Question

sodium chloride, nacl, is supplied in a 5.0% $left(\frac{\text{w}}{\text{v}}
ight)$ solution. this hypertonic solution is given to patients who need electrolyte replenishment. what volume should be given to provide a dose of 46. g? round your answer to 2 significant figures.

Explanation:

Step1: Define % (w/v) formula

A 5.0% (w/v) solution means $\frac{5.0\ \text{g NaCl}}{100\ \text{mL solution}}$, or $\frac{5.0\ \text{g}}{0.10\ \text{L solution}}$.

Step2: Rearrange to solve for volume

Rearrange % (w/v) to solve for volume:
$\text{Volume (L)} = \frac{\text{Mass of NaCl (g)}}{\text{Concentration (g/L)}}$
First convert % (w/v) to g/L:
$5.0\% \ (\text{w/v}) = \frac{5.0\ \text{g}}{0.10\ \text{L}} = 50\ \text{g/L}$

Step3: Calculate volume

Substitute values into the formula:
$\text{Volume} = \frac{46\ \text{g}}{50\ \text{g/L}} = 0.92\ \text{L}$

Step4: Round to 2 significant figures

The given values (5.0%, 46 g) have 2 significant figures, so the result stays 0.92 L.

Answer:

0.92 L