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

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

### Step 2: Calculate the Mass of Methanol
Since we have a 2 m solution, we can calculate the mass of methanol in 2 moles:
\[ \text{Mass of methanol} = \text{Number of moles} \times \text{Molar mass} \]
Given that the molar mass of methanol is 32 g/mol:
\[ \text{Mass of methanol} = 2 \, \text{moles} \times 32 \, \text{g/mol} = 64 \, \text{g} \]

### Step 3: Calculate the Mass of the Solution
In a 2 m solution, there are 2 moles of methanol dissolved in 1 kg of water. Therefore, the total mass of the solution is:
\[ \text{Mass of solution} = \text{Mass of methanol} + \text{Mass of water} = 64 \, \text{g} + 1000 \, \text{g} = 1064 \, \text{g} = 1.064 \, \text{kg} \]

### Step 4: Calculate the Volume of the Solution
Using the density of the solution, we can calculate the volume:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \implies \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
Given that the density of the solution is 0.981 kg/L:
\[ \text{Volume of solution} = \frac{1.064 \, \text{kg}}{0.981 \, \text{kg/L}} \approx 1.085 \, \text{L} \]

### Step 5: Calculate the Number of Moles of Methanol in 2 Liters
Now, we can find out how many moles of methanol are present in 2 liters of this solution:
\[ \text{Moles of methanol in 2 L} = \left( \frac{2 \, \text{moles}}{1.085 \, \text{L}} \right) \times 2 \, \text{L} \]
Calculating this gives:
\[ \text{Moles of methanol in 2 L} \approx 3.68 \, \text{moles} \]

### Final Answer
The number of moles of methanol in 2 liters of a 2 m solution is approximately **3.68 moles**.

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