When 400g of a `20%` solution was cooled , 50g of the solute precipitated. What is the per cent concentration of the remaining solution ?

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the amount of solute in the original solution
The original solution is 400 g with a concentration of 20%.

\[ \text{Amount of solute} = \text{Total mass of solution} \times \left(\frac{\text{Percentage concentration}}{100}\right) \]

\[ \text{Amount of solute} = 400 \, \text{g} \times \left(\frac{20}{100}\right) = 80 \, \text{g} \]

### Step 2: Determine the amount of solute remaining after precipitation
From the problem, we know that 50 g of the solute precipitated.

\[ \text{Remaining solute} = \text{Initial solute} - \text{Precipitated solute} \]

\[ \text{Remaining solute} = 80 \, \text{g} - 50 \, \text{g} = 30 \, \text{g} \]

### Step 3: Calculate the mass of the remaining solution
The total mass of the solution remains the same (400 g), but we need to account for the mass of the solute that has precipitated.

\[ \text{Mass of remaining solution} = \text{Total mass of solution} - \text{Precipitated solute} \]

\[ \text{Mass of remaining solution} = 400 \, \text{g} - 50 \, \text{g} = 350 \, \text{g} \]

### Step 4: Calculate the percentage concentration of the remaining solution
Now we can calculate the percentage concentration of the remaining solution using the formula:

\[ \text{Percentage concentration} = \left(\frac{\text{Remaining solute}}{\text{Mass of remaining solution}}\right) \times 100 \]

\[ \text{Percentage concentration} = \left(\frac{30 \, \text{g}}{350 \, \text{g}}\right) \times 100 \approx 8.57\% \]

### Final Answer
The percentage concentration of the remaining solution is approximately **8.57%**.

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