Calculate the number of moles of methanol in `7` 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 7-liter solution with a concentration of 2 molarity (2M), we can follow these steps:

### Step 1: Understand the 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 Volume of the Solution
We are given that we have a 7-liter solution. Therefore, we can find the total number of moles of methanol in this volume.

### Step 3: Calculate the Number of Moles of Methanol in 7 Liters
Using the molarity:
\[ \text{Number of moles of methanol} = \text{Molarity} \times \text{Volume of solution in liters} \]
\[ \text{Number of moles of methanol} = 2 \, \text{mol/L} \times 7 \, \text{L} = 14 \, \text{moles} \]

### Step 4: Verify the Mass of Methanol
To ensure our calculations are correct, we can also verify the mass of methanol in the solution. The molar mass of methanol (CH₃OH) is given as 32 g/mol.

The mass of methanol in 2 moles is:
\[ \text{Mass of methanol} = \text{Number of moles} \times \text{Molar mass} = 2 \, \text{moles} \times 32 \, \text{g/mol} = 64 \, \text{g} \]

### Step 5: Calculate the Mass of the Solution
The density of the solution is given as 0.981 kg/L. The mass of 7 liters of solution can be calculated as:
\[ \text{Mass of solution} = \text{Density} \times \text{Volume} = 0.981 \, \text{kg/L} \times 7 \, \text{L} = 6.867 \, \text{kg} \]

### Step 6: Conclusion
The number of moles of methanol in 7 liters of a 2M solution is:
\[ \text{Number of moles of methanol} = 14 \, \text{moles} \]