of sig. fig. in the answer. As a result, the volume of NaOH should be rounded to three sig. fig.