Problem 50 - Chemistry and Chemical Reactivity

Question

Which of the following methods would you use to prepare \(300 .\) mL. of \(0.500 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} ?\) (a) Add \(30.0 \mathrm{mL}\), of \(1.50 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) to \(270 .\) mL. of water. (b) Dilute \(250 .\) mL of \(0.600 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{2}\) to a volume of \(300 . \mathrm{mL}.\)

Step-by-Step Solution

Answer

Option B is the correct choice.

Step 1: Understand the Problem

We need to prepare 300 mL of a 0.500 M solution of \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\). We have two options, and we need to identify which one correctly achieves this concentration and volume.

Step 2: Option A Analysis

In Option A, we add 30.0 mL of a 1.50 M solution to 270 mL of water. Calculate the final concentration using the formula \(C_f = \frac{C_iV_i}{V_f}\), where \(C_i = 1.50\ \mathrm{M}\), \(V_i = 30.0\ \mathrm{mL}\), and \(V_f = 300\ \mathrm{mL}\).

Step 3: Calculate Concentration for Option A

Substitute the values into the formula: \[C_f = \frac{1.50\ \mathrm{M} \times 30.0\ \mathrm{mL}}{300\ \mathrm{mL}} = 0.150\ \mathrm{M}.\]

Step 4: Option B Analysis

In Option B, a 250 mL of 0.600 M solution is diluted to 300 mL. Calculate the final concentration using \(C_f = \frac{C_iV_i}{V_f}\), where \(C_i = 0.600\ \mathrm{M}\), \(V_i = 250\ \mathrm{mL}\), and \(V_f = 300\ \mathrm{mL}\).

Step 5: Calculate Concentration for Option B

Substitute the values into the formula: \[C_f = \frac{0.600\ \mathrm{M} \times 250\ \mathrm{mL}}{300\ \mathrm{mL}} = 0.500\ \mathrm{M}.\]

Step 6: Compare Results

Option B results in the desired concentration of 0.500 M, while Option A results in a concentration of 0.150 M, which is too low.

Step 7: Conclude the Correct Option

Option B is the correct method to prepare the desired concentration and volume of \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\).

Key Concepts

Molarity

Molarity is a way to express the concentration of a solution. It shows how much solute (the substance being dissolved) is present in a certain volume of solution. We calculate it by dividing the number of moles of solute by the volume of the solution in liters. The formula is given as:\[ M = \frac{n}{V} \]where \( M \) is molarity, \( n \) is the number of moles of solute, and \( V \) is the volume of solution in liters.

• If you know the mass of the solute and its molar mass, you can find the moles by using \( n = \frac{\text{mass}}{\text{molar mass}} \).
• Molarity helps us understand the strength and properties of a solution. Higher molarity means more solute is dissolved in a given volume.

Understanding molarity is crucial when working with chemical reactions, where precise concentration ratios are necessary.

Dilution

Dilution is the process of decreasing the concentration of a solution by adding more solvent, usually water. The key condition here is that you maintain the amount of solute constant. The concentration is reduced, yet the total number of moles of solute remains unchanged. To calculate the concentration after dilution, we use the formula:\[ C_iV_i = C_fV_f \]where \( C_i \) is the initial concentration, \( V_i \) is the initial volume, \( C_f \) is the final concentration, and \( V_f \) is the final volume.

• This equation helps in preparing solutions of desired concentrations from more concentrated stock solutions by simply adding the right amount of solvent.
• During dilution, you often pour the concentrated solution into the solvent, not the other way around, to minimize the risk of unwanted reactions or splashes.

Understanding the dilution process and calculating correctly is essential in many laboratory settings.

Concentration Calculations

Concentration calculations are essential for preparing solutions with the precise amounts necessary for experiments or industrial processes. Calculating concentrations helps ensure that reactions proceed correctly and at an expected rate. There are several methods of expressing and calculating concentration, with molarity being one of the most common.To find the final concentration when mixing solutions or adding solvent, you can employ the dilution formula, which maintains the ratio of the solute to the overall solution.

• Using the formula \( C_f = \frac{C_iV_i}{V_f} \), you can determine how the volume changes influence the concentration.
• Option analysis, as presented in problem solutions, emphasizes comparing outcomes from different methods to ensure the correct process is used for desired concentration.

Concentration calculations aid in achieving the right balance in preparations, ensuring that no excess reagents are used, improving safety, and controlling costs.