Molarity By Dilution Worksheet Answers

Mastering Molarity: A Comprehensive Guide with Dilution Worksheet Solutions

Understanding molarity and dilution is crucial in chemistry, especially for students venturing into solutions and stoichiometry. This comprehensive guide will walk you through the concept of molarity, the process of dilution, and provide detailed solutions to common molarity by dilution worksheets. We'll tackle the underlying principles, offer practical examples, and address frequently asked questions to solidify your understanding. By the end, you'll confidently tackle any molarity or dilution problem.

Understanding Molarity

Molarity (M) is a measure of concentration, specifically the amount of solute dissolved in a given volume of solution. It's defined as the number of moles of solute per liter of solution. The formula is:

Molarity (M) = moles of solute / liters of solution

Let's break this down:

• Moles of solute: This represents the amount of substance (the thing being dissolved) in moles. You can calculate moles using the molar mass of the substance. Remember, molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol).

• Liters of solution: This is the total volume of the solution, including both the solute and the solvent (what the solute is dissolved in, usually water). It's crucial to express the volume in liters for molarity calculations.

Example: If you dissolve 0.5 moles of sodium chloride (NaCl) in 1 liter of water, the molarity of the solution is 0.5 M (0.5 moles / 1 liter = 0.5 M).

The Dilution Equation

Dilution is the process of decreasing the concentration of a solution by adding more solvent. While the amount of solute remains constant during dilution, the volume of the solution increases, leading to a lower molarity. The dilution equation provides a straightforward way to calculate the new concentration or volume after dilution:

M1V1 = M2V2

Where:

• M1 is the initial molarity of the concentrated solution.
• V1 is the initial volume of the concentrated solution.
• M2 is the final molarity of the diluted solution.
• V2 is the final volume of the diluted solution.

This equation is based on the principle of conservation of moles. The number of moles of solute remains unchanged during dilution; therefore, the product of molarity and volume remains constant.

Solving Molarity by Dilution Worksheet Problems: Step-by-Step Approach

Let's walk through several examples, mirroring common molarity by dilution worksheet problems. We'll break down the steps to make the process clear and repeatable.

Problem 1: You have 250 mL of a 2.0 M solution of hydrochloric acid (HCl). You want to dilute this solution to a concentration of 0.5 M. What will be the final volume of the diluted solution?

Solution:

1. Identify the knowns: M1 = 2.0 M, V1 = 250 mL, M2 = 0.5 M.
2. Convert volumes to liters: V1 = 250 mL * (1 L / 1000 mL) = 0.25 L
3. Apply the dilution equation: M1V1 = M2V2 => (2.0 M)(0.25 L) = (0.5 M)(V2)
4. Solve for V2: V2 = [(2.0 M)(0.25 L)] / (0.5 M) = 1.0 L
5. Convert back to mL (if needed): V2 = 1.0 L * (1000 mL / 1 L) = 1000 mL

Therefore, the final volume of the diluted solution will be 1000 mL or 1 L.

Problem 2: You need to prepare 500 mL of a 0.1 M solution of sodium hydroxide (NaOH) from a stock solution of 2.5 M NaOH. What volume of the stock solution should you use?

Solution:

1. Identify the knowns: M1 = 2.5 M, V2 = 500 mL, M2 = 0.1 M.
2. Convert volumes to liters: V2 = 500 mL * (1 L / 1000 mL) = 0.5 L
3. Apply the dilution equation: M1V1 = M2V2 => (2.5 M)(V1) = (0.1 M)(0.5 L)
4. Solve for V1: V1 = [(0.1 M)(0.5 L)] / (2.5 M) = 0.02 L
5. Convert back to mL: V1 = 0.02 L * (1000 mL / 1 L) = 20 mL

You should use 20 mL of the 2.5 M NaOH stock solution and dilute it to a final volume of 500 mL.

Problem 3: A student dilutes 10.0 mL of a 6.0 M solution to a final volume of 100.0 mL. What is the molarity of the diluted solution?

Solution:

1. Identify the knowns: M1 = 6.0 M, V1 = 10.0 mL, V2 = 100.0 mL
2. Convert volumes to liters (though, for this problem, it's not strictly necessary as the ratio will remain the same): V1 = 0.010 L, V2 = 0.100 L
3. Apply the dilution equation: M1V1 = M2V2 => (6.0 M)(0.010 L) = M2(0.100 L)
4. Solve for M2: M2 = [(6.0 M)(0.010 L)] / (0.100 L) = 0.6 M

The molarity of the diluted solution is 0.6 M.

Advanced Dilution Problems: Serial Dilutions

Serial dilutions involve a series of dilutions, where a portion of a concentrated solution is diluted, and then a portion of that diluted solution is further diluted, and so on. This technique is often used in labs to achieve very low concentrations.

Problem 4: You have a 10 M stock solution. You perform a 1:10 dilution (1 part stock solution to 9 parts solvent), followed by a 1:100 dilution of the resulting solution. What is the final molarity?

Solution:

• First dilution (1:10): The concentration is reduced by a factor of 10. Molarity becomes 10 M / 10 = 1 M.
• Second dilution (1:100): The concentration is reduced by a factor of 100. Molarity becomes 1 M / 100 = 0.01 M.

The final molarity after the serial dilutions is 0.01 M.

Frequently Asked Questions (FAQ)

Q1: Why is it important to use liters for volume in molarity calculations?

A1: Molarity is defined as moles per liter. Using a different unit would give an incorrect molarity value. The definition is based on a liter as the standard volume unit.

Q2: What happens if I use milliliters instead of liters in the dilution equation?

A2: You'll still get the correct ratio, but the numerical value for the volume will be different. It's best to stick to liters to avoid confusion and ensure consistency with the definition of molarity.

Q3: Can I use the dilution equation for solutions with different solvents?

A3: The dilution equation is most accurate when the solvent remains the same throughout the dilution process. Significant changes in solvent can affect the volume additivity and thus influence the accuracy of the calculation.

Q4: What are some common sources of error in molarity and dilution calculations?

A4: Common errors include incorrect unit conversions (mL to L), inaccurate volume measurements, and failing to account for the total volume of the diluted solution.

Conclusion

Mastering molarity and dilution is fundamental to success in chemistry. By understanding the definitions, formulas, and the step-by-step approach to solving problems, you can confidently tackle any molarity or dilution worksheet. Remember to always pay close attention to units, double-check your calculations, and practice regularly. With consistent effort, these concepts will become second nature, paving the way for a deeper understanding of chemical solutions and reactions. The key is consistent practice and a solid grasp of the underlying principles. Remember to always prioritize accuracy and precision in your measurements and calculations.