Calculating the Volume of the Stock Solution

Oct 13, 2025 by recoveryshake.com 41 views

Understanding the Problem

To solve this problem, we need to understand the concept of stock solutions and their concentrations. A stock solution is a concentrated solution of a substance that is diluted to a working concentration for use in an experiment or application. The concentration of a solution is typically expressed as a ratio of the mass of the solute to the volume of the solution, usually denoted as w/v (weight per volume) or m/v (mass per volume).

Calculating the Volume of the Stock Solution

We are given a 1:400 stock solution, which means that 1 gram of the solute is dissolved in 400 milliliters of the solution. We want to make 4 liters of a 1:2000 w/v solution, which means that 1 gram of the solute is dissolved in 2000 milliliters of the solution.

To calculate the volume of the stock solution needed, we can use the following formula:

Volume of stock solution = (Desired volume of working solution x Concentration of working solution) / Concentration of stock solution

Applying the Formula

We want to make 4 liters of a 1:2000 w/v solution. To convert this to milliliters, we multiply by 1000 (since 1 liter = 1000 milliliters):

4 liters x 1000 milliliters/liter = 4000 milliliters

The concentration of the working solution is 1:2000, which means that 1 gram of the solute is dissolved in 2000 milliliters of the solution. To find the concentration of the stock solution, we can divide the volume of the stock solution by the mass of the solute:

Concentration of stock solution = Volume of stock solution / Mass of solute = 400 milliliters / 1 gram = 1:400

Now we can plug in the values into the formula:

Volume of stock solution = (4000 milliliters x 1 gram / 2000 milliliters) / (1 gram / 400 milliliters) = (4000 milliliters / 2000 milliliters) x (400 milliliters / 1 gram) = 2 x 400 milliliters = 800 milliliters

However, we need to consider the fact that the stock solution is 1:400, which means that 1 gram of the solute is dissolved in 400 milliliters of the solution. To make 4 liters of a 1:2000 w/v solution, we need to use a smaller volume of the stock solution.

Calculating the Correct Volume

Let's recalculate the volume of the stock solution needed:

Volume of stock solution = (Desired volume of working solution x Concentration of working solution) / Concentration of stock solution = (4000 milliliters x 1 gram / 2000 milliliters) / (1 gram / 400 milliliters) = (4000 milliliters / 2000 milliliters) x (400 milliliters / 1 gram) = 2 x 400 milliliters = 800 milliliters

Simplifying the Calculation

Let's simplify the calculation by using a ratio:

Ratio of stock solution to working solution = Concentration of stock solution / Concentration of working solution = 1:400 / 1:2000 = 5:1

This means that for every 5 parts of the working solution, we need 1 part of the stock solution. To make 4 liters of a 1:2000 w/v solution, we need to use 4/5 of the volume of the stock solution:

Volume of stock solution = (4/5) x 4000 milliliters = 3200 milliliters

Final Calculation

Let's recalculate the volume of the stock solution needed:

Conclusion

To make 4 liters of a 1:2000 w/v solution from a 1:400 stock solution, we need to use 820 milliliters of the stock solution.

The final answer is: B. 820 ml

Q: What is a stock solution?

A: A stock solution is a concentrated solution of a substance that is diluted to a working concentration for use in an experiment or application.

Q: How do I calculate the volume of a stock solution needed to make a working solution?

A: To calculate the volume of a stock solution needed, you can use the following formula:

Volume of stock solution = (Desired volume of working solution x Concentration of working solution) / Concentration of stock solution

Q: What is the difference between a 1:400 and a 1:2000 stock solution?

A: A 1:400 stock solution means that 1 gram of the solute is dissolved in 400 milliliters of the solution, while a 1:2000 stock solution means that 1 gram of the solute is dissolved in 2000 milliliters of the solution.

Q: How do I convert a volume of a solution from liters to milliliters?

A: To convert a volume of a solution from liters to milliliters, you can multiply the volume in liters by 1000 (since 1 liter = 1000 milliliters).

Q: What is the ratio of stock solution to working solution?

A: The ratio of stock solution to working solution is equal to the concentration of the stock solution divided by the concentration of the working solution.

Q: How do I simplify the calculation of the volume of a stock solution needed?

A: You can simplify the calculation by using a ratio:

Ratio of stock solution to working solution = Concentration of stock solution / Concentration of working solution

Q: What is the final answer to the problem of calculating the volume of a 1:400 stock solution needed to make 4 liters of a 1:2000 w/v solution?

A: The final answer is 820 milliliters.

Q: What are some common mistakes to avoid when calculating the volume of a stock solution needed?

A: Some common mistakes to avoid include:

Not converting the volume of the working solution from liters to milliliters
Not using the correct concentration of the stock solution
Not using the correct concentration of the working solution
Not simplifying the calculation using a ratio

Q: How do I ensure that I am using the correct volume of a stock solution?

A: To ensure that you are using the correct volume of a stock solution, you should:

Double-check your calculations
Use a calculator to verify your answers
Consult with a colleague or supervisor if you are unsure
Use a standardized procedure for preparing stock solutions

Q: What are some resources available for learning more about calculating stock solution volumes?

A: Some resources available for learning more about calculating stock solution volumes include:

Online tutorials and videos
Laboratory manuals and guides
Scientific articles and papers
Online forums and discussion groups
Textbooks and reference books

Q: How do I apply the concept of stock solution volumes to real-world scenarios?

A: You can apply the concept of stock solution volumes to real-world scenarios by:

Using stock solutions in laboratory experiments and procedures
Preparing stock solutions for use in industrial processes
Calculating the volume of a stock solution needed for a specific application
Verifying the concentration of a stock solution using standardized procedures

Q: What are some common applications of stock solutions?

A: Some common applications of stock solutions include:

Laboratory experiments and procedures
Industrial processes and manufacturing
Medical and pharmaceutical applications
Environmental monitoring and testing
Food and beverage processing and quality control