Questions: Mannitol, a carbohydrate, is supplied as a 25% (w/v) solution. This hypertonic solution is given to patients who have sustained a head injury with associated brain swelling. What volume should be given to provide a dose of 34 g ? Be sure your answer has the correct number of significant figures. mL 100

Mannitol, a carbohydrate, is supplied as a 25% (w/v) solution. This hypertonic solution is given to patients who have sustained a head injury with associated brain swelling. What volume should be given to provide a dose of 34 g ? Be sure your answer has the correct number of significant figures.
mL
100

Transcript text: Mannitol, a carbohydrate, is supplied as a $25 . \%\left(\frac{\mathrm{w}}{\mathrm{v}}\right)$ solution. This hypertonic solution is given to patients who have sustained a head injury with associated brain swelling. What volume should be given to provide a dose of $34 . \mathrm{g}$ ? Be sure your answer has the correct number of significant figures. $\square$ mL $\square$ 100

Solution

Solution Steps

Step 1: Understand the Problem

We need to determine the volume of a 25% (w/v) mannitol solution required to provide a dose of 34 grams of mannitol. The concentration of the solution is given as 25% (w/v), which means there are 25 grams of mannitol in every 100 mL of solution.

Step 2: Set Up the Equation

The concentration of the solution is given as 25% (w/v), which can be expressed as: \[ \frac{25 \, \text{g}}{100 \, \text{mL}} \] We need to find the volume $ V $ in mL that contains 34 grams of mannitol. We can set up the equation: \[ \frac{25 \, \text{g}}{100 \, \text{mL}} = \frac{34 \, \text{g}}{V \, \text{mL}} \]

Step 3: Solve for the Volume

Cross-multiply to solve for $ V $: \[ 25 \times V = 34 \times 100 \] \[ V = \frac{34 \times 100}{25} \] \[ V = \frac{3400}{25} \] \[ V = 136 \, \text{mL} \]