A 20.0-mL sample of 0.200 M HBr solution is titrated with 0.200 M NaOH solution. Calculate the pH of the solution after the following volumes of base have been added:
(c) 20.0 mL.

Verified step by step guidance

1. <strong>Step 1:</strong> Identify the type of reaction occurring. This is a neutralization reaction between a strong acid (HBr) and a strong base (NaOH). The reaction can be represented as: \[ \text{HBr} + \text{NaOH} \rightarrow \text{NaBr} + \text{H}_2\text{O} \]
2. <strong>Step 2:</strong> Calculate the moles of HBr initially present in the solution. Use the formula: \[ \text{moles of HBr} = \text{volume (L)} \times \text{molarity (M)} \]. For 20.0 mL of 0.200 M HBr, convert the volume to liters and calculate the moles.
3. <strong>Step 3:</strong> Calculate the moles of NaOH added. Similarly, use the formula: \[ \text{moles of NaOH} = \text{volume (L)} \times \text{molarity (M)} \]. For 20.0 mL of 0.200 M NaOH, convert the volume to liters and calculate the moles.
4. <strong>Step 4:</strong> Determine the limiting reactant. Since both HBr and NaOH have the same concentration and volume, they will react in a 1:1 ratio, and both will be completely consumed in the reaction.
5. <strong>Step 5:</strong> Calculate the pH of the resulting solution. After complete neutralization, the solution contains only water and the salt NaBr, which does not affect the pH. Therefore, the pH of the solution is neutral, which is 7.

Key Concepts

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant (in this case, NaOH) to a solution containing the analyte (HBr) until the reaction reaches its equivalence point, where the amount of titrant added is stoichiometrically equivalent to the amount of analyte present.

pH and Neutralization

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. In a neutralization reaction between a strong acid (HBr) and a strong base (NaOH), the pH at the equivalence point is typically 7, indicating a neutral solution. Understanding how to calculate pH before and after the equivalence point is crucial for solving titration problems.

Stoichiometry of Acid-Base Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. For the reaction between HBr and NaOH, the balanced equation shows a 1:1 molar ratio. This means that equal moles of HBr and NaOH will neutralize each other, allowing for the calculation of remaining concentrations and pH after specific volumes of base are added.