Calculate the number of moles of methanol in `10` litres in its `2m` solution, if the density of the solution `0.981kgL^(-1)` (molar mass of methanol `=32g "mol"^(-1)`)

Answer

To solve the problem of calculating the number of moles of methanol in a 10-liter solution with a concentration of 2 molal (m), we will follow these steps:

### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute (in this case, methanol) per kilogram of solvent (water). A 2 molal solution means there are 2 moles of methanol for every 1 kg of water.

### Step 2: Calculate the mass of methanol in 2 moles
Using the molar mass of methanol (32 g/mol), we can find the mass of 2 moles of methanol:
\[ \text{Mass of methanol} = \text{Number of moles} \times \text{Molar mass} = 2 \, \text{moles} \times 32 \, \text{g/mol} = 64 \, \text{g} \]

### Step 3: Calculate the total mass of the solution
Since we have 2 moles of methanol and 1 kg of water (the solvent), we can find the total mass of the solution:
\[ \text{Total mass of solution} = \text{Mass of methanol} + \text{Mass of water} = 64 \, \text{g} + 1000 \, \text{g} = 1064 \, \text{g} = 1.064 \, \text{kg} \]

### Step 4: Calculate the volume of the solution using density
We know the density of the solution is 0.981 kg/L. To find the volume of the solution, we can use the formula:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{1.064 \, \text{kg}}{0.981 \, \text{kg/L}} \approx 1.084 \, \text{L} \]

### Step 5: Calculate the number of moles of methanol in 10 liters
Now that we know that 1.084 liters of solution contains 2 moles of methanol, we can find out how many moles are in 10 liters:
\[ \text{Moles of methanol in 10 L} = \frac{2 \, \text{moles}}{1.084 \, \text{L}} \times 10 \, \text{L} \approx 18.43 \, \text{moles} \]

### Final Answer
The number of moles of methanol in 10 liters of a 2 molal solution is approximately **18.43 moles**.

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