Problem 82 - A Complete Resource Book in Chemistry for JEE Main

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) \(41.4 \%\)

Step-by-Step Solution

Answer

The percentage composition of the remaining solution is 31.4%.

Step 1: Calculate the Initial Amount of Solute

First, determine the amount of solute in the solution. The original solution is 40%, so the mass of solute is:\[800 \text{ g} \times 0.40 = 320 \text{ g}\]Hence, there are 320 g of solute initially.

Step 2: Determine the Amount of Solute Remaining

100 grams of solute precipitate out of the solution, which means:\[320 \text{ g} - 100 \text{ g} = 220 \text{ g}\]220 grams of solute remain dissolved in the solution.

Step 3: Calculate the Remaining Solution's Mass

Since 100 grams of solute precipitated, the new total mass of the solution is:\[800 \text{ g} - 100 \text{ g} = 700 \text{ g}\]So, the remaining solution weighs 700 grams.

Step 4: Calculate the New Percentage Composition

Now, calculate the percentage composition of the remaining solution using the remaining solute mass and the new total mass:\[\frac{220 \text{ g}}{700 \text{ g}} \times 100\% = 31.4\%\]Thus, the percentage composition of the remaining solution is 31.4%.

Key Concepts

Understanding Percentage Composition

Percentage composition is a key concept in chemistry and is crucial for various calculations, especially in solutions. It represents the ratio of the mass of solute divided by the total mass of the solution, multiplied by 100 to express it as a percentage.

• In practical terms, when you have a 40% solution, it means 40 grams of solute is present in every 100 grams of the solution.
• This allows chemists to easily compare different solutions and predict how much solute is available in a given amount of solution.

This concept is immensely helpful not only in laboratory settings but also in industrial processes where precise concentrations are essential. It ensures the right chemical reactions occur without unnecessary wastage of materials.

Solute Precipitation Process

Solute precipitation involves the phase change where a solute comes out of solution, often forming a solid. In our exercise, 100 grams of solute precipitated, which reduces the amount of dissolved solute in the solution.

• Precipitation can be triggered by changes in temperature, pH, or concentration.
• This process is crucial in reactions where the removal of excess solute is necessary to drive the reaction to completion.

Understanding how and why precipitation happens can help predict and control the formation of solids, which is vital in industries like pharmaceuticals and chemical manufacturing.

Calculating Mass of Solute

Determining the mass of the solute is essential in analyzing the solution composition. Initially, you calculate how much solute is present in the solution based on its percentage composition. In this exercise,

• The original solution had a mass of 800 grams with a 40% composition.
• This means the original solute mass was calculated as: \[800 ext{ g} \times 0.40 = 320 ext{ g} \]
• After precipitation, you subtract the precipitated mass from the initial, yielding the remaining solute mass.

These precise measurements allow scientists to understand better how solutes interact within a solution and how much remains for chemical reactions.

Basic Chemical Calculations

Chemical calculations often involve using basic arithmetic to understand the components and changes within a chemical solution. These calculations can range from determining solute mass to figuring out new compositions after reactions occur. For instance, once precipitation reduces solute mass,

• The new total solution mass must be recalculated (800 g - 100 g = 700 g).
• The new percentage composition can then be determined to reflect the current state of the solution, using \[\frac{220 \text{ g}}{700 \text{ g}} \times 100\% = 31.4\% \]

These calculations are foundational in chemistry, used repeatedly in both educational settings and real-world applications to predict outcomes and design processes accurately. They form the basis for understanding more complex chemical interactions and behaviors in diverse environments.