Problem 47 - General Chemistry: Principles and Modern Applications

Question

Given a \(0.250 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}\) stock solution, describe how you would prepare a solution that is \(0.0125 \mathrm{M}\) \(\mathrm{K}_{2} \mathrm{CrO}_{4} .\) That is, what combination(s) of pipet and volumetric flask would you use? Typical sizes of volumetric flasks found in a general chemistry laboratory are \(100.0,250.0,500.0,\) and \(1000.0 \mathrm{mL},\) and typical sizes of volumetric pipets are 1.00,5.00,10.00 \(25.00,\) and \(50.00 \mathrm{mL}\)

Step-by-Step Solution

Answer

For the desired \(0.0125 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}\) solution, use a 50.00 mL pipette to measure stock solution and mix in a 1000.0 mL volumetric flask by adding solvent until the mark.

Step 1: Using Dilution Formula

Let's use the dilution formula \( M1V1 = M2V2 \) , where \( M1 = 0.250 \mathrm{M}\), the molarity of stock solution, and \( M2 = 0.0125 \mathrm{M}\), the molarity of the desired diluted solution. Let's calculate \( V1 \), the volume of stock solution required, while \( V2 \), the total volume of the final diluted solution will be selected from one of the given typical volumetric flask sizes.

Step 2: Determine Volume of stock solution (V1)

Rearranging the dilution formula to calculate for \( V1 = \(\frac{M2}{M1} \cdot V2\).

Step 3: Final Volume Option Iteration

Iterate through typical volumetric flask sizes, for each \( V2 \), calculate \( V1 \) using step 2 formula. Ensure that calculated \( V1 \) matches one of the given typical sizes of pipettes. This ensures accurate and efficient measurement.

Step 4: Verify volumes for pipetting and total solution

Cross-verify that the calculated \( V1 \) can be accurately measured with availabe pipette and that the total volume \( V2 \) can be held by the selected volumetric flask.

Key Concepts

Dilution Formula

The dilution formula is essential when you need to prepare a solution of a lower concentration from a stock solution. The formula is given by \( M_1V_1 = M_2V_2 \), where \( M_1 \) is the molarity of the initial or stock solution, \( V_1 \) is the volume of the stock solution needed, \( M_2 \) is the molarity of the desired diluted solution, and \( V_2 \) is the total volume of the diluted solution. The equation reflects the concept of moles conservation, where the moles of solute in the initial solution (before dilution) equal the moles of solute in the final solution (after dilution).

• To find the volume of stock solution needed, rearrange the formula to \( V_1 = \frac{M_2 \cdot V_2}{M_1} \).
• The choice of \( V_2 \) should be based on the sizes of available volumetric flasks.
• Each calculation of \( V_1 \) should be cross-checked to ensure it can be measured accurately with an available pipet.

This calculation ensures that the resulting solution has the desired concentration.

Volumetric Flask

A volumetric flask is a type of laboratory glassware used to prepare precise volumes of a liquid solution. It has a long neck and a large, round body with a flat bottom that ensures stability. At the neck, there is a single graduation mark, indicating the exact volume it can measure when the liquid level touches this mark.
The specific volume of the flask is accurately calibrated, making it ideal for dilution and preparation of standard solutions. Common flask sizes include 100.0 mL, 250.0 mL, 500.0 mL, and 1000.0 mL:

• It's important to carefully choose a flask size that can hold the total final volume of your solution, known as \( V_2 \).
• Using a flask larger than needed can introduce errors in measurement due to inaccurate leveling.
• Choose the smallest size that exceeds \( V_2 \) to maintain accuracy and precision.

Following proper technique when filling the volumetric flask will ensure that your solution is prepared with precision and repeats in future experiments will be consistent.

Volumetric Pipet

A volumetric pipet is a big player in the world of solution preparation when precision is key. This tool is designed to deliver an exact volume of liquid, essential when transferring a specified amount of a solution into another container for dilution. Volumetric pipets are often used in conjunction with a volumetric flask to ensure that the volume of the stock solution is measured precisely.
Common pipet sizes include 1.00 mL, 5.00 mL, 10.00 mL, 25.00 mL, and 50.00 mL:

• Choose a pipet that can measure the volume \( V_1 \) calculated from the dilution formula.
• If \( V_1 \) isn't an exact match to available pipet sizes, consider using a smaller pipet multiple times to reach the desired volume cumulatively.
• When using, ensure the pipet tip is clean and low bubbles are introduced to maintain precision.

Volumetric pipets ensure that the transfer process is as accurate as possible, contributing to the overall precision of the dilution process.