Problem 45 - Chemistry Matter and Change

Question

What is the concentration of a household ammonia cleaning solution if 49.90 \(\mathrm{mL}\) of 0.5900 \(\mathrm{M} \mathrm{HCl}\) is required to neutralize 25.00 \(\mathrm{mL}\) of the solution?

Step-by-Step Solution

Answer

The concentration of the household ammonia cleaning solution is approximately 1.18 M.

Step 1: Write the balanced chemical equation

The neutralization reaction between hydrochloric acid (HCl) and ammonia (NH3) in a water-based solution produces ammonium chloride (NH4Cl): \[NH_3(aq) + HCl(aq) \rightarrow NH_4Cl(aq)\]

Step 2: Calculate the moles of HCl used during the titration

Use the volume (in liters) and molarity (in M or moles per liter) of the HCl solution to calculate the moles of HCl used. Given data is: Volume HCl = + 49.90 mL = 0.04990 L (converting to liters by dividing by 1000) Concentration HCl = 0.5900 M Moles of HCl = volume x concentration: Moles of HCl = (0.04990 L) x (0.5900 mol/L) = 0.02943 mol

Step 3: Calculate the moles of NH3 in the ammonia solution

According to the balanced chemical equation in step 1, the stoichiometric ratio between HCl and NH3 is 1:1. Therefore, for every mole of HCl, there is one mole of NH3: Moles of NH3 = moles of HCl = 0.02943 mol

Step 4: Calculate the concentration of NH3 solution

Use the moles of NH3 and the volume of ammonia solution (given: 25.00 mL) to calculate the concentration of the ammonia solution: Volume of NH3 solution = 25.00 mL = 0.02500 L (converting to liters by dividing by 1000) Molarity of NH3 = moles of NH3 / volume of NH3 solution Molarity of NH3 = (0.02943 mol) / (0.02500 L) ≈ 1.1772 M The concentration of the household ammonia cleaning solution is approximately 1.18 M.

Key Concepts

Neutralization Reaction

In chemistry, a neutralization reaction is a type of chemical reaction in which an acid and a base react to form a salt and, usually, water. In the context of the exercise, we're dealing with the neutralization of hydrochloric acid (HCl), a strong acid, by ammonia (NH₃), a weak base.

The reaction can be represented by a simple balanced chemical equation:
\[NH_3(aq) + HCl(aq) \rightarrow NH_4Cl(aq)\]
Here, one molecule of ammonia reacts with one molecule of hydrochloric acid to produce one molecule of ammonium chloride. This 1:1 ratio is fundamental to solving stoichiometry problems involving neutralization reactions because it allows us to directly link the moles of acid used to the moles of base present in the solution.

Chemical Titration

A chemical titration is an analytical procedure used to determine the concentration of a known reactant in a solution. The technique involves the gradual addition of a solution of known concentration, called the titrant, to the solution being analyzed. The point at which the reaction between the titrant and the substance being tested is complete is known as the end point.

During titration, indicators or pH meters are often used to signal the end point, which corresponds to the complete neutralization in the case of an acid-base titration. In the exercise, the given volume and molarity of HCl allowed us to determine the precise point at which the household ammonia was neutralized.

To improve understanding of titration, it's helpful to visualize it as a

Molarity Calculation

The concept of molarity calculation is pivotal in chemistry, providing a quantifiable measure of concentration of a solution. Molarity (M) is defined as the number of moles of solute per liter of solution. It can be calculated using the formula:
\[Molarity = \frac{moles\text{ of solute}}{volume\text{ of solution in liters}}\]
To make these calculations accessible, always remember to:

• Convert volumes from milliliters to liters by dividing by 1000, since molarity is moles per liter.
• Use the stoichiometric ratios from balanced equations to relate the moles of different substances.

Applying molarity calculations in our exercise helped us determine the exact concentration of the ammonia solution in the household cleaner. Explicitly stating each conversion and calculation step ensures clarity and enhances comprehension for students tackling similar problems.