# 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.

## Answer and Explanation: 1

**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. |

#### Learn more about this topic:

from

Chapter 13 / Lesson 2Learn the dilute and concentrated solution definition. Compare and contrast dilute vs concentrated solution examples and see how a solution changes physically and chemically as it goes from dilute to concentrate.