Question

Aluminum forms a 1:1 complex with 2-hydroxy-1-naphthaldehyde p-methoxybenzoylhydraxonal, which absorbs UV radiation at 285 nm. Under pseudo-first-order conditions, a plot of the initial rate of the reaction (absorbance units per second) versus the concentration of aluminum (in μM) yields a straight line

described by the equation

$\mathrm{rate}=1.92C_{\mathrm{Al}}-0.250$

Find the concentration of aluminum in a solution that exhibits a rate of 0.53 absorbance units per second under the same experimental conditions.

Short answer

The concentration of aluminum in a solution is$0.41\mathrm{\mu m}$

Step-by-step solution

Given Information

Solution exhibits a rate of 0.53 absorbance units per second

Equation generated by the calibration curve of the initial rate of the reaction (absorbance units per second) versus the concentration of aluminum in ($\mathrm{\mu M}$) is,

$\mathrm{rate}=1.92C_{\mathrm{Al}}-0.250$

Explanation

The concentration of aluminum by substituting the rate given to above equation can be calculated as:

$$\begin{gathered} 0.53\mathrm{A}{\mathrm{s}}^{-1}=1.92{\mathrm{C}}_{\mathrm{Al}}-0.250 \\ 1.92{\mathrm{C}}_{\mathrm{Al}}=0.53+0.250 \\ 1.92{\mathrm{C}}_{\mathrm{Al}}=0.78 \\ {\mathrm{C}}_{\mathrm{Al}}=\frac{0.78}{1.92}=0.41\mathrm{\mu M} \end{gathered}$$