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 (mol/L) of a solution, use the formula: Molarity (M)=moles of soluteliters of solution\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}Molarity (M)=liters of solutionmoles of solute
Step 1: Calculate moles of methanol
Given:
- Mass of methanol = 50.0 g
- Molar mass of CH₃OH = 32.04 g/mol
Moles of CH3OH=50.0 g32.04 g/mol≈1.561 mol\text{Moles of CH}_3\text{OH} = \frac{50.0\ \text{g}}{32.04\ \text{g/mol}} \approx 1.561\ \text{mol}Moles of CH3OH=32.04 g/mol50.0 g≈1.561 mol
Step 2: Convert volume of solution to liters
Given:
- Volume = 500.0 mL = 0.5000 L
Step 3: Calculate molarity
Molarity=1.561 mol0.5000 L=3.122 mol/L\text{Molarity} = \frac{1.561\ \text{mol}}{0.5000\ \text{L}} = 3.122\ \text{mol/L}Molarity=0.5000 L1.561 mol=3.122 mol/L
✅ Final Answer: 3.12 mol/L
📘 Explanation (300 words)
Molarity is a common unit used in chemistry to express the concentration of a solution. It tells us how many moles of solute are present in one liter of solution. To find the molarity of a methanol solution, we need two pieces of information: how many moles of methanol are dissolved and what the total volume of the solution is in liters.
We start by converting the mass of methanol (50.0 g) into moles using the compound’s molar mass, which represents the mass of one mole of a substance. Methanol (CH₃OH) has a molar mass of 32.04 g/mol, which we obtain by summing the atomic masses of its elements (C: 12.01, H: 1.008 × 4, O: 16.00). Dividing the given mass by this molar mass yields 1.561 moles.
Next, we convert the solution’s volume from milliliters to liters because molarity is defined per liter. Since 1000 milliliters make one liter, 500.0 mL equals 0.5000 L.
Finally, we divide the moles of methanol by the volume of the solution in liters to get the molarity: 1.561 mol0.5000 L=3.122 mol/L\frac{1.561\ \text{mol}}{0.5000\ \text{L}} = 3.122\ \text{mol/L}0.5000 L1.561 mol=3.122 mol/L
Thus, the concentration of the methanol solution is approximately 3.12 mol/L. This value reflects how densely the methanol is packed into the given volume of solvent, which is crucial for predicting how the solution will behave in chemical reactions.