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Chapter 1: Problem 22

You need to prepare \(500 \mathrm{~mL}\) of a dilute glucose standard \((200 \mathrm{mg} / \mathrm{L})\) from a stock standard \((2500 \mathrm{mg} / \mathrm{L})\). How much of the stock standard would you need? a. \(5 \mathrm{~mL}\) b. \(10 \mathrm{~mL}\) c. \(20 \mathrm{~mL}\) d. \(40 \mathrm{~mL}\) e. \(80 \mathrm{~mL}\)

Short Answer

Expert verified
You need 20 mL of the stock standard.

Step by step solution

01

Understand the dilution formula

To find out how much of the stock standard is needed, use the dilution formula: \[ C_1V_1 = C_2V_2 \] where \( C_1 \) is the concentration of the stock solution, \( V_1 \) is the volume of the stock solution to be used, \( C_2 \) is the concentration of the dilute solution, and \( V_2 \) is the volume of the dilute solution.
02

Identify given values

From the problem, we know the following values: \( C_1 = 2500 \mathrm{~mg/L} \) (stock concentration) \( C_2 = 200 \mathrm{~mg/L} \) (final concentration) \( V_2 = 500 \mathrm{~mL} \) (final volume)
03

Convert units if necessary

Ensure all units are consistent. Here, all concentrations are in \( \mathrm{mg/L} \) and volumes should be in \( \mathrm{mL} \): No conversion needed as all units are consistent.
04

Solve for \( V_1 \)

Rearrange the dilution formula to solve for \( V_1 \): \[ V_1 = \frac{C_2V_2}{C_1} \] Substitute the known values: \[ V_1 = \frac{200 \mathrm{~mg/L} \times 500 \mathrm{~mL}}{2500 \mathrm{~mg/L}} \] Calculate the result: \[ V_1 = \frac{100,000}{2,500} = 20 \mathrm{~mL} \]
05

Verify the result

Check that the calculated volume \( V_1 = 20 \mathrm{~mL} \) matches one of the provided options. The correct answer is 20 mL.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Clinical Chemistry Dilution
Dilution is a crucial technique in clinical chemistry for preparing solutions with a precise concentration. It involves adding a solvent, typically water, to a solution of known higher concentration to achieve a lower concentration.
In our exercise example, the goal was to create a 200 mg/L glucose solution from a stock solution of 2500 mg/L. We used the dilution formula to determine the exact volume of the stock solution needed.
This method is used frequently in clinical labs to ensure accurate testing and analysis.
Stock Solution Preparation
A stock solution is a concentrated solution that can be diluted to lower concentrations for various applications. Preparing stock solutions ensures uniformity and convenience when multiple tests require the same solute.
When making a stock solution:
  • Calculate the required amount of solute.
  • Dissolve it in a solvent to the desired concentration.
  • Store the solution under appropriate conditions to maintain stability.
In our problem, a stock glucose solution of 2500 mg/L was used. From this, we calculated the needed volume to achieve the final desired concentration of 200 mg/L.
Concentration Calculation
Calculating concentration is fundamental in laboratory settings. The concentration of a solution is often expressed in mg/L or mol/L.
The formula used for dilution calculations: C_1V_1 = C_2V_2 allows us to determine how much stock solution ( V_1 ) is required to make a final solution of a given concentration and volume ( C_2 ). To solve, simply rearrange the formula: V_1 = C_2V_2 / C_1 . This equation ensures that the solute quantity remains consistent before and after dilution.
Laboratory Techniques
Precise laboratory techniques are vital for successful dilution and concentration calculations. These techniques include:
  • Accurate Measurement: Using pipettes, burettes, and graduated cylinders for precise volume measurements.
  • Proper Mixing: Ensuring thorough mixing of solute and solvent to achieve uniform concentration.
  • Clean Instruments: Using clean and calibrated equipment to avoid contamination and ensure accuracy.
Consistent application of these techniques ensures reliable and reproducible results, which is critical in clinical chemistry and other scientific fields.

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