Question

normal saline, a 0.90 %(w/v) solution of salt (nacl) in water, is often used as an iv carrier fluid in hospitals. calculate the volume of this solution that contains 615. mg of nacl. be sure your answer has a unit symbol and is rounded to the correct number of significant digits.

Explanation:

Step1: Convert mass of NaCl to grams

Given mass of NaCl is \(61.5\ mg\). Since \(1\ g = 1000\ mg\), then \(m = 61.5\ mg\times\frac{1\ g}{1000\ mg}=0.0615\ g\)

Step2: Use the \((w/v)\) formula

The \((w/v)\) formula is \(\%(w/v)=\frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}}\times100\). We know \(\%(w/v) = 0.90\%\) and mass of solute \(m = 0.0615\ g\). Rearranging the formula for volume \(V\), we get \(V=\frac{\text{mass of solute (g)}}{\%(w/v)}\times100\)

Substitute the values: \(V=\frac{0.0615\ g}{0.90}\times100\ mL\)

Step3: Calculate the volume

\(V=\frac{0.0615\times100}{0.90}\ mL=\frac{6.15}{0.90}\ mL = 6.83\ mL\)

Answer:

\(6.8\ mL\)