Carbonic acid is a weak diprotic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\) with \(K_{a_{1}}=4.43 \times 10^{-7}\) and \(K_{\mathrm{a}_{2}}=4.73 \times 10^{-11} .\) The equiv- alence points for the titration come at approximately pH 4 and 9. Suitable indicators for use in titrating carbonic acid or carbonate solutions are methyl orange and phenolphthalein. (a) Sketch the titration curve that would be obtained in titrating a sample of \(\mathrm{NaHCO}_{3}(\mathrm{aq})\) with \(1.00 \mathrm{M} \mathrm{HCl}\) (b) Sketch the titration curve for \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) with 1.00 M HCl. (c) What volume of \(0.100 \mathrm{M} \mathrm{HCl}\) is required for the complete neutralization of \(1.00 \mathrm{g} \mathrm{NaHCO}_{3}(\mathrm{s}) ?\) (d) What volume of \(0.100 \mathrm{M} \mathrm{HCl}\) is required for the complete neutralization of \(1.00 \mathrm{g} \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s}) ?\) (e) A sample of NaOH contains a small amount of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) For titration to the phenolphthalein end point, \(0.1000 \mathrm{g}\) of this sample requires \(23.98 \mathrm{mL}\) of \(0.1000 \mathrm{M} \mathrm{HCl} .\) An additional \(0.78 \mathrm{mL}\) is required to reach the methyl orange end point. What is the percent \(\mathrm{Na}_{2} \mathrm{CO}_{3},\) by mass, in the sample?

Step by step solution

01

Sketch the titration curve for \(\mathrm{NaHCO}_{3}(\mathrm{aq})\)

In a weak base-strong acid titration of \(\mathrm{NaHCO}_{3}\) with \T1.00\T0 \mathrm{M} \mathrm{HCl}, the curve would start high (basic) and then drop down slowly till the half equivalence point. From there it would drop sharply (at the equivalence point) and then flatten out again, ending up at low pH (acidic).

02

Sketch the titration curve for \(\mathrm{Na}_{2}\mathrm{CO}_{3}(\mathrm{aq})\)

The titration curve for a \(\mathrm{Na}_{2}\mathrm{CO}_{3}(\mathrm{aq})\) and \T1.00 \T0 \mathrm{M} \mathrm{HCl} titration would depict two equivalence points as sodium carbonate is a diprotic base and can accept two protons. Starting from basic, the pH decreases till the first equivalence point, then increases and decreases again till the second equivalence point, and finally ends in an acidic pH environment.

03

Calculate volume of HCl for complete neutralization of \(\mathrm{NaHCO}_{3}(\mathrm{s})\)

Calculate the molar mass of \(\mathrm{NaHCO}_{3}\), which yields approximately \( 84 \,g/mol\). Then determine the moles of \(\mathrm{NaHCO}_{3}\) found in \(1.00\,g\) with the equation \(moles = mass/molar mass\). Afterwards, as each mole of \(\mathrm{NaHCO}_{3}\) reacts with one mole of HCl, the amount of moles of HCl needed for neutralization is the same. Using the molarity equation \(M = mol/L\), the required volume of HCl can be determined.

04

Calculate volume of HCl for complete neutralization of \(\mathrm{Na}_{2}\mathrm{CO}_{3}(\mathrm{s})\)

Similar approach can be deployed as in Step 3. Here, the molar mass of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is about \( 106 \,g/mol\). One mole of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) reacts with two moles of HCl, so the volume of HCl can be calculated using the molarity equation.

05

Calculate the percent \(\mathrm{Na}_{2}\mathrm{CO}_{3}\)

The amount of NaOH is calculated by subtracting the volume of HCL required for titration to the phenolphthalein end point from the total volume. Molar mass of NaOH is used to calculate the grams of NaOH. The grams of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is calculated from the known mass of the sample. Lastly, the percent of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is calculated using the equation \(percent\, mass= (mass\, of\, \mathrm{Na}_{2}\mathrm{CO}_{3}/total\, mass) \times 100%\)

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