Problem 80 - Chemistry: Atoms First

Question

What is the concentration of \(\mathrm{NaCl}\) in a solution if titration of \(15.00 \mathrm{mL}\) of the solution with \(0.2503 \mathrm{M} \mathrm{AgNO}_{3}\) requires 20.22 mL of the AgNO_ solution to reach the end point? \(\mathrm{AgNO}_{3}(a q)+\mathrm{NaCl}(a q) \rightarrow \mathrm{AgCl}(s)+\mathrm{NaNO}_{3}(a q)\)

Step-by-Step Solution

Answer

The concentration of \(\mathrm{NaCl}\) in the solution is 0.3374 M.

Step 1: Write Down the Balanced Equation

First, confirm the balanced chemical equation for the reaction between \(\mathrm{AgNO}_{3}\) and \(\mathrm{NaCl}\). This is given as\[ \mathrm{AgNO}_{3}(a q) + \mathrm{NaCl}(a q) \rightarrow \mathrm{AgCl}(s) + \mathrm{NaNO}_{3}(a q) \].The stoichiometry is 1:1 for \(\mathrm{AgNO}_{3}\) and \(\mathrm{NaCl}\).

Step 2: Calculate Moles of AgNO3

Calculate the moles of \(\mathrm{AgNO}_{3}\) used in the titration. The molarity of \(\mathrm{AgNO}_{3}\) is given, and the volume used is measured. Utilize the formula: Moles = Molarity × Volume (in liters).\[ \text{Moles of AgNO}_{3} = 0.2503 \, M × 0.02022 \, L = 0.005061306 \, moles \].

Step 3: Calculate Moles of NaCl

Utilize the stoichiometry from the balanced equation to find the moles of \(\mathrm{NaCl}\). Since it is a 1:1 ratio,\[ \text{Moles of NaCl} = \text{Moles of AgNO}_{3} = 0.005061306 \, moles \].

Step 4: Calculate Molarity of NaCl

Finally, use the moles of \(\mathrm{NaCl}\) and the volume of \(\mathrm{NaCl}\) solution to find its concentration. Volume of \(\mathrm{NaCl}\) solution should be converted to liters.\[ \text{Molarity of NaCl} = \frac{\text{Moles of NaCl}}{\text{Volume of NaCl solution in liters}} = \frac{0.005061306}{0.01500} = 0.3374204 \, M \].

Key Concepts

Molarity Calculation

In chemistry, molarity is a measure of the concentration of a solute in a solution or how much of a substance is dissolved in a certain volume of solvent. It's expressed as moles of solute per liter of solution, commonly written as mol/L or M. Understanding molarity is crucial for performing a titration, which is a lab technique to determine the concentration of an unknown solution by reacting it with a solution of known concentration.

To calculate the molarity of a solute in a solution, you can use the formula:
\[ \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]
For instance, if you're given the moles of solute and the volume of the solution, you can plug these values into the formula to find the molarity. This is exactly what we do in the exercise to determine the concentration of NaCl with the given information.

Stoichiometry

Stoichiometry is the field of chemistry that pertains to the calculation of reactants and products in chemical reactions. It's based on the law of conservation of mass and the concept that elements combine in fixed ratios. In a balanced chemical equation, the stoichiometry indicates the proportions of each substance involved. In the context of titration, stoichiometry allows you to relate the amounts of reactants and products.

When performing these calculations, one must understand the mole ratio between reactants and products. In our example, the equation shows a one-to-one mole ratio between \(\mathrm{AgNO}_{3}\) and \(\mathrm{NaCl}\), which simplifies our calculation because we can directly equate the moles of \(\mathrm{AgNO}_{3}\) used to the moles of \(\mathrm{NaCl}\) in the sample.

Remember, the key to stoichiometry is the balanced chemical equation, and the mole ratio derived from it.

Balanced Chemical Equation

A balanced chemical equation is integral to understanding chemical reactions. It shows the reactants converting to products and ensures that the law of conservation of mass is observed. Balancing an equation involves making sure that the same number of each type of atom appears on both sides of the reaction arrow.

In the example provided, the reaction \(\mathrm{AgNO}_{3}(aq) + \mathrm{NaCl}(aq) \rightarrow \mathrm{AgCl}(s) + \mathrm{NaNO}_{3}(aq)\) is already balanced, with one mole of \(\mathrm{AgNO}_{3}\) reacting with one mole of \(\mathrm{NaCl}\) to produce one mole of \(\mathrm{AgCl}\) and one mole of \(\mathrm{NaNO}_{3}\). This balance is not arbitrary but derives from the need to account for all atoms participating in the reaction.

In titrations, the balanced chemical equation helps you understand the precise point at which the reactants have completely reacted (the endpoint), ensuring the accurate determination of the unknown concentration.