Question

Calculate the molarity of a solution of hydrobromic acid \((\mathrm{HBr})\) if 30.35 \(\mathrm{mL}\) of 0.1000 \(\mathrm{M}\) NaOH is required to titrate 25.00 \(\mathrm{mL}\) of the acid to the equivalence point.

Short answer

The molarity of the hydrobromic acid (HBr) solution is calculated as follows: write the balanced equation, \( \mathrm{HBr} + \mathrm{NaOH} \rightarrow \mathrm{NaBr} + \mathrm{H_2O} \), find the moles of NaOH (0.003035 mol), determine the moles of HBr (0.003035 mol), and calculate the molarity of HBr using its moles and volume (0.1214 M).

Step-by-step solution

1. Write down the balanced chemical equation for the reaction.

The balanced chemical equation for the reaction between hydrobromic acid and sodium hydroxide is: \( \mathrm{HBr} + \mathrm{NaOH} \rightarrow \mathrm{NaBr} + \mathrm{H_2O} \) From the balanced equation, we can see that 1 mole of HBr reacts with 1 mole of NaOH.

2. Calculate the number of moles of NaOH from its volume and molarity.

The given molarity of NaOH solution is 0.1000 M, and the volume used in the titration is 30.35 mL. We can find the moles of NaOH by multiplying molarity and volume (in liters): Moles of NaOH = Molarity × Volume (in Liters) Moles of NaOH = 0.1000 mol/L × 30.35 mL × (1 L / 1000 mL) = 0.003035 mol

3. Determine the moles of HBr using stoichiometric ratios from the balanced equation.

As per the balanced chemical equation, 1 mole of HBr reacts with 1 mole of NaOH. Therefore, the number of moles of HBr is the same as the number of moles of NaOH. Moles of HBr = 0.003035 mol

4. Calculate the molarity of the HBr solution using its moles and volume.

We have the number of moles of HBr and the volume of the HBr solution (25.00 mL), so we can now calculate the molarity of the HBr solution. Molarity of HBr = (Moles of HBr) / (Volume of HBr solution in Liters) Molarity of HBr = 0.003035 mol / (25.00 mL × 1 L / 1000 mL) = 0.1214 M The molarity of the hydrobromic acid (HBr) solution is 0.1214 M.

Key concepts

Titration

Titration is an analytical procedure used to determine the concentration of a solution by reacting it with a standard solution of known concentration. It's especially useful when dealing with acids and bases, as in the problem at hand. During a titration, the solution with unknown concentration is slowly reacted with the titrant (in this case, \(\mathrm{NaOH}\) solution) until the equivalence point is reached, which is the point where the reactants have completely reacted with each other.

Determining the equivalence point can be done through the use of indicators, which change color at a certain pH, or by using a pH meter to track the pH changes. The volume of titrant used to reach the equivalence point can then be used to calculate the molarity of the unknown solution, using stoichiometry principles.

Stoichiometry

Stoichiometry is the part of chemistry that relates to measuring and calculating the quantities of reactants and products in chemical reactions. It is founded on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Thus, stoichiometry involves calculations based on balanced chemical equations to ensure that all atoms of reactants are accounted for in the products.

In the given exercise, stoichiometry is used to deduce that one mole of \(\mathrm{HBr}\) reacts with one mole of \(\mathrm{NaOH}\). By knowing the amount of \(\mathrm{NaOH}\) used in the titration, we can directly deduce the amount of \(\mathrm{HBr}\) present in the solution. The core of these calculations is the mole ratio, which is derived from the coefficients of the balanced chemical equation.

Balanced Chemical Equations

Balanced chemical equations are pivotal in stoichiometry as they provide the mole ratios of reactants and products involved in a reaction. To be 'balanced,' a chemical equation must have the same number of atoms of each element on both sides of the reaction arrow. The balancing of equations is rooted in the law of conservation of mass and it signifies that the quantity of matter and energy remains the same before and after a chemical reaction.

In our exercise, the balanced chemical equation \(\mathrm{HBr} + \mathrm{NaOH} \rightarrow \mathrm{NaBr} + \mathrm{H_2O}\) indicates a one-to-one ratio between the reactants \(\mathrm{HBr}\) and \(\mathrm{NaOH}\). This ratio is essential in determining the number of moles of \(\mathrm{HBr}\) from the moles of \(\mathrm{NaOH}\) used in the titration.

Solution Concentration

Solution concentration is a measure of the quantity of solute (substance being dissolved) present in a given quantity of solvent or solution. There are various ways to express concentration, but molarity is one of the most common units in chemistry. Molarity (M) is defined as the number of moles of solute per liter of solution.

The molarity calculation in the student's exercise uses the formula: \(\text{Molarity of HBr} = \frac{\text{Moles of HBr}}{\text{Volume of HBr solution in Liters}}\). By finding out how many moles of \(\mathrm{HBr}\) were present in the reaction and dividing by the volume of the \(\mathrm{HBr}\) solution (converted to liters), the molarity of \(\mathrm{HBr}\) could be accurately determined. This concentration is crucial for understanding the strength and reactive capabilities of the \(\mathrm{HBr}\) solution in various chemical contexts.