Problem 10 - Chemistry: Principles and Reactions

Question

Itwenty-five \(\mathrm{mL}\) of a \(0.388 \mathrm{M}\) solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is mixed with \(35.3 \mathrm{~mL}\) of \(0.229 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\). What is the molarity of the resulting solution? Assume that the volumes are additive.

Step-by-Step Solution

Answer

Answer: The molarity of the resulting solution is approximately 0.295 M.

Step 1: Calculate the moles of solute in each solution

To calculate the moles of Na2SO4 in each solution, we will multiply the volume of each solution by its molarity. For the first solution, 25mL of 0.388M Na2SO4: Moles of Na2SO4 = M1 × V1 Moles of Na2SO4 = 0.388 M × 0.025 L = 0.0097 moles For the second solution, 35.3mL of 0.229M Na2SO4: Moles of Na2SO4 = M2 × V2 Moles of Na2SO4 = 0.229 M × 0.0353 L = 0.00808 moles

Step 2: Calculate the total moles of solute in the resulting solution

Add the moles of Na2SO4 found in step 1 from both solutions to find the total moles of Na2SO4 in the resulting solution: Total moles of Na2SO4 = moles from solution 1 + moles from solution 2 Total moles of Na2SO4 = 0.0097 moles + 0.00808 moles = 0.01778 moles

Step 3: Calculate the total volume of the resulting solution

Since the volumes of the two solutions are additive, sum their volumes to find the total volume: Total volume = Volume of Solution 1 + Volume of Solution 2 Total volume = 0.025 L + 0.0353 L = 0.0603 L

Step 4: Calculate the molarity of the resulting solution

Divide the total moles of the solute (Na2SO4) by the total volume of the solution to find the molarity of the resulting solution: Resulting molarity (M) = Total moles of Na2SO4 ÷ Total volume Resulting molarity (M) = 0.01778 moles ÷ 0.0603 L ≈ 0.295 M The molarity of the resulting solution is approximately 0.295 M.

Key Concepts

Molarity Calculation

Calculating molarity is an essential skill in chemistry to understand the concentration of a solution. Molarity, often denoted by \(M\), is defined as the number of moles of solute per liter of solution. To find the molarity, you would use the formula:

• \( M = \frac{n}{V} \)

where \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters.
In this exercise, the task is to determine the molarity of a solution after mixing two separate solutions. Determining molarity requires knowing both the total moles of solute present and the total volume of the solution after being combined.

Solute Moles

Finding the number of moles of the solute is a crucial part of determining molarity. Moles provide a way to express amounts of a chemical substance. To calculate moles from molarity and volume, you can use the formula:

• \( ext{Moles} = M \times V \)

where \( M \) is molarity and \( V \) is volume in liters.
In our example, two different solutions containing \( ext{Na}_2 ext{SO}_4 \) are mixed. For each solution:

• The first has a volume of 0.025 L (25 mL) and a molarity of 0.388 M, resulting in approximately 0.0097 moles.
• The second has a volume of 0.0353 L (35.3 mL) and a molarity of 0.229 M, which yields approximately 0.00808 moles.

This computation gives us the total moles needed to find the final molarity after the solutions are mixed.

Volume Addition

Volume addition is the process of summing the volumes of two or more solutions to get the total volume. In our problem, the concept of volume addition assumes that the volumes of solutions add together linearly when mixed.
For example, when mixing 25 mL and 35.3 mL of \( ext{Na}_2 ext{SO}_4 \) solutions, the total volume will be the sum of both volumes. Converting milliliters to liters, the total volume in liters is:

• \( 0.025 ext{ L} + 0.0353 ext{ L} = 0.0603 ext{ L} \)

This total volume is then used in the molarity calculation of the resulting solution.

Mixed Solutions

When mixing solutions, the goal is often to find the properties of the new solution created, such as molarity. A mixed solution combines the solutes and solvents of the contributing solutions, creating a new concentration.
In this task, the final molarity of the mixed \( ext{Na}_2 ext{SO}_4 \) solutions is calculated by dividing the total moles of solute by the total volume of the mixture:

• \[ ext{Molarity of resulting solution} = rac{ ext{Total moles of solute}}{ ext{Total volume of solution}} \]
• The total moles of \( ext{Na}_2 ext{SO}_4 \) is 0.01778 moles, and the total volume is 0.0603 L.

By performing the division, we determine the resultant molarity to be approximately 0.295 M. This process illustrates how properties of mixed solutions can be determined based on the known values of the individual solutions.