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Chapter 12: Problem 30

A \(30.00-\mathrm{mL}\) volume of aqueous sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), is titrated using \(0.200 \mathrm{MaOH}\) and an indicator that turns color only after all the sulfuric acid protons have reacted with \(\mathrm{OH}^{-}\) ions. The solution turns color when \(48.32 \mathrm{~mL}\) of base has been added. What is the molar concentration of the sulfuric acid?

Short Answer

Expert verified
The molar concentration of the aqueous sulfuric acid is 0.1611 M.

Step by step solution

01

Balanced equation

The balanced chemical equation for the titration between sulfuric acid and sodium hydroxide is: \[2 \mathrm{NaOH} + \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4} + 2 \mathrm{H}_{2} \mathrm{O}\] Step 2: Calculate the number of moles of NaOH added during titration
02

Moles of NaOH

To calculate the moles of NaOH added, we will use the given volume and molarity of NaOH. Moles of NaOH = Volume of NaOH × Molarity of NaOH = \(48.32 \, \mathrm{mL} \times 0.200 \, \mathrm{M}\) To convert mL to L, we will divide by 1000: \[48.32 \, \mathrm{mL} \times \frac{1 \, \mathrm{L}}{1000 \, \mathrm{mL}} = 0.04832 \, \mathrm{L}\] So, moles of NaOH = \(0.04832 \, \mathrm{L} \times 0.200 \, \mathrm{M} = 0.009664 \, \mathrm{mol}\) Step 3: Use stoichiometry to find the moles of H2SO4
03

Moles of H2SO4

From the balanced equation, we know that 2 moles of NaOH react with 1 mole of H2SO4. So we can find the moles of H2SO4 using the following relation: \[\frac{\text{moles of H2SO4}}{\text{moles of NaOH}} = \frac{1}{2}\] Thus, moles of H2SO4 = \(\frac{1}{2} \times 0.009664 \, \mathrm{mol} = 0.004832 \, \mathrm{mol}\) Step 4: Calculate the molar concentration of H2SO4
04

Molar concentration of H2SO4

To calculate the molar concentration of H2SO4, we will use the given volume and the moles of H2SO4 that we found in the previous step. Molarity of H2SO4 = \(\frac{\text{moles of H2SO4}}{\text{volume of H2SO4}}\) To convert the volume of H2SO4 to liters, we will divide by 1000: \[30.00 \, \mathrm{mL} \times \frac{1 \mathrm{L}}{1000 \mathrm{mL}} = 0.03000 \, \mathrm{L}\] So, Molarity of H2SO4 = \(\frac{0.004832 \, \mathrm{mol}}{0.03000 \, \mathrm{L}} = 0.1611 \, \mathrm{M}\) Therefore, the molar concentration of the aqueous sulfuric acid is 0.1611 M.

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