Calculating Moles of Sodium Carbonate in a Solution: A Comprehensive Guide

The calculation of moles in a solution can seem complex, but using the correct formulas and understanding the basic principles can help simplify the process. This guide will explain how to calculate the moles of sodium carbonate, Na2CO3, in a 2.0 M solution using a 10.0 mL volume. Additionally, we will cover the concept of molarity and how it relates to moles and solution volume.

Understanding the Formula for Moles in a Solution

To find the number of moles of a substance in a given volume of a solution, the formula for molarity is utilized:

moles molarity × volume in liters

First, it is important to ensure that the volume is converted from milliliters to liters. For example, converting 10.0 mL to liters:

10.0 mL 0.0100 L

Substituting the values into the molarity formula, we get:

moles 2.0 M × 0.0100 L 0.020 moles

Therefore, there are 0.020 moles of Na2CO3 in 10.0 mL of a 2.0 M solution.

The Definition of Molarity and Its Application

Molarity, denoted by the symbol M, is a measure of the concentration of a solution in terms of moles of the solute per liter of the solution. The formula to calculate molarity is:

Msolution nsolute / Vsolution

Where:

Msolution molarity of the solution, measured in moles per liter (mol/L) nsolute number of moles of the solute, measured in moles (mol) Vsolution volume of the solution, measured in liters (L)

Rearranging the formula to solve for moles:

nsolute Msolution × Vsolution

Given the molarity (2.0 M) and the volume (0.0100 L), we can plug these values into the formula:

nsolute 2.0 M × 0.0100 L 0.020 mol

Practical Application and Misconception Clarification

The confusion arose from the initial incorrect format of the question. The correct question should be:

“How many moles of Na2CO3 are in 10.0 mL of a 2.0 M solution?”

A 2.0 M solution means that there are 2 moles of the solute (Na2CO3) in 1 liter of the solution. For 10.0 mL:

1L 1000 mL 2 moles

10 mL x moles

Cross-multiplying gives:

x (10 × 2) / 1000 0.02 moles

Alternatively:

10 mL 100 times less than 1 L

Therefore, moles 100 times less than 2 moles 0.02 moles

Additional Examples of Moles Calculation

To further illustrate the concept, consider a 2.0 M solution of Na2CO3. If you have 1 dm3 (1000 mL) of the solution, it contains 2.0 moles of Na2CO3. To find the moles in 50 mL:

50 mL solution / 1000 mL of solution × 2.0 mol Na2CO3 0.1 mol Na2CO3

For the required 10 mL of the solution:

10 mL solution / 1000 mL of solution × 2.0 mol Na2CO3 0.02 mol Na2CO3

The correct answer is c 0.02 mol.

Conclusion

Calculating the moles of a substance in a solution is a straightforward process once you understand the principles of molarity and the correct formulas to use. Whether you're dealing with a 20 mL sample or a 1000 mL solution, the same principles apply. This guide should help you accurately determine the number of moles of sodium carbonate in your solutions.