What volume of a 5% w/v solution is required to deliver a dose of 40mg?
Answer (2)
Define V as the volume of the 5% solution.
Express the amount of active ingredient: 0.05 V .
Set up the equation: 0.05 V = 40 .
Solve for V : V = 0.05 40 = 800 . The required volume is $\boxed{800 \text{ ml}}.
Explanation
Understanding the Problem We need to determine the volume of a 5% solution that contains 40ml of active ingredient. The problem provides the concentration of the solution (5%) and the desired amount of active ingredient (40ml).
Setting up the Equation Let V be the volume of the 5% solution we need. The amount of active ingredient in the solution is 5% of the total volume V , which can be written as 0.05 V . We want this amount to be equal to 40ml.
Formulating the Equation We can set up the equation: 0.05 V = 40
Solving for V To solve for V , we divide both sides of the equation by 0.05: V = 0.05 40
Finding the Volume Calculating the value of V : V = 0.05 40 = 800 Therefore, we need 800 ml of the 5% solution to obtain 40ml of active ingredient.
Examples
In pharmacology, calculating solution volumes is crucial for preparing medications. For instance, if a drug is available as a 5% solution, a pharmacist needs to determine how much of this solution is required to deliver a specific dose, say 40ml of the active ingredient. This calculation ensures accurate dosing and patient safety. Similarly, in environmental science, one might need to determine the volume of a 5% disinfectant solution needed to treat a contaminated water source to achieve a desired concentration of the active disinfectant.
To deliver a dose of 40 mg from a 5% w/v solution, you need to find the volume that provides this amount of active ingredient. Given the concentration, 40 mg corresponds to 0.8 mL of the 5% solution. Therefore, the required volume is 0.8 mL.
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