Question

A solution with a final volume of 500.0ML was prepared by dissolving 25.00ML of methanol (CH3OH,density=0.7914g/ML) in chloroform. a. calculate the molarity of methanol in the solution, b.The solution has density of 1.454g/ML. Find the molarity of methanol. At wt: H= 1g/mol; C= 12g/mol; O= 16g/mol

Answer 1

To solve this problem, we will first calculate the mass of methanol and then use that to determine the molarity of methanol in the solution. We will take each part step-by-step.

### Part A: Molarity of Methanol in the Solution

#### Step 1: Calculate the mass of methanol.

Given:
- Volume of methanol (CH₃OH) = 25.00 mL
- Density of methanol = 0.7914 g/mL

To find the mass of methanol:
\[
\text{Mass of methanol} = \text{Volume} \times \text{Density}
\]
\[
\text{Mass of methanol} = 25.00 \, \text{mL} \times 0.7914 \, \text{g/mL} = 19.785 \, \text{g}
\]

#### Step 2: Calculate the number of moles of methanol.

We need the molar mass of methanol (CH₃OH):
- C = 12.01 g/mol
- H = 1.008 g/mol × 4 = 4.032 g/mol
- O = 16.00 g/mol

Thus, the molar mass of CH₃OH:
\[
\text{Molar mass of CH₃OH} = 12.01 + 4.032 + 16.00 = 32.042 \, \text{g/mol}
\]

Now we calculate the number of moles:
\[
\text{Moles of methanol} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{19.785 \, \text{g}}{32.042 \, \text{g/mol}} \approx 0.617 \, \text{mol}
\]

#### Step 3: Calculate the molarity of methanol.

The final volume of the solution = 500.0 mL = 0.500 L

Molarity (M) is defined as moles of solute per liter of solution:
\[
\text{Molarity of methanol} = \frac{\text{Moles of methanol}}{\text{Volume of solution in L}} = \frac{0.617 \, \text{mol}}{0.500 \, \text{L}} = 1.234 \, \text{M}
\]

### Part B: Molarity of Methanol Using the Density of the Solution

Given:
- Density of the solution = 1.454 g/mL
- Final volume of the solution = 500.0 mL

#### Step 1: Calculate the mass of the solution.

Mass of the solution:
\[
\text{Mass of the solution} = \text{Density} \times \text{Volume} = 1.454 \, \text{g/mL} \times 500.0 \, \text{mL} = 727.0 \, \text{g}
\]

#### Step 2: Calculate the mass of chloroform in the solution.

Assuming all the mass that isn’t methanol is chloroform:
- Mass of chloroform = Mass of solution - Mass of methanol
\[
\text{Mass of chloroform} = 727.0 \, \text{g} - 19.785 \, \text{g} \approx 707.215 \, \text{g}
\]

### Step 3: Calculate the molarity of methanol.

Using the same moles of methanol calculated before (0.617 mol), we can calculate the molarity again:
\[
\text{Molarity of methanol} = \frac{0.617 \, \text{mol}}{0.500 \, \text{L}} = 1.234 \, \text{M}
\]

**Final Answers:**
a. The molarity of methanol in the solution is **1.234 M**.
b. The molarity of methanol in the solution (using the solution density) is also **1.234 M**.