Q14-14P - Organic Chemistry (Mcmurry)

Question

If pure vitamin A has ${\mathbf{\lambda }}_{\max }$ =5 325 ($\mathrm{\epsilon }$= 50,100), what is the vitamin A concentration in a sample whose absorbance at 325 nm is A = 0.735 in a cell with a path length of 1.00 cm?

Step-by-Step Solution

Answer

The concentration of vitamin A is ${\text{1.47×10}}^{\text{-5}}\text{\hspace{0.17em}M}$.

Step-by-Step Solution Step 1:Molar Absorptivity

Molar absorptivity, also known as the molar extension coefficient represented by$\mathbf{"}\mathbf{\epsilon }\mathbf{"}$ , is used to measure a wavelength's absorption intensity or efficiency.

Unit of Molar absorptivity is $\mathbf{"}\mathbf{L}\text{\hspace{0.17em}}{\mathbf{mol}}^{-1}{\mathbf{cm}}^{-1}\mathbf{"}$ .

Step 1: Calculation of vitamin A concentration

The formula to calculate the concentration of vitamin A is as follows:

$\text{c = }\frac{\text{A}}{\text{ε × l}}$

Here:

• Molar absorptivity $\left(\text{ε}\right)$ is ${\text{5.01×10}}^{\text{4}}\text{\hspace{0.17em}L/mol}\cdot \text{cm}$
• Absorbance (A) is 0.735
• The sample pathlength is 1.00 cm

The known value is substituted as:

$\begin{array}{l}\text{c = }\frac{\text{0.735}}{{\text{ 5.01×10}}^{\text{4}}\text{\hspace{0.17em}L/mol×cm×1.00\hspace{0.17em}cm }}\\ {\text{ = 1.47×10}}^{\text{-5}}\text{\hspace{0.17em}M}\end{array}$

Thus the concentration of vitamin A is ${\text{1.47×10}}^{\text{-5}}\text{\hspace{0.17em}M}$