Problem 121 - 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-mL volumetric flask. After filling the volumetric flask to the mark with distilled water (indicating the volume of the new solution is \(250 . \mathrm{mL}\) ), what is the concentration of the diluted \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) solution?

Step-by-Step Solution

Answer

The final concentration is \(0.00110 \mathrm{M}\).

Step 1: Calculate Initial Moles of Na2CO3

To find the number of moles of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) in the initial solution, use the molarity formula: \[\text{moles} = \text{molarity} \times \text{volume (in L)}\] The initial solution is \(25.0 \mathrm{mL}\) or \(0.0250 \mathrm{L}\) with a concentration of \(0.110 \mathrm{M}\). \[\text{moles} = 0.110 \times 0.0250 = 0.00275 \text{ moles}\]

Step 2: Calculate Concentration After Initial Dilution

Dilute the \(0.00275\) moles of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) to \(100.0 \mathrm{mL}\) or \(0.100 \mathrm{L}\). Use the formula: \[\text{molarity} = \frac{\text{moles}}{\text{volume in L}}\] So, \[\text{molarity} = \frac{0.00275}{0.100} = 0.0275 \mathrm{M}\]

Step 3: Calculate Moles in 10.0 mL of Diluted Solution

From the concentrated solution, calculate the moles in \(10.0 \mathrm{mL}\) or \(0.0100 \mathrm{L}\): \[\text{moles} = 0.0275 \times 0.0100 = 0.000275 \text{ moles}\]

Step 4: Calculate Concentration in 250 mL Solution

Now, this \(0.000275\) moles is diluted to a total volume of \(250 \mathrm{mL}\) or \(0.250 \mathrm{L}\). Calculate the new concentration: \[\text{molarity} = \frac{0.000275}{0.250} = 0.00110 \mathrm{M}\]

Key Concepts

Dilution

Dilution involves reducing the concentration of a solute in a solution, often by adding more solvent. Imagine making lemonade less sour by adding water—this is dilution. The initial number of moles of solute remains constant; only the volume changes.

Use the formula \( C_1 V_1 = C_2 V_2 \), where \( C_1 \) and \( V_1 \) are the initial concentration and volume, and \( C_2 \) and \( V_2 \) are the final concentration and volume, respectively.

• Volume and concentration are inversely related. Increase in volume leads to a decrease in concentration.
• The process maintains the same amount of solute, perfect for laboratory experiments requiring specific concentrations.

Understanding dilution helps in accurately preparing chemical solutions with desired strengths.

Molarity Calculations

Molarity measures the concentration of a solution, expressed in moles of solute per liter of solution (\( ext{M} \)). It's calculated using the formula:\[ ext{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \]In molarity calculations, it's essential to convert all volumes to liters and use proper significant figures.

Steps for calculating molarity:

• Find the number of moles using the initial concentration and volume.
• Divide the moles by the total volume of the solution after dilution.

This concept is crucial for preparing solutions with precise concentrations for experiments and industrial applications.

Chemical Solutions

Chemical solutions are homogeneous mixtures of two or more substances. In a solution, the solute is the substance being dissolved, like salt in water. The solvent is the substance in which the solute dissolves, typically more abundant.

Characteristics of chemical solutions:

• Uniform composition throughout.
• Solute and solvent can't be separated by filtration.
• Clear and do not scatter light significantly.

Understanding solutions is fundamental in chemistry, affecting everything from reaction rates to product formation in both natural and industrial processes. Solutions facilitate chemical reactions by allowing molecules to interact in a dissolved state, thereby increasing the efficiency and speed of these interactions.