how many grams of a drug substance should be added to 240ml of water to make a 4% (w/w) solution
The Correct Answer and Explanation is :
o prepare a 4% weight/weight (w/w) solution by adding a drug substance to 240 milliliters (mL) of water, it’s essential to understand that a 4% w/w solution means that 4 grams of the solute (the drug) are present in every 100 grams of the final solution.n this context, the total weight of the solution includes both the weight of the water and the added drug.
Step-by-Step Calculation:
- Convert Volume of Water to Weight:
- ater has a density of approximately 1 gram per milliliter (g/mL). – herefore, 240 mL of water weighs approximately 240 grams.
- Define Variables:
- et ( x ) represent the weight of the drug to be added in grams. – he total weight of the solution will then be ( 240 \, \text{g} + x ).
- Set Up the Equation:
- 4% w/w solution implies that the drug constitutes 4% of the total solution’s weight. – his relationship can be expressed mathematically as: [
\frac{x}{240 + x} = 0.04
]
- Solve for ( x ):
- ultiply both sides by ( 240 + x ) to eliminate the denominator: [
x = 0.04 \times (240 + x)
] - istribute 0.04 on the right-hand side: [
x = 9.6 + 0.04x
] - ubtract ( 0.04x ) from both sides to isolate terms involving ( x ): [
x – 0.04x = 9.6
]
[
0.96x = 9.6
] - ivide both sides by 0.96: [
x = \frac{9.6}{0.96}
]
[
x = 10 \, \text{grams}
]
herefore, to create a 4% w/w solution, you should add 10 grams of the drug substance to 240 grams of water.his calculation ensures that the drug makes up 4% of the total weight of the solution, which will be 250 grams (240 grams of water + 10 grams of drug).
Verification:
- Total Weight of Solution: 40 g (water) + 10 g (drug) = 250 g- Percentage of Drug in Solution: (\frac{10 \, \text{g}}{250 \, \text{g}} \times 100\% = 4\%)
his confirms that the solution is indeed 4% w/w.
Alternative Approach:
nother method to determine the amount of drug needed is to use the formula:
[
\text{Mass of drug} = \frac{\text{Desired concentration} \times \text{Mass of solvent}}{100\% – \text{Desired concentration}}
]
Applying the values:
[
\text{Mass of drug} = \frac{4\% \times 240 \, \text{g}}{100\% – 4\%} = \frac{9.6 \, \text{g}}{0.96} = 10 \, \text{g}
]
his method provides the same result, confirming that adding 10 grams of the drug to 240 grams of water yields a 4% w/w solution.
Note on Volume and Weight:
t’s important to note that while 240 mL of water is approximately 240 grams, this direct conversion holds true because the density of water is 1 g/mL.or other solvents with different densities, you would need to adjust the calculations accordingly.
n summary, by adding 10 grams of the drug substance to 240 grams of water, you achieve a solution where the drug constitutes 4% of the total weight, meeting the desired concentration.