Express a 1:40 solution of Sodium Hydroxide in terms of % w/v.

Question

BlackTom AI · Accepted Answer

Percent w/v means grams of solute per 100 mL of solution. For solutions written as 1:40 (in pharmaceutical notation) the ratio is 1 part solute per 40 parts solution, i.e. 1 g of solute in 40 mL of solution (weight/volume convention).

1) Convert the ratio to g/mL:
- 1 g per 40 mL = 1/40 g per mL.
- Compute 1 ÷ 40 = 0.025 g/mL.

2) Convert g/mL to % w/v (g per 100 mL):
- Multiply grams per mL by 100 mL to get g per 100 mL.
- 0.025 g/mL × 100 mL = 2.5 g per 100 mL.
- By definition, 2.5 g/100 mL = 2.5% w/v.

Intermediate arithmetic shown:
- 1/40 = 0.025
- 0.025 × 100 = 2.5

Why this is correct: % w/v is explicitly grams per 100 mL, so converting 1 g in 40 mL to the same basis (per 100 mL) yields 2.5 g/100 mL. Therefore a 1:40 solution is 2.5% w/v.

Why the other choices are incorrect:
- 0.25% would correspond to 0.25 g/100 mL → 0.0025 g/mL → 1 g in 400 mL (1:400), not 1:40.
- 0.4% would correspond to 0.4 g/100 mL → 1 g in 250 mL (1:250), not 1:40.
- 1.25% corresponds to 1.25 g/100 mL → 1 g in 80 mL (1:80), not 1:40.
- 25% corresponds to 25 g/100 mL → 1 g in 4 mL (1:4), clearly not 1:40.

Conclusion: Converting 1 g per 40 mL to grams per 100 mL gives 2.5 g/100 mL, so the % w/v is 2.5%, which matches the provided correct answer (d. 2.5).

Express a 1:40 solution of Sodium Hydroxide in terms of % w/v.Single choice

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