200 ml of water is added to 50ml of 60% (m/v) solution of glucose. What will be final strength of the solution?
The correct answer and explanation is:
Correct Answer:
The final strength of the solution is 12% (m/v).
Explanation:
To solve this, we use the concept of mass/volume percent concentration (% m/v), which is defined as: \text{% (m/v)} = \left(\frac{\text{mass of solute (g)}}{\text{volume of solution (ml)}}\right) \times 100
Step 1: Determine the mass of glucose in the original solution.
The original solution is 50 ml of 60% (m/v) glucose solution. mass of glucose=60100×50=30 grams\text{mass of glucose} = \frac{60}{100} \times 50 = 30 \text{ grams}
Step 2: Add 200 ml of water.
Adding 200 ml of water increases the total volume of the solution: final volume=50 ml+200 ml=250 ml\text{final volume} = 50 \text{ ml} + 200 \text{ ml} = 250 \text{ ml}
Step 3: Calculate the new % (m/v) concentration.
Since the mass of glucose remains the same (30 grams), but the volume increases, the new concentration is: \text{final % (m/v)} = \left(\frac{30}{250}\right) \times 100 = 12\%
This means that after diluting the original solution with 200 ml of water, the concentration of glucose becomes 12% (m/v). This decrease in concentration is expected because we are adding more solvent without adding more solute, which spreads the same amount of glucose across a larger volume, thereby lowering the solution’s strength.
Dilution is a common process in chemistry and medicine, used to achieve desired concentrations. The amount of solute stays constant, but by increasing the solvent, the solution becomes less concentrated. This calculation assumes complete mixing and no volume contraction.