Question

A 25.00-mL sample of a hydrochloric acid solution of unknown concentration is titrated with \(0.1004 \mathrm{M}\) \(\mathrm{NaOH}\). However, before the acid is titrated, \(27.65\) mL of water is added to it. The phenolphthalein indicator turns red after \(28.70 \mathrm{~mL}\) of \(\mathrm{NaOH}\) has been added. What is the concentration of the \(25.00-\) \(\mathrm{mL}\) sample of hydrochloric acid?

Short answer

The concentration of the initial HCl solution can be calculated as follows: Concentration of HCl = \( \frac{28.70 \mathrm{~mL} \times 0.1004 \mathrm{M}}{25.00 \mathrm{~mL}} \) After performing the calculations, the concentration of the hydrochloric acid solution in the 25.00-mL sample is approximately \(0.1153 \mathrm{M}\).

Step-by-step solution

Calculate the moles of NaOH added.

To find the moles of NaOH added during the titration, use the formula moles = volume × concentration. Given that, 28.70 mL of 0.1004 M NaOH is added, we can calculate the moles of NaOH as follows: Moles of NaOH = Volume of NaOH × Concentration Moles of NaOH = \(28.70 \mathrm{~mL} \times 0.1004 \mathrm{M}\)

Determine the moles of HCl in the original 25 mL sample

In a balanced equation for the reaction between HCl and NaOH, the ratio of moles of HCl to moles of NaOH is 1:1. Therefore, the moles of HCl in the original 25 mL sample is equal to the moles of NaOH added: Moles of HCl = Moles of NaOH

Calculate the concentration of the initial HCl solution

To find the concentration of the initial HCl solution, use the formula: Concentration = Moles / Volume Here, the volume of the initial HCl solution is 25.00 mL. Note that since the addition of water doesn't affect the moles of HCl, we can ignore the 27.65 mL of added water in the calculation. Concentration of HCl = Moles of HCl / Volume of HCl Concentration of HCl = Moles of HCl / 25.00 mL Now, plug in the moles of NaOH value obtained in Step 1 into the formula: Concentration of HCl = \(28.70 \mathrm{~mL} \times 0.1004 \mathrm{M}\) / 25.00 mL Now, perform the calculations to find the concentration of HCl in the 25.00-mL sample. This will give the concentration of the hydrochloric acid solution, which is our final answer.

Key concepts

Mole Calculations

Mole calculations are key when dealing with chemical reactions, as they allow us to determine the number of particles involved in a chemical process. In the context of titration, understanding moles helps us measure how much of one solution reacts with a known quantity of another.

To calculate moles, we use the formula: moles = concentration × volume. Both the concentration and volume need to be in appropriate units; typically, mol/L for concentration and liters for volume. When conducting a titration, we calculate the moles of the titrant (in this case, NaOH) added to the reaction.

For instance, if 28.70 mL of NaOH at 0.1004 M is used, we first convert the volume from milliliters to liters by dividing by 1000. Then, we multiply by the molarity to find the number of moles. This process establishes how many moles of NaOH were used to neutralize the HCl.

Acid-Base Reaction

An acid-base reaction is a chemical process involving the transfer of hydrogen ions between an acid and a base. In this titration scenario, hydrochloric acid (HCl) reacts with sodium hydroxide (NaOH), a strong base.

HCl donates a hydrogen ion (H+) to the OH- ion provided by NaOH, forming water ( H_2O d) and sodium chloride (NaCl). This neutralization reaction is vital as it allows us to determine the unknown concentration of the acid through titration.

Understanding the stoichiometry of the reaction, which tells us that one mole of HCl reacts with one mole of NaOH, is crucial. This 1:1 molar ratio simplifies the calculations, as the moles of each substance will be equal at the equivalence point.

Hydrochloric Acid Concentration

Determining the concentration of hydrochloric acid involves using the result from the moles of NaOH used in the titration. The concentration is defined as the number of moles of solute per liter of solution.

Since the moles of HCl in the original solution match those of the NaOH added (due to the 1:1 reaction ratio), we can use the calculated moles of NaOH to find the original concentration.

Even though we added water to the solution for dilution, this does not change the total number of moles of HCl, only the volume for ease of titration. To find the concentration, divide the moles by the initial 25.00 mL of HCl (converted to liters). This gives the molarity, which represents the strength of the acid solution before dilution.

Phenolphthalein Indicator

The phenolphthalein indicator is a crucial tool in acidic titrations. It acts as a visual cue to determine when the reaction between the acid and base is complete.

Phenolphthalein is colorless in acidic solutions but turns bright pink in basic conditions. During titration, the point at which the indicator changes color signifies the endpoint of the titration. This endpoint occurs slightly past the equivalence point, but for strong acid and strong base titrations like HCl with NaOH, this difference is negligible.

Using such an indicator helps ensure accuracy by signaling the completion of the titration process, thus allowing for precise calculations of unknown concentrations.

Stoichiometry

Stoichiometry is the study of the quantitative relationships in chemical reactions, providing essential insights into the amounts of reactants needed or products formed. In the case of titration involving HCl and NaOH, stoichiometry tells us that their reaction follows a simple 1:1 molar ratio.

This means that one mole of hydrochloric acid reacts completely with one mole of sodium hydroxide. This relationship simplifies our calculations since the moles of HCl initially present in the solution equal the moles of NaOH required to reach the endpoint of the titration.

By utilizing stoichiometry, we can effectively determine the unknown concentration of the acid. We do so by linking the data obtained from the base (NaOH) used in the reaction. This ensures that the calculations are not only accurate but also straightforward and logical.