A nurse is preparing to administer valproic acid 75 mg PO to a client who has acute mania. Available is valproic acid syrup 30 mg/5 mL. How many mL should the nurse administer?
(Round the answer to the nearest tenth. Use a leading zero if it applies. Do not use a trailing zero.)
The Correct Answer and Explanation is:
To solve the problem of determining how many mL of valproic acid syrup the nurse should administer, the ratio and proportion method can be used. The nurse has valproic acid syrup with a concentration of 30 mg per 5 mL and needs to give a dose of 75 mg. Here’s the step-by-step process:
Step 1: Identify the known values.
- The prescribed dose is 75 mg of valproic acid.
- The available concentration of valproic acid is 30 mg in 5 mL.
Step 2: Set up the proportion.
We need to find out how many mL of the syrup contain 75 mg. The proportion can be written as:
[
\frac{30 \, \text{mg}}{5 \, \text{mL}} = \frac{75 \, \text{mg}}{x \, \text{mL}}
]
Where:
- 30 mg is the known concentration,
- 75 mg is the required dose,
- 5 mL is the volume for the 30 mg dose,
- (x) is the unknown volume in mL that we need to calculate.
Step 3: Solve for (x).
To solve the proportion, cross-multiply:
[
30 \times x = 75 \times 5
]
[
30x = 375
]
Next, divide both sides by 30:
[
x = \frac{375}{30}
]
[
x = 12.5 \, \text{mL}
]
Step 4: Final answer.
The nurse should administer 12.5 mL of valproic acid syrup.
Explanation:
Valproic acid is often prescribed for managing conditions like acute mania, as seen in clients with bipolar disorder. Administering the correct dose is critical for achieving therapeutic effects without causing toxicity. Using the ratio and proportion method ensures accuracy in determining how much of a liquid medication to give when the available concentration differs from the prescribed dose.
In this case, knowing that 30 mg is contained in 5 mL, we can set up a proportion that matches the prescribed 75 mg dose to an unknown quantity of mL. This is essential for liquid medications to ensure precision, especially with potent drugs like valproic acid. Additionally, rounding to the nearest tenth ensures the dose is appropriate and avoids overdose.