Q.A solution is prepared by adding 2 g of a substance A to 18 g of water. Calculate the mass per cent of the solute.

The key idea is that mass per cent is simply the mass of the solute divided by the total mass of the solution, multiplied by 100.

Step 1: Identify the masses.

Mass of solute (A) = 2 g

Mass of solvent (water) = 18 g

Step 2: Find the total mass of the solution.

Total mass = 2 g + 18 g = 20 g

Step 3: Apply the formula for mass per cent.

Why mass per cent works

Mass per cent (or weight/weight percentage) is one of the simplest ways to express concentration. It tells you: out of every 100 grams of solution, how many grams are the solute? The key insight is that the solution's total mass is just the sum of solute and solvent — there's no volume shrinkage or expansion to worry about here, unlike with volume-based units. So the calculation is straightforward: divide the part by the whole, then scale to 100.

Where mass of solution = mass of solute + mass of solvent.

Step-by-step

1. Identify the given masses.

   The solute (substance A) is 2 g. The solvent (water) is 18 g. No other components are present.

2. Find the total mass of the solution.

   Add the two:

3. Apply the mass per cent formula.

4. Simplify the fraction.

Then multiply by 100:

So the mass per cent of the solute is 10%.

Method: Mass Percentage Formula Method

This is the most direct method for calculating concentration when both solute and solvent masses are given.

Concept First (Why this works)

Mass per cent tells us how many grams of solute are present in 100 grams of solution. It’s a ratio scaled to 100 — that’s why we multiply by 100.

Steps

Step 1: Identify the given quantities

• Mass of solute (substance A) = $2 \, \text{g}$
• Mass of solvent (water) = $18 \, \text{g}$

Step 2: Calculate the total mass of the solution

Step 3: Apply the mass percentage formula

Step 4: Substitute and compute

Step 5: Write the final answer with units

Quick Check

• The solute is one-tenth of the total mass → 10% is correct.
• Always ensure the denominator is solution mass, not solvent mass alone — a common exam mistake.

Here are the common mistakes students make when calculating mass per cent (also called mass percentage or weight/weight percentage), along with clear, exam-focused corrections.

Mistake 1: Using the wrong formula

What students do wrong:

They calculate mass per cent as:

Why it’s wrong:

Mass per cent is defined as the mass of the solute divided by the total mass of the solution (solute + solvent), not just the solvent.

Correct formula:

How to avoid:

Always write the formula before plugging numbers. Remember: solution = solute + solvent.

Mistake 2: Forgetting to add the masses

What students do wrong:

They directly use 18 g (mass of water) as the denominator.

Example of error:

Why it’s wrong:

The denominator should be $2 + 18 = 20$ g, not 18 g.

Correct calculation:

How to avoid:

Always compute total mass of solution first:

$\text{Mass of solution} = \text{mass of solute} + \text{mass of solvent}$.

Mistake 3: Confusing solute and solvent

What students do wrong:

They treat water as the solute and substance A as the solvent.

Why it’s wrong:

In a solution, the solute is the substance present in smaller amount (here, 2 g of A). Water (18 g) is the solvent.

How to avoid:

Identify:

• Solute = substance being dissolved (usually smaller mass)
• Solvent = substance doing the dissolving (usually larger mass)

Mistake 4: Not simplifying or rounding incorrectly

What students do wrong:

They leave the answer as $\frac{200}{20} = 10$ without the % sign, or round to 10.0% when the question expects 10%.

How to avoid:

• Always include the % symbol in the final answer.
• Follow the significant figures given in the question (here, 2 g and 18 g → 1 or 2 significant figures → 10% is fine).

Mistake 5: Using volume instead of mass

What students do wrong:

If the question gave volume (e.g., 18 mL water), they might treat mL as grams without checking density.

Why it’s wrong:

Mass per cent requires mass, not volume. For water, 18 mL ≈ 18 g only at room temperature, but the concept must be clear.

How to avoid:

If volume is given, convert to mass using density ($\text{mass} = \text{density} \times \text{volume}$) before applying the formula.

Quick Summary – How to Get It Right Every Time

Final correct answer for this question: