Concentration of Solutions
Percent by Mass / Volume
Percent by mass/volume, or %(m/v), refers to the mass of solute dissolved in milliliters solution. It is calculated by dividing the grams of solute by the milliliters of solution and multiplying by 100. Thus,
\[
\begin{aligned}
\%\,\text{mass/volume}
&=
\frac{
\text{mass of solute}
}{
\text{volume of solution}
}
\times 100
\end{aligned}
\]
Consider the following problem:
Problem 6. A medical technologist needs to prepare a 5% (m/v) 1 L NaCl solution. How many grams of NaCl must be weighed out?
Answer
1. Known: % NaCl (m/v) = 5; volume of solution = 1 L or 1000 mL
2. Unknown: mass of NaCl
3. Process: Use the equation:
\[
\begin{aligned}
\%\,\left(\frac{m}{v}\right)
&=
\frac{
\text{mass of NaCl}
}{
\text{volume of NaCl}
}
\times 100
\end{aligned}
\]
Manipulating this equation, you have:
\[
\begin{aligned}
\text{mass of NaCl}
&=
\frac{
\text{volume of NaCl} \times \%\,(\text{m/v})
}{
100
}
\end{aligned}
\]
or simply like this:
NaCl = 1000 mL (5.00/100 ) = 50g
4. Answer: The medical technologist needs to weigh exactly 50 g NaCl to prepare a 5% NaCl solution.
