# What is the concentration of a 0.5% (w/v) solution when expressed as mg/mL? a. 0.005 mg/mL b....

## Question:

What is the concentration of a 0.5% (w/v) solution when expressed as mg/mL?

a. 0.005 mg/mL

b. 0.05 mg/mL

c. 0.5 mg/mL

d. 5 mg/mL

## Weight by Volume Concentration:

The weight-by-volume concentration is a way to express the concentration of solutes in a solution. It is defined as the mass of the solute per {eq}100\;\rm mL {/eq} of the solution.

Although the quantity is not dimensionless ( it has a unit of mass/volume), the weight by volume concentration is often expressed as a simple percentage without the inclusion of any units.

We are given:

• The weight by volume percentage of a solution, {eq}r=0.5\% {/eq}

The weight-by-volume concentration of a constituent in a mixture is given by the equation:

{eq}r_i=\dfrac{m_i}{V}\times 100\%\\ {/eq}

Here,

• {eq}m_i {/eq} is the mass of the {eq}i^{th} {/eq} constituent in the solution in grams.
• {eq}V {/eq} is the total volume of the solution in milliliters.

After plugging the given values into the above equation, we have:

{eq}\begin{align*} 0.5\%&=\dfrac{m}{V}\times 100\%\\[2ex] \Rightarrow \dfrac{m}{V}&=\dfrac{0.5}{100}\;\rm g/mL\\[2ex] &=\dfrac{5}{1000}\;\rm g/mL\\[2ex] &=\dfrac{5}{1000}\times \dfrac{1\;\rm g}{1\;\rm mL}\\[2ex] &=\dfrac{5}{1000}\times \dfrac{1000\;\rm mg}{1\;\rm mL}\\[2ex] &=\boxed{5\;\rm mg/mL} \end{align*} {/eq}

 Option (d) is the correct choice.