Question

Potassium hydrogen phthalate, known as KHP (molar mass = \(204.22 \mathrm{~g} / \mathrm{mol}\) ), can be obtained in high purity and is used to determine the concentration of solutions of strong bases by the reaction $$\mathrm{HP}^{-}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{P}^{2-}(a q)$$ If a typical titration experiment begins with approximately \(0.5 \mathrm{~g}\) KHP and has a final volume of about \(100 \mathrm{~mL}\), what is an appropriate indicator to use? The \(\mathrm{p} K_{\mathrm{a}}\) for \(\mathrm{HP}^{-}\) is \(5.51\).

Short answer

An appropriate indicator for this titration experiment would be Bromothymol blue, as its pH range (6.0 - 7.6) is the closest to the calculated equivalence point pH of 5.51.

Step-by-step solution

Calculate moles of KHP present initially

Given the mass of KHP and its molar mass, we can find the moles of KHP present initially: Moles of KHP = mass/molar mass Moles of KHP = \( \frac{0.5 \mathrm{~g}}{204.22 \mathrm{~g/mol}} \) ≈ 0.00245 mol

Determine the concentration of OH⁻ and HP⁻ at equivalence point

At the equivalence point, the moles of OH⁻ are equal to the moles of HP⁻. Knowing that the final volume is about 100 mL, we can determine the concentration of OH⁻ (and HP⁻) at the equivalence point: \[C_{eq}(OH^-) = C_{eq}(HP^-) = \frac{moles}{volume}\] \[C_{eq}(OH^-) = \frac{0.00245 \mathrm{mol}}{100 \mathrm{~mL} \times \frac{1 \mathrm{L}}{1000\mathrm{~mL}}} = 0.0245 \mathrm{M}\]

Determine the pH at equivalence point

To determine the pH at the equivalence point, we can use the pKa for HP⁻: \[pK_a = 5.51 = -\log(K_a)\] \[K_a = 10^{-5.51}\] The expression for Kₐ is given by: \[K_a = \frac{[\mathrm{H}^+][\mathrm{P}^{2-}]}{[\mathrm{HP}^-]}\] At the equivalence point, the concentration of HP⁻ and P²⁻ are equal: \[[\mathrm{HP}^-] = [\mathrm{P}^{2-}] = C_{eq}\] Substituting the values into the Kₐ expression and completing the calculations yields: \[10^{-5.51} = \frac{[\mathrm{H}^+](0.0245)}{0.0245}\] Which simplifies to: \[[\mathrm{H}^+] = 10^{-5.51}\] Finally, we determine the pH at the equivalence point with: \[pH \approx -\log([\mathrm{H}^+])\] \[pH \approx -\log(10^{-5.51}) = 5.51\]

Select an appropriate indicator

Now that we know the pH at the equivalence point is 5.51, we can choose an appropriate indicator. Common indicators and their pH ranges are: 1. Methyl orange: pH range 3.1 - 4.4 2. Bromothymol blue: pH range 6.0 - 7.6 3. Phenolphthalein: pH range 8.2 - 10.0 None of the common indicators have an exact pH range that includes 5.51. However, the closest one is Bromothymol blue. Although its pH range starts slightly higher than our equivalence point pH, it would still yield a reasonably accurate endpoint in the titration. Thus, Bromothymol blue is an appropriate indicator for this titration experiment.

Key concepts

Potassium Hydrogen Phthalate

Potassium hydrogen phthalate (KHP) is a standard substance in analytical chemistry. With a known high purity and a precisely determined molar mass of 204.22 g/mol, KHP is an ideal primary standard for titrations involving strong bases. It dissociates in solution to form HP⁻ ions, which then react with hydroxide ions (OH⁻) in a base titration.

When KHP is used in a titration experiment, the exact amount of substance is crucial because it directly influences the calculation of the base's concentration. It’s measured mass is used to determine the moles of KHP which, in turn, helps to find the moles of OH⁻ when the reaction reaches the equivalence point where moles of KHP equal the moles of OH⁻.

Equivalence Point

The equivalence point in a titration is a critical moment during the procedure when the amount of titrant, typically a base in the context of KHP, is stoichiometrically equal to the amount of substance of interest, in this case, the amount of acid. It's essential to understand that at the equivalence point, the solution contains equal molar amounts of the corresponding base and conjugate acid of the weak acid we started with.

For the titration of KHP with a strong base, the equivalence point is reached when all HP⁻ ions are neutralized by OH⁻ ions, thus forming water (H₂O) and the phthalate ion (P²⁻). This can be mathematically expressed in terms of concentrations and used alongside the acid dissociation constant (Ka) or its logarithmic equivalent (pKa) to determine the pH of the solution at this point. The pH at the equivalence point, which in the case of KHP is approximately 5.51, is not necessarily neutral (pH 7), as it commonly depends on the nature of the weak acid and its conjugate base.

Acid-Base Indicator

In the realm of titrations, an acid-base indicator is a chemical dye that changes color at a particular pH level. This characteristic can be exploited to visually determine the endpoint of a titration, which is typically close to the theoretical equivalence point. The choice of an indicator is crucial; it should have a color change range that falls within the pH change of the reaction around the equivalence point.

For instance, if the pH at the equivalence point is known, like 5.51 for KHP titrations, selecting an indicator such as Bromothymol blue, although not perfect, can be adequate as its color change range straddles this pH level. Even though the pH change range does not match exactly, this indicator will still change color noticeably, signaling that the endpoint of titration has been reached, allowing for precise measurements. Understanding how to select the correct indicator ensures a successful titration and accurate results.