Problem 25 - Chemical Principles

Question

Calculate the volume of \(0.150 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) required to neutralize (a) one-half and (b) all the hydroxide ions in \(25.0 \mathrm{~mL}\) of \(0.110 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\). (c) What is the molarity of \(\mathrm{Na}^{+}\)ions at the stoichiometric point? (d) Calculate the \(\mathrm{pH}\) of the solution after the addition of \(20.0 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\) to \(25.0 \mathrm{~mL}\) of \(0.110 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq})\).

Step-by-Step Solution

Answer

(a) Volume of HCl for half neutralization is 0.825 mL. (b) Volume of HCl for complete neutralization is 1.65 mL. (c) Molarity of Na+ ions at the stoichiometric point is 0.110 M. (d) The pH after adding 20.0 mL of HCl to NaOH is 13.22.

Step 1: Determine moles of NaOH

Calculate the moles of NaOH using the concentration and volume. The formula is: moles = molarity \(\times\) volume in liters. For 25.0 mL of 0.110 M NaOH, moles of NaOH = 0.110 M \(\times\) 0.0250 L.

Step 2: Calculate volume of HCl to neutralize half the NaOH

Half the moles of NaOH is neutralized by half the moles of HCl because the stoichiometry of the reaction is 1:1. First, find half the moles of NaOH from Step 1, then use the molarity of HCl to find the volume required: volume = moles / molarity.

Step 3: Calculate volume of HCl to neutralize all the NaOH

Using the moles of NaOH from Step 1, determine the volume of 0.150 M HCl required to neutralize all the NaOH using the formula: volume = moles / molarity.

Step 4: Determine molarity of Na+ at the stoichiometric point

At the stoichiometric point, all NaOH has reacted and the number of moles of Na+ is equal to the initial moles of NaOH. The volume is the sum of the volumes of NaOH and HCl. The molarity of Na+ is the moles of Na+ divided by the total volume in liters.

Step 5: Calculate pH after adding HCl to NaOH

Determine the remaining moles of NaOH after the reaction with 20.0 mL of 0.150 M HCl. Then, find the concentration of OH- left. The pOH is calculated from this concentration and pH is obtained using the relation pH = 14 - pOH.

Key Concepts

Stoichiometry

Stoichiometry is akin to a recipe for chemical reactions. It provides the proportions of reactants and products involved, based on the balanced chemical equation. This balance ensures that matter is conserved, reflecting the fact that atoms are neither created nor destroyed in chemical reactions.

For example, in the neutralization reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH), the stoichiometry is 1:1, meaning one mole of HCl reacts with one mole of NaOH to produce one mole of water (H₂O) and one mole of sodium chloride (NaCl).

This is expressed by the balanced equation: \[\mathrm{HCl(aq)} + \mathrm{NaOH(aq)} \rightarrow \mathrm{NaCl(aq)} + \mathrm{H_2O(l)}\].

Understanding stoichiometry allows us to predict the outcomes of reactions, such as how much of each reactant is needed or how much of a product is produced.

Molarity

Molarity (M) is a measurement of the concentration of a solution, defined as the number of moles of solute dissolved in one liter of solution. It is a key concept when preparing solutions in chemistry and is fundamental for reactions that occur in solution, like acid-base reactions.

The formula for molarity is: \[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}\].

In our exercise, molarity helps determine the required volume of HCl to neutralize a given amount of NaOH. For instance, to find the volume of a 0.150 M HCl solution required to react with a certain number of moles of NaOH, the formula is rearranged to solve for volume: \[\text{Volume (L)} = \frac{\text{moles of solute}}{\text{Molarity (M)}}\].

Thus, with the stoichiometry and molarity at hand, one can calculate how much of one reactant is needed to completely react with a known quantity of another.

pH Calculation

The pH scale is a measure of the acidity or basicity of an aqueous solution. It ranges from 0 to 14, with 7 being neutral, values less than 7 representing acidic solutions, and values greater than 7 representing basic solutions.

The pH is calculated by taking the negative logarithm (base 10) of the hydrogen ion concentration: \[\text{pH} = -\log_{10}[\mathrm{H}^+]\].

In our exercise, after the addition of HCl to the NaOH solution, some NaOH remains unreacted. This leftover NaOH determines the basicity of the solution. The pH can be determined by first calculating the hydroxide ion (OH^-) concentration, converting it to pOH, and then using the relationship that \(\text{pH} + \text{pOH} = 14\) to find the pH.

Acid-Base Titration

Acid-base titration is a laboratory method used to determine the concentration of an unknown solution by reacting it with a solution of known concentration, called the titrant. Titrations are based on neutralization reactions, where an acid and a base react to form water and a salt.

The point at which the number of moles of hydrogen ions (H⁺) equals the number of moles of hydroxide ions (OH^-) is known as the equivalence or stoichiometric point. At this stage, the number of moles of acid equals the moles of base originally in solution. In a titration curve, this point is typically indicated by a sharp change in pH.

In the exercise, we effectively conduct a titration to find the volume of HCl needed to react with NaOH. One can also deduce the molarity of sodium ions at the stoichiometric point, which reflects the complete reaction of the initial NaOH.