Problem 45 - Chemistry The Science in Context

Question

Window Cleaner (a) What is the concentration of ammonia in a popular window cleaner if \(25.34 \mathrm{mL}\) of \(1.162 \mathrm{M} \mathrm{HCl}\) is needed to titrate a \(10.00 \mathrm{mL}\) sample of the cleaner? (b) Suppose that the sample was diluted to about \(50 \mathrm{mL}\) with deionized water prior to the titration to make it easier to mount a pH electrode in it. What effect did this dilution have on the volume of titrant needed?

Step-by-Step Solution

Answer

Answer: The concentration of ammonia in the window cleaner is approximately 2.94 M. Diluting the ammonia sample to 50 mL does not have any effect on the volume of titrant needed.

Step 1: Find moles of HCl used in titration

We are given the volume and concentration of HCl used for titration. We can use this information to calculate the moles of HCl that reacted with the ammonia in the window cleaner. The equation for finding the moles is given by: moles = volume × concentration Where volume is in liters. moles of HCl = (25.34 mL * (1 L / 1000 mL)) * 1.162 M HCl moles of HCl = 0.0294 moles (approximately)

Step 2: Use stoichiometry to find moles of ammonia

For the reaction between ammonia and HCl, the balanced chemical equation is: NH3 (aq) + HCl (aq) → NH4Cl (aq) From the balanced equation, we can see that the mole ratio between NH3 and HCl is 1:1. Therefore, the number of moles of ammonia will be the same as the number of moles of HCl. moles of NH3 = 0.0294 moles (approximately)

Step 3: Calculate the concentration of ammonia

Now that we have the moles of ammonia, we can calculate the concentration of ammonia in the sample. The equation for finding the concentration is given by: concentration = moles / volume In this case, the volume of the window cleaner sample is given as 10.00 mL. So, the concentration can be calculated as follows: concentration of NH3 = (0.0294 moles) / (10.00 mL * (1 L / 1000 mL)) concentration of NH3 = 2.94 M (approximately) Answer to (a): The concentration of ammonia in the window cleaner is approximately 2.94 M.

Step 4: Analyze the effect of dilution on titrant volume

In part (b), we are asked to find if diluting the ammonia sample to 50 mL had any effect on the volume of titrant needed. It is important to note that when a solution is diluted, the number of moles of the solute remains the same. In this case, the number of moles of ammonia did not change due to dilution. Since the titration process is based on the stoichiometry between the moles of the titrant and the solution being titrated, the volume of the titrant needed will also stay the same regardless of the dilution. Answer to (b): The dilution of the ammonia sample to 50 mL did not have any effect on the volume of titrant needed.

Key Concepts

Concentration Calculation

Calculating the concentration of a solution is a key aspect in understanding its properties and behavior, especially in acid-base titration scenarios. To determine the concentration of ammonia in the window cleaner, we start by calculating the moles of hydrochloric acid (HCl) used in the titration. We do this by using the formula:

• moles = volume × concentration

Where the volume is converted from milliliters to liters. As given, 25.34 mL of 1.162 M HCl is used, which upon conversion and multiplication gives us approximately 0.0294 moles of HCl.
The number of moles of a solute in a solution helps us find out how concentrated the solution is. Once the moles are known, the concentration of ammonia can be calculated using the equation:

• concentration = moles / volume

By substituting the determined moles of ammonia and the original 10.00 mL sample volume (converted to liters), we deduce that the concentration of ammonia in the cleaner is approximately 2.94 M.

Stoichiometry

Stoichiometry plays a crucial role in understanding the chemical reaction between ammonia and hydrochloric acid. This aspect involves using the balanced chemical equation for the reaction, which is:

• NH\(_3\) (aq) + HCl (aq) → NH\(_4\)Cl (aq)

From this equation, we see that one mole of NH\(_3\) reacts with one mole of HCl, demonstrating a 1:1 mole ratio. This means that the number of moles of ammonia is equal to the number of moles of HCl involved in the reaction.
Understanding the mole relationship is essential in titration as it lets us calculate unknown concentrations. In this case, since we found approximately 0.0294 moles of HCl used, the same amount of moles corresponds to ammonia. This stoichiometric relationship allows students to effectively solve titration problems in an organized, step-by-step manner.

Dilution Effect

The concept of dilution is often misunderstood, especially concerning titration and similar chemical analyses. When a solution is diluted by adding more solvent, the concentration decreases, but the number of moles of solute does not change.
In the exercise, the ammonia sample was diluted to 50 mL with deionized water for easier measurement. However, this dilution does not affect the volume of titrant needed for the reaction. This is because the moles of ammonia remain constant before and after the dilution.

• The relationship between moles and volume in titration is crucial for this understanding.

As the stoichiometry of the titration reaction relies on the moles of reactants, and since they did not change, the titration volume also remains unaffected.
Thus, it illustrates that while solution dilution affects concentration, it does not impact the stoichiometric requirements of the titration reaction itself.