Calculate the number of moles of methanol in `3` litres in its `2m` solution, if the density of the solution `0.981kgL^(-1)` (molar mass of methanol `=32g "mol"^(-1)`)

Explanation

To calculate the number of moles of methanol in a 3-liter solution with a concentration of 2M (molar) and a density of 0.981 kg/L, we can follow these steps:

### Step 1: Understand the Concentration
A 2M solution means there are 2 moles of methanol in 1 liter of solution.

### Step 2: Calculate the Total Moles in 3 Liters
Since the concentration is 2 moles per liter, for 3 liters:
\[ \text{Total moles of methanol} = 2 \, \text{moles/L} \times 3 \, \text{L} = 6 \, \text{moles} \]

### Step 3: Calculate the Mass of Methanol in 2 Moles
The molar mass of methanol (CH₃OH) is given as 32 g/mol. Therefore, the mass of 2 moles of methanol is:
\[ \text{Mass of methanol} = 2 \, \text{moles} \times 32 \, \text{g/mol} = 64 \, \text{g} \]

### Step 4: Calculate the Total Mass of the Solution
Since the solution is 2M, it contains 2 moles of methanol and the rest is water. The mass of water in 1 liter of solution can be calculated as follows:
- The total mass of the solution can be calculated using density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \implies \text{Mass} = \text{Density} \times \text{Volume} \]
For 1 liter of solution:
\[ \text{Mass of solution} = 0.981 \, \text{kg/L} \times 1 \, \text{L} = 0.981 \, \text{kg} = 981 \, \text{g} \]

### Step 5: Calculate the Mass of Water
The mass of water in the solution can be found by subtracting the mass of methanol from the total mass of the solution:
\[ \text{Mass of water} = \text{Mass of solution} - \text{Mass of methanol} = 981 \, \text{g} - 64 \, \text{g} = 917 \, \text{g} \]

### Step 6: Calculate the Volume of the Solution
Now, we need to find the volume of the solution that contains the 2 moles of methanol:
\[ \text{Volume of solution} = \frac{\text{Mass of solution}}{\text{Density}} = \frac{981 \, \text{g}}{0.981 \, \text{kg/L}} = 1 \, \text{L} \]

### Step 7: Calculate the Moles of Methanol in 3 Liters
Now we can find the number of moles of methanol in 3 liters of solution:
\[ \text{Moles in 3 L} = \frac{2 \, \text{moles}}{1 \, \text{L}} \times 3 \, \text{L} = 6 \, \text{moles} \]

### Final Answer
Thus, the number of moles of methanol in 3 liters of a 2M solution is **6 moles**.

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