Question

A patient receives \(100 . \mathrm{mL}\) of \(20 . \%(\mathrm{~m} / \mathrm{v})\) mannitol solution every hour. a. How many grams of mannitol are given in \(1 \mathrm{~h}\) ? b. How many grams of mannitol does the patient receive in \(12 \mathrm{~h} ?\)

Short answer

a. 20 grams b. 240 grams

Step-by-step solution

Determine the Grams of Mannitol per Hour

First, convert the percentage concentration to a usable form. A 20% (m/v) solution means 20 grams of mannitol in 100 mL of solution. Since the patient receives 100 mL of the solution every hour, they receive 20 grams of mannitol every hour.

Calculate the Total Grams of Mannitol in 12 Hours

To find out how many grams of mannitol the patient receives in 12 hours, multiply the hourly amount by 12: \( 20 \text{ grams/hour} \times 12 \text{ hours} = 240 \text{ grams} \).

Key concepts

percentage concentration

To solve problems involving solutions and their concentrations, it is important to understand what percentage concentration means. In chemistry, a percentage concentration refers to the amount of solute present in a given amount of solution. For example, a 20% (m/v) mannitol solution means there are 20 grams of mannitol in every 100 mL of the solution.
This value indicates the mass of the solute (mannitol) per volume of solution (mL). Thus, you can directly convert this concentration to grams for the given volume of the solution. Such knowledge forms the basis for further calculations in dosage and concentration problems.

mannitol solution

Mannitol is a type of sugar alcohol used in medical treatments as a diuretic and to reduce intracranial pressure among other uses. A solution indicates that the mannitol is dissolved in a solvent, typically water. When dealing with mannitol solutions, it's crucial to know the concentration. Understanding the concentration tells us how much mannitol is present per unit volume of the solution. This information, such as a 20% (m/v) concentration, allows for precise dosage calculations.
For example, in this problem, knowing that a patient receives 100 mL of a 20% (m/v) mannitol solution every hour allows us to easily calculate the amount of mannitol delivered over time.

unit conversion

Unit conversion is a fundamental skill in chemistry and is crucial for solving dosage and concentration problems accurately. In our problem, the concentration is given as 20% (m/v), which we can interpret as 20 grams of mannitol per 100 mL of solution. To determine the amount of mannitol per given volume, simply scale this ratio accordingly.
In other words, if the patient receives 100 mL of the solution every hour, the calculation remains straightforward as: 20 grams of mannitol in 100 mL means 20 grams every hour. This understanding enables you to extend the calculation over different time periods or solution volumes.

dosage calculation

Accurate dosage calculation ensures patients receive the correct amount of medication. For this, understanding the concentration and how to apply it is essential. In the given problem, you determined that the patient receives 20 grams of mannitol each hour from a 20% (m/v) solution at 100 mL/hour. To find the total dosage over 12 hours, you multiply the hourly dose by 12.
So, 20 grams/hour multiplied by 12 hours equals 240 grams. With these dosage calculations, medical professionals can administer the correct amount of medication over the treatment period, ensuring both safety and efficacy.