In chemistry, molarity (M) is a unit of concentration that expresses the number of moles of solute per liter of solution. It's crucial to understand that molarity refers to the total volume of the solution, not just the volume of the solvent. In this case, the solution is composed of methanol (solute) and water (solven...
Calculating the Moles of Methanol
To determine the volume difference, we need to first calculate the moles of methanol present in the solution. We can use the following formula:
Moles of solute = Molarity × Volume of solution (in liters)
We are given the molarity of methanol (14.29 M) and the total volume of the solution (631 mL + 501 mL = 1132 mL). Converting the volume to liters: 1132 mL / 1000 mL/L = 1.132 L.
Now we can calculate the moles of methanol:
Moles of methanol = 14.29 M × 1.132 L = 16.16 moles
Calculating the Mass of Methanol
Next, we can calculate the mass of methanol using the molar mass of methanol (32.04 g/mol):
Mass of methanol = Moles of methanol × Molar mass of methanol
Plugging in the values:
Mass of methanol = 16.16 moles × 32.04 g/mol = 517.7 g
Calculating the Volume of Pure Methanol
Knowing the mass of methanol and its density (0.792 g/mL), we can calculate the volume of pure methanol:
Volume of methanol = Mass of methanol / Density of methanol
Plugging in the values:
Volume of methanol = 517.7 g / 0.792 g/mL = 653 mL
Calculating the Volume Difference
Finally, we can calculate the difference between the volume of the solution (1132 mL) and the combined volume of the pure methanol (653 mL) and water (501 mL):
Volume difference = Volume of solution - (Volume of methanol + Volume of water)
Plugging in the values:
Volume difference = 1132 mL - (653 mL + 501 mL) = -22 mL
Therefore, the difference in volume between the solution and the total volume of water and methanol mixed is approximately -20 mL. The negative sign indicates that the final volume of the solution is smaller than the sum of the volumes of the individual components.
Explanation of the Volume Difference
The observed volume difference arises from the phenomenon of volume contraction upon mixing. When methanol and water are mixed, the molecules interact with each other through hydrogen bonding. These interactions lead to a more compact arrangement of molecules in the solution compared to the individual components. This reduction in the average intermolecular spacing results in a decrease in the overall volume of the solution.
Conclusion
This calculation demonstrates how the volume of a solution can be different from the sum of the volumes of its individual components. The volume difference is a result of molecular interactions and volume contraction, highlighting the importance of considering these factors when working with solutions in chemistry.