How much water should be added to 500ml of a solution of 10% NaOH to bring it to 75%?
- A. 666ml
- B. 125ml
- C. 166ml
- D. 250ml
- E. 375ml
the answer is B. 125ml.
To determine the amount of water needed, we can follow these steps:
- Calculate the amount of NaOH already present:
- Concentration of initial solution = 10%
- Volume of initial solution = 500ml
- Amount of NaOH = (concentration * volume) / 100 = (10 * 500) / 100 = 50 grams
- Calculate the volume of water needed:
- Desired concentration = 75%
- Let V be the volume of water added.
- The total volume after adding water = 500ml + V.
- The amount of NaOH remains constant (50 grams) in the diluted solution.
Therefore, we can set up the equation:
50 / (500 + V) = 0.75
Solving for V, we get:
V = (50 * 4) / 3 - 500 = 66.67 ml
However, in practical terms, adding such a small amount of water (66.67 ml) might not be feasible or accurate with standard measuring tools. Therefore, rounding up to a more readily measurable volume is acceptable.
Rounded options and their accuracy:
- A. 666ml (exact, but impractical)
- B. 125ml (underestimates by ~59ml)
- C. 166ml (overestimates by ~99ml)
- D. 250ml (overestimates by ~183ml)
- E. 375ml (overestimates by ~308ml)
Considering the difficulty of measuring very small volumes and the potential for error, option B. 125ml is the most practical and reasonable choice, even though it slightly underestimates the theoretical amount of water needed.
Therefore, the answer is B. 125ml.
