Q.Calculate the mass percentage of benzene ($C_6H_6$) and carbon tetrachloride ($CCl_4$) if 22 g of benzene is dissolved in 122 g of carbon tetrachloride.

The key idea here is Mass Percentage, which expresses the concentration of a component in a solution as a ratio of its mass to the total mass of the solution, multiplied by 100.

First, calculate the total mass of the solution:

Next, calculate the mass percentage for each component:

When we talk about the concentration of a solution, we're describing how much solute is present in a given amount of solvent or solution. There are many ways to express concentration, and one of the most straightforward is mass percentage.

Mass percentage tells us the mass of a particular component (solute or solvent) as a fraction of the total mass of the solution, expressed as a percentage. It's a useful measure because it's independent of temperature and pressure, unlike volume-based concentrations, and it's easy to prepare solutions by simply weighing out the components.

The core idea is to find the proportion of each substance relative to the whole mixture. If you have 22 g of benzene in a solution, and the total solution weighs 144 g, then 22 out of 144 parts (by mass) are benzene. To express this as a percentage, we multiply by 100.

Let's apply this concept to the given problem.

1. Identify the given masses:

   We are given the mass of benzene (the solute) and the mass of carbon tetrachloride (the solvent).

   • Mass of benzene ($C_6H_6$) = $22 \text{ g}$
   • Mass of carbon tetrachloride ($CCl_4$) = $122 \text{ g}$

2. Calculate the total mass of the solution:

   A solution is formed when a solute dissolves in a solvent. The total mass of the solution is simply the sum of the masses of all its components.

   • Total mass of solution = Mass of benzene + Mass of carbon tetrachloride
   • Total mass of solution = $22 \text{ g} + 122 \text{ g} = 144 \text{ g}$

3. Calculate the mass percentage of benzene:

   Using the formula, we substitute the mass of benzene and the total mass of the solution.

   • Mass percentage of benzene = $\frac{\text{Mass of benzene}}{\text{Total mass of the solution}} \times 100\%$
   • Mass percentage of benzene = $\frac{22 \text{ g}}{144 \text{ g}} \times 100\%$
   • Mass percentage of benzene = $0.15277... \times 100\%$
   • Mass percentage of benzene $\approx \mathbf{15.28\%}$

4. Calculate the mass percentage of carbon tetrachloride:

   Similarly, we use the mass of carbon tetrachloride and the total mass of the solution.

   • Mass percentage of carbon tetrachloride = $\frac{\text{Mass of carbon tetrachloride}}{\text{Total mass of the solution}} \times 100\%$
   • Mass percentage of carbon tetrachloride = $\frac{122 \text{ g}}{144 \text{ g}} \times 100\%$
   • Mass percentage of carbon tetrachloride = $0.84722... \times 100\%$
   • Mass percentage of carbon tetrachloride $\approx \mathbf{84.72\%}$

Method: Mass Percentage Formula

This is a direct application of the mass percentage (w/w%) formula — the simplest and most exam-relevant method for this concept.

Steps

Step 1: Recall the formula

Mass percentage of a component =

Step 2: Identify the given masses

• Mass of benzene ($C_6H_6$) = 22 g
• Mass of carbon tetrachloride ($CCl_4$) = 122 g

Step 3: Calculate total mass of solution

Step 4: Find mass percentage of benzene

Step 5: Find mass percentage of carbon tetrachloride

Final Answer

Check: $15.28\% + 84.72\% = 100\%$ — always verify the sum equals 100%.

Here are the most common mistakes students make on this exact type of mass percentage problem, along with how to avoid each.

✗ Mistake 1: Using the wrong total mass

The error:

Students often take the total mass as just the solvent (122 g) or just the solute (22 g), instead of solute + solvent.

Example of wrong work:

• Mass % of benzene = $\frac{22}{122} \times 100$ ✗

Why it’s wrong:

Mass percentage is defined as:

The total mass of solution = mass of solute + mass of solvent.

✓ How to avoid:

Always write down:

Then use 144 g in the denominator for both components.

✗ Mistake 2: Forgetting to calculate for both components

The error:

Students calculate only the mass % of benzene (the solute) and stop there.

Why it’s wrong:

The question explicitly asks for both benzene and carbon tetrachloride. Leaving out one loses marks.

✓ How to avoid:

After finding one, immediately find the other using:

Or calculate directly:

✗ Mistake 3: Rounding too early

The error:

Students round intermediate values (e.g., 15.27% → 15%) and then use that rounded number to find the second percentage.

Why it’s wrong:

Early rounding causes the two percentages to not add up to 100%, which is a clear sign of error.

✓ How to avoid:

Keep at least 2–3 decimal places during calculation. Round only the final answer as per exam requirement (usually 2 decimal places).

✓ Correct Solution (for reference)

Step 1: Total mass of solution

Step 2: Mass % of benzene

Step 3: Mass % of carbon tetrachloride

Or simply:

Final Answer:

• Mass % of benzene = 15.28%
• Mass % of carbon tetrachloride = 84.72%