Question

A 25.0-mL volume of a sodium hydroxide solution requires \(19.6 \mathrm{~mL}\) of a \(0.189 \mathrm{M}\) hydrochloric acid for neutralization. A 10.0 - mL volume of a phosphoric acid solution requires \(34.9 \mathrm{~mL}\) of the sodium hydroxide solution for complete neutralization. Calculate the concentration of the phosphoric acid solution.

Short answer

The concentration of the phosphoric acid solution is determined by first finding the concentration of NaOH using the volume and concentration of HCl that neutralizes it. Then use the volume of NaOH that neutralizes the phosphoric acid and the ratio from the chemical equation to find the molarity of the phosphoric acid solution.

Step-by-step solution

Calculate moles of HCl used to neutralize NaOH

Use the concentration and volume of HCl to calculate the number of moles of HCl using the formula: moles (HCl) = volume (L) x concentration (M). Convert the volume from mL to L by dividing by 1000. Moles HCl = 0.0196 L * 0.189 M.

Calculate moles of NaOH neutralized by HCl

Since the reaction between NaOH and HCl is a 1:1 molar ratio (NaOH + HCl -> NaCl + H2O), the moles of HCl used are equal to the moles of NaOH neutralized. Therefore, the moles of NaOH = moles of HCl calculated in Step 1.

Determine concentration of NaOH

Use the moles of NaOH and the initial volume of NaOH solution to calculate its concentration. Use the formula: concentration (NaOH) = moles NaOH / volume NaOH (L). Convert the 25.0 mL to liters by dividing by 1000 before calculating.

Calculate moles of NaOH used to neutralize phosphoric acid

The volume of NaOH used to neutralize the phosphoric acid is 34.9 mL. First, convert this volume to liters. Then, use the concentration of NaOH calculated in Step 3 to find the moles of NaOH using the formula: moles NaOH = volume (L) × concentration (M).

Determine moles of H3PO4 neutralized

The balanced reaction between NaOH and H3PO4 is: 3NaOH + H3PO4 -> Na3PO4 + 3H2O. Each mole of H3PO4 reacts with 3 moles of NaOH. Therefore, divide the moles of NaOH by 3 to get the moles of H3PO4 neutralized.

Calculate concentration of phosphoric acid solution

Use the moles of H3PO4 found in Step 5 and the volume of phosphoric acid solution to determine the concentration of phosphoric acid. Use the formula: concentration (H3PO4) = moles H3PO4 / volume H3PO4 (L). Convert the 10.0 mL to liters by dividing by 1000 before calculating. The result is the concentration in mol/L or M.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows us to predict the amounts of products and reactants involved in a chemical reaction based on the balanced chemical equation. In the context of acid-base titrations, stoichiometry is crucial as it helps to determine the exact amount of an acid required to neutralize a base, or vice versa.

When performing stoichiometry calculations in a titration, one must consider the balanced chemical equation to establish the molar ratio of reactants. As in the given exercise, the reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl) has a 1:1 molar ratio, meaning one mole of NaOH reacts with one mole of HCl. For the reaction of NaOH with phosphoric acid (H₃PO₄), the molar ratio is 3:1, where three moles of NaOH are required for every mole of H₃PO₄.

Through stoichiometric calculations, we can accurately determine the unknown concentration of a solution by using a reagent of known concentration. This is especially useful in laboratory settings and various industrial processes where precise chemical formulations are essential.

Molar Concentration

Molar concentration, often represented by 'M,' is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. Understanding the concept of molar concentration is fundamental for solving titration problems because it allows the measurement of how much solute is present in a given volume of solution.

To calculate the molar concentration, you can use the formula: \( \text{Concentration (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \). In titration exercises, such as the one provided, it's necessary to convert volumes from milliliters to liters to ensure the units are consistent when applying this formula.

A key step in the given exercise is to determine the molar concentration of a sodium hydroxide solution after performing a titration with hydrochloric acid. By knowing the molar concentration of the acid, we use the measured volume of acid needed to reach the end point of the titration to find the molarity of the base. This calculated molarity is then used to find out the concentration of another acid, phosphoric acid, through a similar titration process.

Neutralization Reaction

A neutralization reaction is a type of chemical reaction where an acid and a base react to form water and a salt. This kind of reaction is essential in the context of titrations, where the goal is often to determine the concentration of an unknown acid or base by neutralizing it with a reagent of known concentration.

In a typical acid-base neutralization, the hydrogen ions from the acid combine with the hydroxide ions from the base to produce water, as illustrated in the exercise with the reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH). Given the formula \( \text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} \), we can see the 1:1 ratio which signifies that equal moles of acid and base react.

However, the neutralization of phosphoric acid with sodium hydroxide, shown as \( 3\text{NaOH} + \text{H}_3\text{PO}_4 \rightarrow \text{Na}_3\text{PO}_4 + 3\text{H}_2\text{O} \), reveals a 3:1 molar ratio. This means that one mole of phosphoric acid requires three moles of sodium hydroxide for complete neutralization. Understanding the products and molar relationships of these reactions is pivotal to accurately compute the concentrations of the reacting solutions.