Question

Equations for the chemiluminescence determination of $S{O}_2$are given on page $383$. Derive an expression for the relationship between the concentration of$S{O}_2$in a sample, the luminescence intensity, and the equilibrium constant for the first reaction.

Short answer

The phrase is generated as a connection between the concentration of Sulphur dioxide, the intensity of Iuminescence, and the reaction's equilibrium constant.

Step-by-step solution

Step 1. Given information

Equation of chemiluminescence determination are given and they have asked about an expression between concentration, luminescence and equilibrium constant.

Step 2. Formula used

Chemiluminescence is light released by a substance as a consequence of a chemical reaction, while luminescence is light emitted as a result of heating.

In analytical chemistry, the standard addition method is most commonly employed, in which the standard is introduced directly to sample aliquots of equal volume.

It's used to figure out how much of an unknown solution there is. Before being measured, each solution is diluted to a certain volume. It's very useful for examining complicated samples. Complex samples are exemplified by the matrix effect. In terms of luminous intensity, the standard adding procedure is as follows:

$c_x=\frac{L_1{c}_s{V}_s}{\left({\mathrm{L}}_2-{\mathrm{L}}_1\right)V_x}$

Step 3. Concentration of Fe(II)

Reaction is given,

$4{\mathrm{H}}_2+2{\mathrm{SO}}_2\rightleftarrows {\mathrm{S}}_2^{*}+4{\mathrm{H}}_2\mathrm{O}.....\left(1\right)$

and ${\mathrm{S}}_2^{*}⟶{\mathrm{S}}_2+\mathrm{hv}......\left(2\right)$

Equilibrium constant for reaction $\left(1\right)$,

$K=\frac{\left[{\mathrm{S}}_2^{*}\right]{\left[{\mathrm{H}}_2\mathrm{O}\right]}^4}{{\left[{\mathrm{SO}}_2\right]}^2{\left[{\mathrm{H}}_2\right]}^4}......\left(3\right)$

we know from reaction second,

role="math" localid="1646209006393" $L=k\left[S_2^{*}\right]......\left(4\right)$

From equation $\left(3\right)\&\left(4\right)$,

$K=\frac{L{\left[{\mathrm{H}}_2\mathrm{O}\right]}^4}{k{\left[{\mathrm{SO}}_2\right]}^2{\left[{\mathrm{H}}_2\right]}^4}......\left(5\right)$

On rearranging the previous equation, we get

$\left[{\mathrm{SO}}_2\right]=\frac{{\left[{\mathrm{H}}_2\mathrm{O}\right]}^2}{{\left[{\mathrm{H}}_2\right]}^2}\sqrt{\frac{L}{kK}}......\left(6\right)$

We can neglect the pressure of concentration and get,

$\left[{\mathrm{SO}}_2\right]=k\sqrt{L}$

Hence, Both equilibrium constant and rate constant are equal.