Problem 76 - General Chemistry: Principles and Modern Applications

Question

Sulfuric acid is a diprotic acid, strong in the first ionization step and weak in the second \(\left(K_{\mathrm{a}_{2}}=1.1 \times 10^{-2}\right)\) By using appropriate calculations, determine whether it is feasible to titrate \(10.00 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) to two distinct equivalence points with \(0.100 \mathrm{M} \mathrm{NaOH}\)

Step-by-Step Solution

Answer

Yes, it is feasible to titrate \(H_{2}SO_{4}\) to two distinct equivalence points with \(0.100 \mathrm{M} \mathrm{NaOH}\), provided there is at least 0.002 L (\(2.00 \mathrm{mL}\)) of the \(\mathrm{NaOH}\) solution available.

Step 1: calculation for the first equivalence point

To calculate the amount of sodium hydroxide \( \mathrm{NaOH} \) required to reach the first equivalence point, we'll compute the number of moles of sulfuric acid \( \mathrm{H}_{2} \mathrm{SO}_{4} \) present, and assume that it will react completely with the same number of moles of \( \mathrm{NaOH} \). Remember that the solution volume should be in liters when calculating molarity. Hence, \n \( \text{Moles of } \mathrm{H}_{2} \mathrm{SO}_{4} = 0.100 \times 10.00/1000 = 0.001 \text{ moles} \). This amount of sulfuric acid will need the exact number of moles of \( \mathrm{NaOH} \) to fully react, hence we also need 0.001 moles of \( \mathrm{NaOH} \). This is the first equivalence point.

Step 2: calculation for the second equivalence point

To calculate the amount of \( \mathrm{NaOH} \) required to reach the second equivalence point, we consider the number of moles of \( \mathrm{HSO}_{4}^{-} \) ion formed after the first stage of ionization, which will be equal to the initial number of moles of \( \mathrm{H}_{2} \mathrm{SO}_{4} \). Hence, we will need an additional 0.001 moles of \( \mathrm{NaOH} \) to fully react with the \( \mathrm{HSO}_{4}^{-} \) ions. This means a total of \( 0.001 + 0.001 = 0.002 \) moles of \( \mathrm{NaOH} \) is required for full titration.

Step 3: Conclusion

We have a 0.100 M solution of \( \mathrm{NaOH} \) which we can use to titrate the \( \mathrm{H}_{2} \mathrm{SO}_{4} \). To confirm that we have enough \( \mathrm{NaOH} \), we should calculate how many moles of \( \mathrm{NaOH} \) we have. We can rearrange the molarity equation, \( M = mol/L \), to find \( mol = M \times L \). So, \( mol_{\mathrm{NaOH}} = 0.100 \times volume \). Since we don’t have any information about volume of \( \mathrm{NaOH} \), we can’t finally confirm whether there is enough \( \mathrm{NaOH} \), but if there is at least 0.002 L (\( 2.00 \mathrm{ mL} \)) of \( \mathrm{NaOH} \), it would be possible to titrate the \( \mathrm{H}_{2} \mathrm{SO}_{4} \) to two distinct equivalence points.

Key Concepts

Diprotic Acid

Sulfuric acid, denoted as \( \mathrm{H}_{2}\mathrm{SO}_{4} \), is a classic example of a diprotic acid. This means it has the capability to donate two protons (\( \mathrm{H}^+ \) ions) per molecule. When sulfuric acid dissolves in water, it undergoes two ionization steps. The first ionization is complete and results in the formation of hydrogen sulfate \( \mathrm{HSO}_{4}^{-} \), while the second ionization is partial and gives sulfate \( \mathrm{SO}_{4}^{2-} \). Because sulfuric acid is strong in its first ionization step, it releases almost all its first proton. The second step, however, has a much smaller ionization constant \( (K_{\mathrm{a}_2}=1.1 \times 10^{-2}) \), indicating its weaker nature.

• First ionization: \( \mathrm{H}_{2}\mathrm{SO}_{4} \rightarrow \mathrm{HSO}_{4}^{-} + \mathrm{H}^+ \)
• Second ionization: \( \mathrm{HSO}_{4}^{-} \rightarrow \mathrm{SO}_{4}^{2-} + \mathrm{H}^+ \)

This stepwise proton donation is crucial in understanding why diprotic acids like sulfuric acid behave differently from monoprotic acids during titration.

Equivalence Point

During a titration, the equivalence point is when the amount of titrant added is just enough to completely neutralize the analyte solution. For sulfuric acid, which is a diprotic acid, there are two equivalence points. The first equivalence point is reached when the amount of base added equals the amount of the first protons offered by \( \mathrm{H}_{2}\mathrm{SO}_{4} \). This occurs because all \( \mathrm{HSO}_{4}^{-} \) ions that were formed from the first ionization have been neutralized by the base. The second equivalence point happens after the second ionization stage, when all remaining \( \mathrm{HSO}_{4}^{-} \) ions have been neutralized to \( \mathrm{SO}_{4}^{2-} \). Finding these two separate equivalence points in a titration allows chemists to determine the concentration of the acid more precisely and observe the distinct reactions involving each ionizable proton.

Ionization Steps

The ionization steps of sulfuric acid play a vital role in determining how it reacts during titration. In the first ionization step, which is complete, sulfuric acid dissociates into hydrogen sulfate and a proton:\[ \mathrm{H}_{2}\mathrm{SO}_{4} \rightarrow \mathrm{HSO}_{4}^{-} + \mathrm{H}^+ \] The second step is partial and significantly impacts titration feasibility. In this step:\[ \mathrm{HSO}_{4}^{-} \rightarrow \mathrm{SO}_{4}^{2-} + \mathrm{H}^+ \] The equilibrium constant \( K_{\mathrm{a}_{2}} \) for this reaction is relatively low, at \( 1.1 \times 10^{-2} \), signifying that not all \( \mathrm{HSO}_{4}^{-} \) will dissociate under typical conditions without further base addition. That's why the total volume and concentration of titrant used in titration must be precisely calculated to account for both ionization steps, especially the weaker second step. Understanding these steps helps in accurately reaching the standard equivalence points.

Molarity Calculation

Molarity, a measure of concentration, is crucial for determining how much titrant is needed during a titration. To find it, calculate the number of moles of solute (like sulfuric acid) divided by the total volume of the solution in liters:\(M = \frac{\text{moles of solute}}{\text{liters of solution}}\) For the first equivalence point of sulfuric acid, calculate the initial moles of the acid as follows:- Given a \( 0.100 \mathrm{M} \) solution in \( 10.00 \mathrm{mL} \), convert this volume into liters \( (0.010 \text{ L}) \).- Multiply this by the molarity to determine the moles: \( 0.100 \times 0.010 = 0.001 \text{ moles} \)Since sulfuric acid is diprotic, at least double these moles of \( \mathrm{NaOH} \) is needed for the full titration, as \( 0.001 \text{ moles} \) reacts with \( \mathrm{NaOH} \) at both equivalence points. Calculating molarity accurately ensures that enough titrant is prepared to reach these points. Accurate molarity calculations help predict and compare quantities required for various stages of chemical reactions.