Question

Calculate the volume necessary (in milliliters) to provide the dosage ordered, using medication labels where available. Express your answer as a decimal fraction to the nearest tenth where indicated. Order: Heparin 7,500 units subcut daily. Express answer in hundredths. Available: Heparin 10,000 units per \(\mathrm{mL}\) _______.

Short answer

0.75 mL

Step-by-step solution

Understand the Problem

We need to find the volume (in mL) required to deliver a dose of 7,500 units of Heparin, given the concentration of the solution is 10,000 units per mL.

Set up the Proportion

To find the required volume, we can set up a proportion based on the concentration: \( 10,000 \text{ units/mL} = 7,500 \text{ units}/x \text{ mL} \).

Solve the Proportion

Cross-multiply to solve for \( x \), where \( x \) is the volume in mL: \[ 10,000x = 7,500 \]

Calculate the Volume

Divide both sides by 10,000 to isolate \( x \): \[ x = \frac{7,500}{10,000} \] Calculate the fraction:\[ x = 0.75 \text{ mL} \]

Express the Answer

The volume necessary to provide the ordered dosage expressed as a decimal fraction to the nearest hundredth is 0.75 mL.

Key concepts

Dosage Calculation

In pharmaceutical calculations, dosage calculation is a crucial skill. It ensures that patients receive the correct amount of medication, which is vital for safety and efficacy. When calculating a dosage, one must identify the amount of medication ordered and the concentration of medication available. By determining these factors, we can calculate the necessary volume to administer the correct dosage. This is particularly important when dealing with medications like Heparin, where precision is required to avoid potential complications. Understanding dosage calculations can prevent overdosage or underdosage, both of which can have serious health implications.

Proportion Method

The proportion method is a common technique used in dosage calculations to find the unknown quantity. This involves setting up a ratio that compares the known concentration of a medication to the desired dosage. For example, if you know the concentration of a medication is 10,000 units per mL, and the ordered dose is 7,500 units, you set up the proportion. This can be written as a simple equation: \(10,000 \, \text{units/mL} = 7,500 \, \text{units}/x \, \text{mL}\). The next step is to solve for \(x\), which represents the volume of the medication needed. Using cross-multiplication helps simplify finding the unknown, making it a reliable method for various dosage calculations. - Set up the ratio of known concentration to ordered dosage. - Cross-multiply to find the unknown value. - Solve the equation to determine the appropriate volume.

Medication Administration

Medication administration is a process that involves the correct dosage and method of delivering medication to a patient. It's an essential step in healthcare that requires attention to detail to avoid errors. Proper medication administration follows the 'Five Rights':

• The Right Patient
• The Right Drug
• The Right Dose
• The Right Route
• The Right Time

Ensuring these rights align helps safeguard the patient's health and optimizes the treatment's effectiveness. In this scenario, administering Heparin subcutaneously (under the skin) at the correct dose of 0.75 mL is critical for the patient’s safety. Healthcare providers should always double-check calculations and verify patient information before administration.

Solution Concentration

Solution concentration tells you how much of a substance is in a certain volume of liquid, generally expressed as units per mL. Understanding how to interpret solution concentration is crucial when calculating dosages. In the exercise, Heparin has a concentration of 10,000 units per mL, meaning each mL of the solution contains 10,000 units of Heparin. Knowing this allows us to accurately calculate how much solution is needed to obtain a specific amount of the drug, like the ordered 7,500 units. A firm grasp of these details ensures accurate medication preparation and administration, minimizing risk and enhancing patient safety. In any dosing situation, knowing the concentration allows for precise calculations and correct medication delivery.