Preparing a Diluted Solution

Oct 13, 2025 by pynkocean.com 14 views

Understanding the Problem

Preparing a diluted solution is a common task in chemistry, especially in laboratory settings. A student needs to prepare 500mL of a 0.2M solution from a 2.0M stock solution. To solve this problem, we need to understand the concept of molarity and how to prepare a diluted solution.

What is Molarity?

Molarity is a measure of the concentration of a solution, expressed in units of moles per liter (mol/L). It is defined as the number of moles of solute present in one liter of solution. In this case, the stock solution has a molarity of 2.0M, which means it contains 2 moles of solute per liter of solution.

Preparing a Diluted Solution

To prepare a diluted solution, we need to know the volume of the stock solution required to achieve the desired concentration. The formula to calculate the volume of stock solution needed is:

V_stock = V_diluted x (M_stock / M_diluted)

where V_stock is the volume of stock solution needed, V_diluted is the volume of diluted solution required, M_stock is the molarity of the stock solution, and M_diluted is the molarity of the diluted solution.

Plugging in the Values

In this case, we want to prepare 500mL of a 0.2M solution from a 2.0M stock solution. Plugging in the values, we get:

V_stock = 500mL x (2.0M / 0.2M) V_stock = 500mL x 10 V_stock = 5000mL

However, this is not the correct answer. We need to convert the volume from milliliters to liters, since molarity is expressed in units of moles per liter.

V_stock = 5000mL / 1000 V_stock = 5L

Converting the Volume

Since the question asks for the volume of stock solution in milliliters, we need to convert the volume from liters to milliliters.

V_stock = 5L x 1000 V_stock = 5000mL

However, this is still not the correct answer. We need to consider the fact that the stock solution is 2.0M, which means it contains 2 moles of solute per liter of solution. To prepare 500mL of a 0.2M solution, we need to use a smaller volume of stock solution.

Calculating the Correct Volume

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

V_stock = V_diluted x (M_stock / M_diluted)

However, we need to consider the fact that the diluted solution is 0.2M, which means it contains 0.2 moles of solute per liter of solution. To prepare 500mL of a 0.2M solution, we need to use a smaller volume of stock solution.

V_stock = 500mL x (2.0M / 0.2M) V_stock = 500mL x 10 V_stock = 5000mL

Using a Conversion Factor

To calculate the correct volume of stock solution needed, we can use a conversion factor. Since the stock solution is 2.0M and the diluted solution is 0.2M, we can set up a proportion:

2.0M / 0.2M = x / 500mL

Solving for x, we get:

x = 500mL x (0.2M / 2.0M) x = 50mL

Conclusion

In conclusion, to prepare 500mL of a 0.2M solution from a 2.0M stock solution, the student needs to use 50mL of stock solution. This is the correct answer.

Answer

The correct answer is:

A. 25mL is incorrect B. 50mL is correct C. 100mL is incorrect D. 250mL is incorrect

Discussion

Preparing a diluted solution is a common task in chemistry, especially in laboratory settings. To solve this problem, we need to understand the concept of molarity and how to prepare a diluted solution. The formula to calculate the volume of stock solution needed is:

V_stock = V_diluted x (M_stock / M_diluted)

We can use a conversion factor to calculate the correct volume of stock solution needed. In this case, we need to use 50mL of stock solution to prepare 500mL of a 0.2M solution from a 2.0M stock solution.

Key Takeaways

Molarity is a measure of the concentration of a solution, expressed in units of moles per liter (mol/L).
To prepare a diluted solution, we need to know the volume of the stock solution required to achieve the desired concentration.
The formula to calculate the volume of stock solution needed is: V_stock = V_diluted x (M_stock / M_diluted)
We can use a conversion factor to calculate the correct volume of stock solution needed.

References

Chemistry textbook, chapter 3: Solutions and Solubility
Online resources: Khan Academy, Chemistry LibreTexts
Q&A: Preparing Diluted Solutions =====================================

Frequently Asked Questions

Preparing diluted solutions is a common task in chemistry, especially in laboratory settings. Here are some frequently asked questions and answers to help you understand the concept better.

Q: What is molarity?

A: Molarity is a measure of the concentration of a solution, expressed in units of moles per liter (mol/L). It is defined as the number of moles of solute present in one liter of solution.

Q: How do I prepare a diluted solution?

A: To prepare a diluted solution, you need to know the volume of the stock solution required to achieve the desired concentration. The formula to calculate the volume of stock solution needed is:

V_stock = V_diluted x (M_stock / M_diluted)

Q: What is the difference between a stock solution and a diluted solution?

A: A stock solution is a concentrated solution that contains a high concentration of solute. A diluted solution is a solution that has been diluted to a lower concentration.

Q: How do I calculate the volume of stock solution needed?

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

V_stock = V_diluted x (M_stock / M_diluted)

Q: What is a conversion factor?

A: A conversion factor is a ratio of two quantities that are equal in value. In the context of preparing diluted solutions, a conversion factor is used to convert the concentration of the stock solution to the desired concentration of the diluted solution.

Q: How do I use a conversion factor to prepare a diluted solution?

A: To use a conversion factor to prepare a diluted solution, you need to set up a proportion:

M_stock / M_diluted = x / V_diluted

Solving for x, you get:

x = V_diluted x (M_stock / M_diluted)

Q: What are some common mistakes to avoid when preparing diluted solutions?

A: Some common mistakes to avoid when preparing diluted solutions include:

Not using the correct concentration of the stock solution
Not using the correct volume of the stock solution
Not taking into account the dilution factor
Not using a conversion factor to convert the concentration of the stock solution to the desired concentration of the diluted solution

Q: How do I ensure that my diluted solution is accurate?

A: To ensure that your diluted solution is accurate, you need to:

Use a high-quality stock solution
Use the correct concentration of the stock solution
Use the correct volume of the stock solution
Take into account the dilution factor
Use a conversion factor to convert the concentration of the stock solution to the desired concentration of the diluted solution

Conclusion

Preparing diluted solutions is a common task in chemistry, especially in laboratory settings. By understanding the concept of molarity and how to prepare a diluted solution, you can ensure that your solutions are accurate and reliable. Remember to use a conversion factor to convert the concentration of the stock solution to the desired concentration of the diluted solution, and to take into account the dilution factor.

Key Takeaways

Molarity is a measure of the concentration of a solution, expressed in units of moles per liter (mol/L).
To prepare a diluted solution, you need to know the volume of the stock solution required to achieve the desired concentration.
The formula to calculate the volume of stock solution needed is: V_stock = V_diluted x (M_stock / M_diluted)
A conversion factor is a ratio of two quantities that are equal in value.
To use a conversion factor to prepare a diluted solution, you need to set up a proportion: M_stock / M_diluted = x / V_diluted

References

Chemistry textbook, chapter 3: Solutions and Solubility
Online resources: Khan Academy, Chemistry LibreTexts