Calculate the number of moles of methanol in `8` litres in its `2m` solution, if the density of the solution `0.981kgL^(-1)` (molar mass of methanol `=32g "mol"^(-1)`)

Answer

To calculate the number of moles of methanol in an 8-liter solution with a molarity of 2M and a density of 0.981 kg/L, we can follow these steps:

### Step 1: Calculate the mass of methanol in the solution
Given that the solution is 2M, this means there are 2 moles of methanol per 1 kg of solvent (water).

- Molar mass of methanol (CH₃OH) = 32 g/mol
- Therefore, the mass of methanol in 2 moles is:
\[ \text{Mass of methanol} = 2 \, \text{moles} \times 32 \, \text{g/mol} = 64 \, \text{g} \]

### Step 2: Calculate the total mass of the solution
Since the solution is 2M, it contains 1 kg of water (solvent) plus the mass of methanol.

- Mass of water = 1 kg = 1000 g
- Total mass of the solution:
\[ \text{Total mass} = \text{mass of methanol} + \text{mass of water} = 64 \, \text{g} + 1000 \, \text{g} = 1064 \, \text{g} = 1.064 \, \text{kg} \]

### Step 3: Calculate the volume of the solution
Using the density of the solution, we can find the volume.

- Density of the solution = 0.981 kg/L
- Volume of the solution can be calculated using the formula:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{1.064 \, \text{kg}}{0.981 \, \text{kg/L}} \approx 1.085 \, \text{L} \]

### Step 4: Calculate the number of moles of methanol in 8 liters of solution
Now, we can find out how many moles of methanol are in 8 liters of this solution.

- We know that 1.085 L of solution contains 2 moles of methanol.
- Therefore, the number of moles of methanol in 8 L can be calculated as follows:
\[ \text{Moles of methanol in 8 L} = \left(\frac{2 \, \text{moles}}{1.085 \, \text{L}}\right) \times 8 \, \text{L} \approx 14.74 \, \text{moles} \]

### Final Answer
The number of moles of methanol in 8 liters of a 2M solution is approximately **14.74 moles**.

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