Problem 139 - Chemistry and Chemical Reactivity

Question

Two students titrate different samples of the same solution of HCl using 0.100 M NaOH solution and phenolphthalein indicator (Figure 4.12 ). The first student pipets \(20.0 \mathrm{mL}\) of the HCl solution into a flask, adds \(20 \mathrm{mL}\) of distilled water and a few drops of phenolphthalein solution, and titrates until a lasting pink color appears. The second student pipets \(20.0 \mathrm{mL}\) of the HCI solution into a flask, adds \(60 \mathrm{mL}\) of distilled water and a few drops of phenolphthalein solution, and titrates to the first lasting pink color. Each student correctly calculates the molarity of an HCl solution. What will the second student's result be? (a) four times less than the first student's result (b) four times greater than the first student's result (c) two times less than the first student's result (d) two times greater than the first student's result (e) the same as the first student's result

Step-by-Step Solution

Answer

(e) the same as the first student's result

Step 1: Understanding Molarity and Dilution

In a titration, molarity is the measure of concentration that remains constant irrespective of the volume change or dilution of the solution. Dilution by adding distilled water does not change the number of moles of solute—here, HCl—present in the original 20 mL sample.

Step 2: Identify the Chemical Reaction

The titration involves a neutralization reaction between HCl and NaOH: \[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \] This reaction is a simple acid-base neutralization, where each mole of NaOH reacts with one mole of HCl.

Step 3: Equal Volume of HCl in Both Experiments

Each student pipets 20.0 mL of the same HCl solution, meaning the initial number of moles of HCl in both experiments is the same. Thus, even when adding different amounts of distilled water, the initial moles of HCl do not change.

Step 4: Addition of Water in Titration

Adding water does not alter the number of moles of HCl present, as dilution does not affect molarity calculation for the titration. It only changes volume but not the chemical properties of the reaction since molarity is independent of the solvent volume in a titration setup.

Step 5: Conclusion on Calculated Molarity

Since both students initially took the same amount of HCl, the number of moles that react with NaOH will be identical. Hence, despite differing amounts of diluted water, the molarity calculated for both students will be the same, as dilution prior to titration does not impact the concentration of the titrant.

Key Concepts

Understanding Molarity

Molarity is a measure of concentration, defined as the number of moles of solute per liter of solution. It's a crucial concept in chemistry because it allows us to describe how concentrated a solution is. For example, a 1 molar (1 M) solution contains 1 mole of solute in every liter of solution. This measurement remains consistent under certain circumstances, making it a reliable way to calculate chemical reactions in solutions. Even if you add extra solvent, such as water, the number of moles of solute remains unchanged, which means the concentration won't change based on volume expansion alone.

• Molarity = moles of solute / liters of solution
• Unchanged by dilutions when moles of solute unchanged

When diluting a solution, you increase the volume but the number of moles of solute remains constant. Thus, molarity can be a constant point of reference in titrations.

Acid-Base Neutralization

Acid-base neutralization is a type of chemical reaction where an acid reacts with a base to produce water and a salt. These reactions are central to many titration experiments. Specifically, in a titration involving hydrochloric acid (HCl) and sodium hydroxide (NaOH), each mole of HCl reacts with a mole of NaOH according to the equation: \[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}\]During the titration, the reaction proceeds until the amount of added base completely neutralizes the acid. This is often detected by a color change in the solution, using an indicator like phenolphthalein that changes at the equivalence point.

• Every mole of NaOH neutralizes one mole of HCl
• Products: NaCl (a salt) and water
• Indicator shows completion of reaction

Exploring Dilution Effects

In the context of titrations, dilution refers to adding more solvent to a solution. This increases the volume without affecting the number of moles of solute present. Therefore, the chemical behavior and concentration calculations of the solution remain unaffected by dilution. When performing a titration, like in our exercise, the amount of distilled water added does not influence the results of the titration because it does not change the number of moles of acid in the solution. It’s important to understand that the initial amount of solute in moles is what dictates the reaction with the titrant, not the volume of the solution.

• Volume increases, but moles of solute remain constant
• Titration results are based on the original moles present
• Important for maintaining consistency in experiments

Basics of a Chemical Reaction in Titration

A chemical reaction involves the transformation of reactants into products through breaking and forming of chemical bonds. In a titration setting, the primary goal is to determine the concentration of an unknown solution by allowing it to react with a solution of known concentration. In our exercise, the chemical reaction is the neutralization of HCl with NaOH, which is carefully measured to identify the endpoint, usually by a color change. This setup allows for the precise calculation of unknown molarity through the reaction stoichiometry. The balanced equation helps in understanding exactly how much of the titrant is necessary to react completely with the analyte in question.

• Key for determining unknown concentrations
• Relies on precise measurement and indicators
• Stoichiometry guides amounts needed for complete reaction