Calculate the number of moles of methanol in `6` 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 a 6-liter solution with a concentration of 2 molarity (2m) and a density of 0.981 kg/L, follow these steps:

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

### Step 2: Calculate the total moles of methanol in 6 liters
Using the definition of molarity:
\[ \text{Moles of methanol} = \text{Molarity} \times \text{Volume in liters} \]
\[ \text{Moles of methanol} = 2 \, \text{moles/L} \times 6 \, \text{L} = 12 \, \text{moles} \]

### Step 3: Calculate the mass of methanol in the solution
The molar mass of methanol (CH₃OH) is given as 32 g/mol. To find the mass of methanol in 12 moles:
\[ \text{Mass of methanol} = \text{Moles} \times \text{Molar mass} \]
\[ \text{Mass of methanol} = 12 \, \text{moles} \times 32 \, \text{g/mol} = 384 \, \text{g} \]

### Step 4: Calculate the total mass of the solution
Since the density of the solution is given as 0.981 kg/L, we can find the total mass of the solution:
\[ \text{Mass of solution} = \text{Density} \times \text{Volume} \]
\[ \text{Mass of solution} = 0.981 \, \text{kg/L} \times 6 \, \text{L} = 5.886 \, \text{kg} = 5886 \, \text{g} \]

### Step 5: Calculate the mass of the solvent (water)
The mass of the solvent (water) can be calculated by subtracting the mass of methanol from the total mass of the solution:
\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of methanol} \]
\[ \text{Mass of solvent} = 5886 \, \text{g} - 384 \, \text{g} = 5502 \, \text{g} \]

### Step 6: Verify the solution concentration
To ensure the solution is indeed 2m, we can check:
- 2 moles of methanol corresponds to 32 g/mol * 2 = 64 g of methanol in 1 kg of water.
- The total mass of the solution is 1 kg (water) + 64 g (methanol) = 1064 g.
- The density confirms the concentration.

### Final Result
The number of moles of methanol in 6 liters of a 2m solution is **12 moles**.

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