Question

It took \(25.06 \pm 0.05 \mathrm{mL}\) of a sodium hydroxide solution to titrate a 0.4016-g sample of KHP (see Exercise 83). Calculate the concentration and uncertainty in the concentration of the sodium hydroxide solution. (See Appendix 1.5.) Neglect any uncertainty in the mass

Short answer

The concentration of the sodium hydroxide solution is \(0.0784 \textrm{M}\), and the uncertainty in the concentration is ±\(1.56 \times 10^{-4} \textrm{M}\). Therefore, the final answer is \(0.0784 \pm 1.56 \times 10^{-4} \textrm{M}\).

Step-by-step solution

Calculate moles of KHP.

KHP, also known as KHC8H4O4 (Potassium hydrogen phthalate), has a molecular weight of 204.22 g/mol. To find the moles of KHP, we will use the given mass and the molecular weight. Moles of KHP = mass of KHP / molecular weight of KHP Moles of KHP = (0.4016 g) / (204.22 g/mol) Moles of KHP = \(1.965 \times 10^{-3} \textrm{mol}\)

Stoichiometry of the reaction between KHP and sodium hydroxide.

The stoichiometric reaction between KHP and sodium hydroxide (NaOH) is given below: KHP + NaOH → KNaP + H2O In this reaction, the mole ratio between KHP and NaOH is 1:1, meaning that one mole of KHP reacts with one mole of NaOH. Since we have calculated the moles of KHP, we can now determine the moles of NaOH involved in the reaction: Moles of NaOH = moles of KHP Moles of NaOH = \(1.965 \times 10^{-3} \textrm{mol}\)

Calculate the concentration of sodium hydroxide.

Now that we know the moles of NaOH involved in the reaction, we can use the titrated volume to find its concentration. Concentration of NaOH = moles of NaOH / volume of NaOH (in liters) Concentration of NaOH = \((1.965 \times 10^{-3} \textrm{mol}) / (0.02506 \textrm{L})\) Concentration of NaOH = \(0.0784 \textrm{M}\)

Calculate the uncertainty in the concentration of sodium hydroxide.

We are given an uncertainty of ±0.05 mL in the volume measurement for the titration. We need to find the uncertainty in the concentration calculation. % Uncertainty in volume = (absolute uncertainty in volume / volume) x 100 % Uncertainty in volume = (0.05 mL / 25.06 mL) x 100 % Uncertainty in volume = 0.199 % Now we need to find the uncertainty in the concentration. Since the only uncertainty provided is in the volume of the titrated sodium hydroxide, we will use the percentage uncertainty in volume for our calculation. % Uncertainty in concentration = % Uncertainty in volume % Uncertainty in concentration = 0.199 % Now, we calculate the absolute uncertainty in the concentration. Absolute uncertainty in concentration = (0.199 / 100) x 0.0784 M Absolute uncertainty in concentration = \(±1.56 \times 10^{-4} \textrm{M}\)

Report the concentration and uncertainty of the sodium hydroxide solution.

The concentration of the sodium hydroxide solution is 0.0784 M, and the uncertainty in the concentration is ±\(1.56 \times 10^{-4} \textrm{M}\). The final answer is \(0.0784 \pm 1.56 \times 10^{-4} \textrm{M}\).

Key concepts

Titration

Titration is an essential laboratory technique used widely in chemistry to determine the concentration of an unknown solution. It involves gradually adding a titrant (a solution of known concentration) to a solution of the analyte (substance to be measured) until the reaction is just complete. This is typically indicated by a color change or an electrical measurement, signaling the equivalence point has been reached. A key aspect of titration is accuracy. Careful attention to detail in measurement is crucial. The process often involves:

• Using a burette to add the titrant drop-by-drop
• Ensuring observations align with the expected chemical reaction
• Recording the volume of titrant used to reach the endpoint

This technique allows chemists to calculate the concentration of the analyte by using the known concentration and volume of the titrant.

Stoichiometry

Stoichiometry is the field of chemistry that studies the quantitative relationships between reactants and products in a chemical reaction. This is crucial when performing a titration as it enables the chemist to understand how much of one substance will completely react with another. In the reaction between Potassium hydrogen phthalate (KHP) and sodium hydroxide (NaOH), the balanced chemical equation tells us that they react in a 1:1 molar ratio. This simplification means that the moles of KHP used will be equal to the moles of NaOH needed for complete reaction: KHP + NaOH → KNaP + H2O Thanks to stoichiometry, if we know the amount of KHP reacted, we can directly determine the moles of NaOH from the same value. This fundamental concept ensures precise calculations for further analysis.

Concentration Calculations

Calculating the concentration of a solution after a titration is crucial since it provides the amount of substance present in a given volume. The concentration is typically expressed in moles per liter (Molarity, M). This can be calculated once the moles of titrant used are known and the volume of the solution is measured.For example, if after titration with NaOH, you find 0.001965 mol of NaOH was used to neutralize KHP in a volume of 25.06 mL, the concentration of NaOH, in Molarity, is calculated as follows: \[ ext{Concentration} = \frac{0.001965 \ ext{mol}}{0.02506 \ ext{L}} = 0.0784 \ ext{M} \]Understanding this calculation ensures accurate reagent formulation for further experimentation and analysis in chemistry.

Uncertainty Analysis

Uncertainty analysis is an integral part of scientific measurement, addressing the reliability and precision of results. In titration, even minor errors can affect the accuracy of the calculated concentration. Consideration of measurement uncertainty, such as the ±0.05 mL accuracy of a burette, is crucial.To evaluate uncertainty, the percentage uncertainty in the measured volume is calculated:\[ \text{Percentage Uncertainty} = \left( \frac{\text{Absolute Uncertainty}}{\text{Volume Used}} \right) \times 100 = \left( \frac{0.05}{25.06} \right) \times 100 = 0.199\% \]This percentage directly translates into the uncertainty of the concentration, providing a complete picture of precision. The absolute uncertainty in this concentration, given in our sample, is ±1.56×10⁻⁴ M.Incorporating uncertainty analysis helps refine experimental designs, ensuring better accuracy and trust in experimental data.