Question

\(800 \mathrm{~g}\) of a \(40 \%\) solution by weight was cooled. \(100 \mathrm{~g}\) of solute precipitated. The percentage composition of remaining solution is (a) \(31.4 \%\) (b) \(57.6 \%\) (c) \(45.8 \%\) (d) \(41.4 \%\)

Short answer

The percentage composition of the remaining solution is \(31.4\%\).

Step-by-step solution

Calculate the Initial Amount of Solute

Start by finding the amount of solute in the initial solution using the percentage composition. Since the solution is 40% solute by weight, the initial solute amount is \(0.4 \times 800 \text{ g} = 320 \text{ g}\).

Determine Remaining Solute

When the solution is cooled, 100 g of solute precipitates out. Subtract this from the initial solute amount. Thus, the solute left in the solution is \(320 \text{ g} - 100 \text{ g} = 220 \text{ g}\).

Find Weight of Remaining Solution

Since 100 g of solute is removed, the weight of the remaining solution is \(800 \text{ g} - 100 \text{ g} = 700 \text{ g}\).

Calculate New Percentage Composition

Now, find the percentage composition of the remaining solution using the formula: \[ \text{Percentage composition} = \left( \frac{\text{Remaining solute}}{\text{Weight of remaining solution}} \right) \times 100 \% \] Substitute the known values: \[ \frac{220 \text{ g}}{700 \text{ g}} \times 100 \% = 31.4 \% \]

Key concepts

Solution Concentration

Understanding solution concentration is pivotal in chemistry. It describes the amount of solute present in a given quantity of solvent. Concentration can be determined in various ways, but weight percentage is especially common when dealing with solid solutes in liquid solvents.
In this case, a 40% solution by weight implies that 40 grams out of every 100 grams of solution is solute. Here, the initial amount of solute in a solution weighing 800 grams is calculated by multiplying the total weight by the percentage as a decimal.

• Initial solute amount: \(0.4 \times 800 = 320\) grams.

Maintaining solution concentration is important because it influences reactions and product formations in a chemical experiment.

Precipitation

Precipitation refers to the process through which solute particles form a solid, separating from the rest of the solution. This can occur when the solution's temperature decreases, causing solubility to reduce.
In our exercise, as the solution cools down, 100 grams of the solute precipitate out, leading to a decrease in the total amount of dissolved solute.

• Amount of solute that precipitated: 100 grams.
• Remaining solute: 220 grams (after subtracting from the initial 320 grams).

Precipitation is often a crucial step in chemical processes, used to recover purified substances from a solution.

Solute Removal

Removing solute from a solution changes its composition and properties. Solute removal, through methods like precipitation, affects both the solution's volume and concentration.
After removing 100 grams of solute, the weight of our solution changes as well.

• Original solution weight: 800 grams.
• Weight of solution after solute removal: 700 grams.

Solute removal can be an intentional step in processes such as refining, purification, or even to alter the concentration for a specific experiment.
The new percentage composition of the solution is calculated as the amount of remaining solute divided by the new total weight of solution, all multiplied by 100 to get a percentage.

• New percentage composition: \( \left( \frac{220}{700} \right) \times 100\% = 31.4\% \)

Changing the amount of solute helps control the concentration, which is vital in various chemical applications.