Problem 106 - Chemistry and Chemical Reactivity

Question

Suppose you dilute \(25.0 \mathrm{mL}\) of a \(0.110 \mathrm{M}\) solution of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) to exactly \(100.0 \mathrm{mL}\). You then take exactly \(10.0 \mathrm{mL}\) of this diluted solution and add it to a \(250-\mathrm{mL}\) volumetric flask. After filling the volumetric flask to the mark with distilled water (indicating the volume of the new solution is exactly \(250 \mathrm{mL}\) ), what is the concentration of the diluted \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) solution?

Step-by-Step Solution

Answer

The final concentration of the solution is \(0.00110 \, \text{M}\).

Step 1: Understanding the Initial Concentration

First, identify the initial concentration of the solution. You are given that the concentration of the initial solution is \(0.110 \, \text{M}\) and the volume is \(25.0 \, \text{mL}\).

Step 2: Calculate Moles of Na2CO3

To find the moles before dilution, use the formula \(\text{moles} = M \times V\), where \(M\) is molarity and \(V\) is volume in liters. Convert the initial volume to liters: \(25.0 \, \text{mL} = 0.0250 \, \text{L}\). Multiply \(0.110 \, \text{M}\) by \(0.0250 \, \text{L}\) to find the moles of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\).

Step 3: Dilute the Solution

After determining the moles of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\), the next step is dilution. The first dilution is to \(100.0 \, \text{mL}\). Since dilution doesn’t change the number of moles, the concentration of the new solution can be calculated by dividing the moles by the new volume in liters: \(0.100 \, \text{L}\).

Step 4: Calculating Moles in the New Solution

Now take \(10.0 \, \text{mL}\) from the \(100.0 \, \text{mL}\) solution which contains the diluted \(\mathrm{Na}_{2} \mathrm{CO}_{3}\). Convert \(10.0 \, \text{mL}\) to liters: \(0.0100 \, \text{L}\). Calculate the moles in this \(10.0 \, \text{mL}\) using the concentration from Step 3.

Step 5: Further Dilution

Next, the \(10.0 \, \text{mL}\) is added to a \(250.0 \, \text{mL}\) volumetric flask, diluting it further. The total volume after this dilution is \(250.0 \, \text{mL} = 0.250 \, \text{L}\).

Step 6: Calculate Final Concentration

The final concentration can be calculated by dividing the moles from Step 4 by the new total volume: \(0.250 \, \text{L}\). Use \(\text{M} = \frac{\text{moles}}{\text{liters}}\) to find the concentration of the final solution.

Key Concepts

Molarity

Molarity is a fundamental concept in chemistry used to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution. For instance, a molarity of 0.110 M indicates that there are 0.110 moles of solute, which in our case is sodium carbonate (Na2CO3), in one liter of the solution.
This makes molarity particularly useful for calculations involving reactions in solution, allowing you to easily determine how much of a solution is needed to react with a given amount of a reactant.
To calculate molarity, use the formula:\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]By understanding and applying this formula, you can efficiently determine the concentration of a solution before, during, and after dilution processes.

Concentration

Concentration refers to the amount of a substance (solute) present in a certain volume of solution. It's what gives us the molarity and informs us about how strong or weak a solution is. The concentration can change based on the volume of solvent added and is pivotal during dilutions.
When you dilute a solution, the concentration decreases because the same number of moles of solute is spread out over a larger volume of solvent.

• Initial concentration: This indicates the concentration before any dilution has occurred (0.110 M in our example).
• Changed concentration from dilution: After diluting 25 mL to 100 mL, then subsequently taking 10 mL of that diluted solution for further dilution.

Maintaining focus on concentration changes is key during multi-step dilution processes. This helps in accurately calculating final concentrations after several dilutions.

Volumetric Flask

A volumetric flask is a piece of laboratory glassware that is used to prepare solutions to an accurate final volume. It's designed to contain a precise volume at a particular temperature.
In our exercise, the volumetric flask is essential for dilutions: - It ensures that when you fill it to the mark with a solution, you have an exact volume of 250 mL. - This precision is crucial for maintaining the accuracy of our final concentration calculations.
By filling the flask to the mark with diluted solutions, we maintain consistent measurement standards, leading to reliable and reproducible results in chemical experiments. This standard practice helps eliminate errors due to volume measurements and ensures that chemical reactions proceed as expected.

Na2CO3 Solutions

Sodium carbonate (Na2CO3) is a commonly used compound in chemistry, often dissolved in water to make solutions for experimental purposes.
It dissociates in water to form sodium (Na+) and carbonate (CO3 2-) ions, which often participate in various chemical reactions, particularly buffer solutions or titrations.

• When using Na2CO3 solutions, it’s crucial to understand its solubility and how it affects other ions in solution.
• Balancing reactions with Na2CO3 is common due to its reactivity and role as a base in chemical processes.

Understanding the behavior of Na2CO3 in solution allows us to accurately predict its interactions in a chemical reaction, especially when preparing specific molar concentrations for use in various experimental analyses.