When 400 g of a `20%` solution by weight was cooled, 50 g of solute precipitated. What is the percentage by mass of solute in the remaining solution ?

Options

A. `8.57%`
B. `15%`
C. `12.25%`
D. `9.5%`

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Calculate the mass of solute in the initial solution.
We know that we have a 20% solution by weight, which means that 20% of the total mass of the solution is solute.

\[ \text{Mass of solute} = \frac{20}{100} \times 400 \, \text{g} = 80 \, \text{g} \]

### Step 2: Calculate the mass of solvent in the initial solution.
Since the solution consists of solute and solvent, the remaining percentage (80%) will be the mass of the solvent.

\[ \text{Mass of solvent} = \frac{80}{100} \times 400 \, \text{g} = 320 \, \text{g} \]

### Step 3: Determine the mass of solute remaining after precipitation.
When the solution is cooled, 50 g of solute precipitates out. We need to find the remaining mass of solute.

\[ \text{Remaining mass of solute} = \text{Initial mass of solute} - \text{Mass of solute precipitated} \]
\[ \text{Remaining mass of solute} = 80 \, \text{g} - 50 \, \text{g} = 30 \, \text{g} \]

### Step 4: Calculate the mass of the remaining solution.
The total mass of the solution decreases by the mass of the solute that precipitated.

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

### Step 5: Calculate the percentage by mass of solute in the remaining solution.
Now we can find the percentage of solute in the remaining solution using the formula:

\[ \text{Percentage by mass of solute} = \left( \frac{\text{Mass of remaining solute}}{\text{Mass of remaining solution}} \right) \times 100 \]
\[ \text{Percentage by mass of solute} = \left( \frac{30 \, \text{g}}{350 \, \text{g}} \right) \times 100 \approx 8.57\% \]

### Final Answer:
The percentage by mass of solute in the remaining solution is approximately **8.57%**.

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