Molarity and Concentration

Oct 13, 2025 by magicalceylontours.com 114 views

Understanding the Problem

Calculating the volume of a solution is a crucial task in chemistry, especially when working with concentrated solutions. In this problem, we are given a 9.4 M silver perchlorate solution that contains 125 g of silver perchlorate (AgClO₄). Our goal is to calculate the volume of this solution in milliliters (mL), ensuring that our answer has the correct number of significant digits.

Molarity and Concentration

Before we dive into the calculation, let's review the concept of molarity. Molarity (M) is defined as the number of moles of solute per liter of solution. In this case, we are given a 9.4 M solution, which means that there are 9.4 moles of silver perchlorate per liter of solution.

Calculating the Number of Moles

To calculate the number of moles of silver perchlorate, we need to know its molar mass. The molar mass of silver perchlorate (AgClO₄) is 207.32 g/mol. We can calculate the number of moles using the following formula:

moles = mass / molar mass

Plugging in the values, we get:

moles = 125 g / 207.32 g/mol = 0.603 mol

Calculating the Volume

Now that we have the number of moles, we can calculate the volume of the solution using the molarity formula:

M = moles / L

Rearranging the formula to solve for volume, we get:

L = moles / M

Plugging in the values, we get:

L = 0.603 mol / 9.4 M = 0.064 L

Converting to Milliliters

To convert the volume from liters to milliliters, we can use the following conversion factor:

1 L = 1000 mL

Therefore, we can convert the volume as follows:

0.064 L x 1000 mL/L = 64 mL

Significant Figures

When working with measurements, it's essential to consider significant figures. The number of significant figures in a measurement depends on the precision of the instrument or method used to make the measurement. In this case, we have a measurement of 125 g, which has 3 significant figures. Therefore, our answer should also have 3 significant figures.

Conclusion

In conclusion, we have calculated the volume of a 9.4 M silver perchlorate solution that contains 125 g of silver perchlorate. Our answer is 64 mL, with 3 significant figures.

Additional Information

For those interested in learning more about molarity and concentration, here are some additional resources:

References

Calculating the Volume of a Solution: A Step-by-Step Guide

Step 1: Calculate the Number of Moles

mass = 125 g
molar mass = 207.32 g/mol
moles = mass / molar mass
moles = 125 g / 207.32 g/mol = 0.603 mol

Step 2: Calculate the Volume

M = 9.4 M
L = moles / M
L = 0.603 mol / 9.4 M = 0.064 L

Step 3: Convert to Milliliters

1 L = 1000 mL
0.064 L x 1000 mL/L = 64 mL

Step 4: Consider Significant Figures

The number of significant figures in a measurement depends on the precision of the instrument or method used to make the measurement.
In this case, we have a measurement of 125 g, which has 3 significant figures.
Therefore, our answer should also have 3 significant figures.

Step 5: Calculate the Final Answer

The final answer is 64 mL, with 3 significant figures.
Calculating the Volume of a Solution: Q&A =============================================

Q: What is molarity, and how is it related to the volume of a solution?

A: Molarity (M) is defined as the number of moles of solute per liter of solution. In the context of calculating the volume of a solution, molarity is used to determine the number of moles of solute present in a given volume of solution.

Q: How do I calculate the number of moles of a solute in a solution?

A: To calculate the number of moles of a solute, you need to know the mass of the solute and its molar mass. The molar mass is the mass of one mole of the substance. You can calculate the number of moles using the following formula:

moles = mass / molar mass

Q: What is the molar mass of silver perchlorate (AgClO₄)?

A: The molar mass of silver perchlorate (AgClO₄) is 207.32 g/mol.

Q: How do I calculate the volume of a solution using molarity?

A: To calculate the volume of a solution using molarity, you need to know the number of moles of solute and the molarity of the solution. You can use the following formula:

L = moles / M

Q: What is the difference between liters and milliliters?

A: 1 liter (L) is equal to 1000 milliliters (mL). Therefore, to convert the volume of a solution from liters to milliliters, you can multiply the volume in liters by 1000.

Q: How many significant figures should I use when reporting the volume of a solution?

A: The number of significant figures in a measurement depends on the precision of the instrument or method used to make the measurement. In general, you should report the volume of a solution with the same number of significant figures as the measurement of the solute.

Q: Can I use this method to calculate the volume of any solution?

A: Yes, this method can be used to calculate the volume of any solution, provided that you know the molarity of the solution and the mass of the solute.

Q: What are some common sources of error when calculating the volume of a solution?

A: Some common sources of error when calculating the volume of a solution include:

Incorrect measurement of the mass of the solute
Incorrect calculation of the molar mass of the solute
Incorrect calculation of the number of moles of solute
Incorrect conversion of the volume from liters to milliliters

Q: How can I improve the accuracy of my calculations?

A: To improve the accuracy of your calculations, make sure to:

Use precise measurements of the mass of the solute
Use accurate values for the molar mass of the solute
Double-check your calculations for errors
Use a calculator or computer program to perform calculations

Q: What are some real-world applications of calculating the volume of a solution?

A: Calculating the volume of a solution has many real-world applications, including:

Pharmaceutical manufacturing: Calculating the volume of a solution is crucial in the production of pharmaceuticals, where precise concentrations of active ingredients are required.
Chemical synthesis: Calculating the volume of a solution is essential in chemical synthesis, where precise concentrations of reactants are required to produce the desired product.
Environmental monitoring: Calculating the volume of a solution is used in environmental monitoring to determine the concentration of pollutants in water and air samples.

Conclusion

Calculating the volume of a solution is a crucial task in chemistry, with many real-world applications. By understanding the concept of molarity and how to calculate the number of moles of a solute, you can accurately determine the volume of a solution. Remember to consider significant figures and common sources of error when performing calculations.