A solution contains 33 g of common salt dissolved in 320 g of water; calculate the concentration of the solution in terms of mass by mass percentage.

Introduction / Context:
This chemistry question tests the concept of expressing the concentration of a solution in terms of mass by mass percentage. Such questions are very common in school examinations and competitive tests because mass percentage is one of the most widely used ways to describe how much solute is present in a given amount of solution. Understanding this idea helps students in topics like stoichiometry, preparation of laboratory solutions, and even day to day applications such as reading labels on packaged food or medicines.

Given Data / Assumptions:

• The solute is common salt, which we can treat as sodium chloride.
• Mass of solute (common salt) = 33 g.
• Mass of solvent (water) = 320 g.
• Total mass of the solution is equal to the sum of the masses of solute and solvent.
• The temperature and volume effects are ignored because we are working only with mass by mass percentage.

Concept / Approach:
Mass by mass percentage tells us how many grams of solute are present in 100 g of the final solution. The standard formula used is:
mass percent of solute = (mass of solute / mass of solution) * 100 We first find the total mass of the solution by adding solute and solvent masses, and then substitute the values into the formula. All masses must be in the same units, which they already are here (grams).

Step-by-Step Solution:
Step 1: Calculate mass of solution. mass of solution = mass of solute + mass of solvent mass of solution = 33 g + 320 g = 353 g Step 2: Use the mass percent formula. mass percent of salt = (mass of solute / mass of solution) * 100 mass percent of salt = (33 / 353) * 100 Step 3: Perform the calculation approximately. 33 / 353 is about 0.09348 mass percent of salt ≈ 0.09348 * 100 ≈ 9.35% So the concentration of the solution in terms of mass by mass percentage is approximately 9.35 percent.

Verification / Alternative Check:
We can check if this value is sensible by estimating. The solute mass 33 g is a little less than one tenth of the total mass 353 g. One tenth of 353 g is 35.3 g, which would correspond to 10 percent. Since 33 g is slightly smaller than 35.3 g, the percentage should be slightly less than 10 percent. The calculated value 9.35 percent fits this rough estimation well, so the answer is consistent and reasonable.

Why Other Options Are Wrong:
Option B: 9.09% is based on an incorrect total mass or rounded fraction; it does not match the correct ratio 33 out of 353. Option C: 10.30% would imply more solute per 100 g of solution than we actually have, so it overestimates the concentration. Option D: 13.05% is far too large for 33 g of salt in 353 g of solution and would require more solute than is given.

Common Pitfalls:
Students often forget to include the solvent when calculating mass of solution and mistakenly divide by 320 g instead of 353 g. Another frequent error is to confuse mass percent with mass by volume percent or to mix units such as grams and kilograms without converting. Careful attention to what the formula asks for, and always adding solute and solvent to obtain total solution mass, avoids these mistakes.

Final Answer:
The concentration of the solution in terms of mass by mass percentage is 9.35%.