Q. 9.51 - An Introduction to General, Organic, and Biological Chemistry

Question

A patient receives $100 mL of 20\% (m/v)$ mannitol solution every hour.

a. How many grams of mannitol are given in $1 h$?

b. How many grams of mannitol does the patient receive in ?

Step-by-Step Solution

Answer

(part a) $20 g$ of mannitol are given in one hour.

(part b) $300 g$ of mannitol does the patient receive in $15$ hours.

Step1: Introduction (part a).

Mannitol is a medication used to treat inflammation and stress in the eye and around the brain. Mannitol can also be used to assist the body in producing more urine. This medication is prescribed to people who have kidney failure.

Step2: Given Information (part a).

The following details are provided:

A patient receiving$100 mL of 20\% (m/v)$ mannitol solution every hour.

Step3: Explanation (part a).

Find the grams of mannitol given in one hour.

$100 \mathrm{ml} \mathrm{solution}=20 \mathrm{g}\text{ mannitol }$

$\frac{20 \mathrm{g}\text{ mannitol }}{100 \mathrm{ml}\text{ solution }}\text{and }\frac{100 \mathrm{ml}\text{ solution }}{20 \mathrm{g}\text{ mannitol }}$

Rewrite the formula,

$$\begin{gathered} =100 \mathrm{ml} \mathrm{sotuion}\times \frac{20 \mathrm{g}\text{ mannitol }}{100 \mathrm{ml}\text{ sotution }} \\ =20 \mathrm{g}\text{ mannitol } \end{gathered}$$

Step4: Given Information (part b).

The following details are provided:

A patient receiving $100 mL of 20\% (m/v)$ mannitol every hour.

Step5: Explanation (part b).

The patient is given $20 g$ of mannitol in one hour. As a result, the patient is receiving mannitol within $15$ hours.

$$\begin{gathered} =20 g \times 15 \\ =300 g \end{gathered}$$