50.0 g of methanol (CH3OH, molecular mass = 32.04 g/mol) is dissolved to make 500.0 mL of solution. What is the molarity, mol/L, of the resulting solution?
Would that be?
32.04/.50 = 64.08
The correct answer and explanation is :
To calculate the molarity (M) of a solution, the formula is:
[
\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
]
Step-by-Step Calculation
- Determine the moles of methanol (CH₃OH):
The number of moles is calculated by dividing the mass of the solute by its molar mass. Given:
- Mass of methanol = 50.0 g
- Molar mass of methanol (CH₃OH) = 32.04 g/mol [
\text{Moles of methanol} = \frac{\text{Mass of methanol}}{\text{Molar mass of methanol}} = \frac{50.0 \, \text{g}}{32.04 \, \text{g/mol}} = 1.561 \, \text{mol}
]
- Convert the volume of the solution to liters:
The volume of the solution is given as 500.0 mL. To use it in the molarity formula, we need to convert it to liters: [
\text{Volume in liters} = \frac{500.0 \, \text{mL}}{1000} = 0.5000 \, \text{L}
] - Calculate the molarity:
Now that we have the number of moles of solute and the volume of the solution in liters, we can substitute these values into the molarity formula: [
M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} = \frac{1.561 \, \text{mol}}{0.5000 \, \text{L}} = 3.122 \, \text{M}
]
Thus, the molarity of the methanol solution is 3.12 M.
Explanation of the Steps:
To understand this, let’s break it down:
- Moles of Solute: The number of moles of methanol is found by dividing the mass of the methanol (50.0 g) by its molar mass (32.04 g/mol). This step gives us how many individual molecules of methanol are present in the solution.
- Volume of Solution: The volume is given as 500.0 mL, which is converted into liters (since molarity uses liters).
- Molarity Calculation: Molarity represents the concentration of a solution, specifically the number of moles of solute per liter of solution. By dividing the number of moles by the volume of the solution, we find the molarity.
Thus, the correct answer is 3.12 M, not 64.08. Your formula of 32.04/.50 = 64.08 is incorrect because it doesn’t take into account the number of moles or the correct application of the molarity formula.