Calculate the number of moles of methanol in `9` 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 9-liter solution with a molarity of 2M, we can follow these steps:

### Step 1: Understand the given data
- Molarity (M) of the solution = 2 moles/L
- Volume of the solution = 9 L
- Density of the solution = 0.981 kg/L
- Molar mass of methanol (CH₃OH) = 32 g/mol

### Step 2: Calculate the total moles of methanol in the solution
Since the molarity is defined as the number of moles of solute (methanol) per liter of solution, we can calculate the total moles of methanol in the 9-liter solution.

\[ \text{Total moles of methanol} = \text{Molarity} \times \text{Volume} \]

\[ \text{Total moles of methanol} = 2 \, \text{moles/L} \times 9 \, \text{L} = 18 \, \text{moles} \]

### Step 3: Calculate the mass of methanol
To find the mass of methanol, we can use the molar mass:

\[ \text{Mass of methanol} = \text{Total moles} \times \text{Molar mass} \]

\[ \text{Mass of methanol} = 18 \, \text{moles} \times 32 \, \text{g/mol} = 576 \, \text{g} \]

### Step 4: Convert mass of methanol to kg
Since the density is given in kg/L, we can convert the mass of methanol to kilograms:

\[ \text{Mass of methanol in kg} = \frac{576 \, \text{g}}{1000} = 0.576 \, \text{kg} \]

### Step 5: Calculate the total mass of the solution
The total mass of the solution can be calculated using the density and volume:

\[ \text{Total mass of solution} = \text{Density} \times \text{Volume} \]

\[ \text{Total mass of solution} = 0.981 \, \text{kg/L} \times 9 \, \text{L} = 8.829 \, \text{kg} \]

### Step 6: Calculate the mass of water in the solution
To find the mass of water in the solution, we subtract the mass of methanol from the total mass of the solution:

\[ \text{Mass of water} = \text{Total mass of solution} - \text{Mass of methanol} \]

\[ \text{Mass of water} = 8.829 \, \text{kg} - 0.576 \, \text{kg} = 8.253 \, \text{kg} \]

### Final Answer
The number of moles of methanol in 9 liters of a 2M solution is **18 moles**.

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