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Chapter 12: Problem 31

A \(50.00-\mathrm{mL}\) volume of aqueous phosphoric acid, \(\mathrm{H}_{3} \mathrm{PO}_{4}\), is titrated using \(0.100 \mathrm{M}\) \(\mathrm{NaOH}\) and an indicator that turns color only after all the phosphoric acid protons have reacted with \(\mathrm{OH}^{-}\) ions. The solution turns color when \(38.60 \mathrm{~mL}\) of base has been added. What is the molar concentration of the phosphoric acid?

Short Answer

Expert verified
The molar concentration of the phosphoric acid can be found by first calculating the moles of NaOH: \(moles_{NaOH} = 38.60\,mL * \frac{0.100\,mol}{1000\,mL} = 0.00386\,mol\). Since phosphoric acid is triprotic, it reacts with three moles of NaOH for every mole of H₃PO₄, so \(moles_{H_{3}PO_{4}} = \frac{0.00386\,mol}{3} = 0.00129\,mol\). Finally, the concentration of H₃PO₄ is found by dividing the moles of H₃PO₄ by the volume of the solution in liters: \(concentration_{H_{3}PO_{4}} = \frac{0.00129\,mol}{0.050\,L} = 0.0258\,M\).

Step by step solution

01

Find moles of NaOH

First, we need to find the moles of NaOH added to the phosphoric acid solution. We can do this using the given volume and concentration of the NaOH solution: Moles of NaOH = volume of NaOH (in L) × concentration of NaOH (in mol/L) Note that the volume of NaOH should be converted from mL to L by dividing by 1000.
02

Calculate moles of H₃PO₄

Now that we have the moles of NaOH, we need to find the moles of H₃PO₄ that reacted with NaOH. Since phosphoric acid is a triprotic acid, we know that 3 moles of NaOH are needed to fully react with 1 mole of H₃PO₄. So we can set up the following equation: Moles of H₃PO₄ = moles of NaOH ÷ 3
03

Calculate concentration of H₃PO₄

Finally, using the moles of H₃PO₄ and the given volume of the phosphoric acid solution, we can calculate the molar concentration of H₃PO₄: Concentration of H₃PO₄ = moles of H₃PO₄ ÷ volume of H₃PO₄ (in L) Note that the volume of H₃PO₄ should be converted from mL to L by dividing by 1000.

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