Calculate the number of moles of methanol in `12` 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 12-liter solution with a concentration of 2 molarity (2m), we will follow these steps:

### Step 1: Understand the definition of molarity
Molarity (M) is defined as the number of moles of solute (in this case, methanol) per liter of solution. A 2m solution means there are 2 moles of methanol in 1 liter of solution.

### Step 2: Calculate the total number of moles in 12 liters
Since we have a 2m solution, we can calculate the total number of moles of methanol in 12 liters:
\[ \text{Total moles of methanol} = \text{Molarity} \times \text{Volume of solution (in liters)} \]
\[ \text{Total moles of methanol} = 2 \, \text{moles/L} \times 12 \, \text{L} = 24 \, \text{moles} \]

### Step 3: Calculate the mass of methanol in the solution
To find the mass of methanol in the solution, we can use the molar mass of methanol (32 g/mol):
\[ \text{Mass of methanol} = \text{Number of moles} \times \text{Molar mass} \]
\[ \text{Mass of methanol} = 24 \, \text{moles} \times 32 \, \text{g/mol} = 768 \, \text{grams} \]

### Step 4: Calculate the mass of the solution
The density of the solution is given as 0.981 kg/L. To find the mass of the solution, we can use the formula:
\[ \text{Mass of solution} = \text{Density} \times \text{Volume} \]
\[ \text{Mass of solution} = 0.981 \, \text{kg/L} \times 12 \, \text{L} = 11.772 \, \text{kg} \, (or \, 11772 \, \text{grams}) \]

### Step 5: Calculate the number of moles of methanol in 12 liters
Since we already calculated that there are 24 moles of methanol in the 12 liters of the 2m solution, we can conclude that:
\[ \text{Number of moles of methanol in 12 liters} = 24 \, \text{moles} \]

### Final Answer
The number of moles of methanol in 12 liters of a 2m solution is **24 moles**.

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