Question

Use the provided initial rate data to derive the rate law for the reaction whose equation is: \({\bf{OC}}{{\bf{l}}^ - }\)(aq) + \({{\bf{I}}^ - }\)(aq) ⟶OI⁻(aq) +\({\bf{C}}{{\bf{l}}^ - }\)(aq)

Trial	(\({\bf{OC}}{{\bf{l}}^ - }\)) (mol/L)	(\({{\bf{I}}^ - }\)) (mol/L)	Initial Rate (mol/L/s)
1.	0.0040	0.0020	0.00184
2.	0.0020	0.0040	0.00092
3.	0.0020	0.0020	0.00046

Determine the rate law expression and the value of the rate constant k with appropriate units for this reaction.

Short answer

The rate, \(r = k\left( {{\bf{OC}}{{\bf{l}}^ - }} \right)\left( {{{\bf{l}}^ - }} \right)\) with rate constant k = 5.75 × 10⁴mol^-2L²s^-1.

Step-by-step solution

Rate of a Reaction

The rate of reaction may be defined as the speed of the reactant react to give product in a particular reaction at a particular time. The concentration of the reactant and product are represented into mole/L.

\({\bf{rate = k}}{\left( {\bf{A}} \right)^{\bf{m}}}{\left( {\bf{B}} \right)^{\bf{n}}}^{}\)

Value of r \(\)

\(\begin{aligned}{}\begin{aligned}{{}{}}{{\bf{rate 2 / rate 3 = 0}}{\bf{.00092 / 0}}{\bf{.00046}}}\\{{\bf{rate 2 / rate 3 = k}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{x}}}{{\left( {{\bf{0}}{\bf{.0040}}} \right)}^{\bf{y}}}{\bf{/\;k}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{x}}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{y}}}}\end{aligned}\\\begin{aligned}{{}{}}{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{2}}{\bf{.00 = 2}}{\bf{.0}}{{\bf{0}}^{\bf{y}}}}\\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{y = 1}}}\end{aligned}\end{aligned}\)

\(\begin{aligned}{}\begin{aligned}{{}{}}{{\bf{rate 1 / rate 2 = 0}}{\bf{.00184 / 0}}{\bf{.00092}}}\\{{\bf{rate 1 / rate 2 = k}}{{\left( {{\bf{0}}{\bf{.0040}}} \right)}^{\bf{x}}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{y}}}{\bf{/ k}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{x}}}{{\left( {{\bf{0}}{\bf{.0040}}} \right)}^{\bf{y}}}}\\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{2}}{\bf{.00 = }}{{\bf{2}}^{\bf{x}}}{{\bf{2}}^{\bf{y}}}}\\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{2}}{\bf{.00 = }}{{\bf{2}}^{\bf{x}}}{{\bf{2}}^{\bf{1}}}}\\{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{4}}{\bf{.00 = }}{{\bf{2}}^{\bf{x}}}}\end{aligned}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{x = 2}}\end{aligned}\)

Value of k

Putting value in rate equation and we can calculate K: \(\)

\(\begin{aligned}{}\begin{aligned}{{}{}}{\,\,\,\,\,\,\,\,\,{\bf{rate = k}}{{\left( {{\bf{OC}}{{\bf{l}}^{\bf{ - }}}} \right)}^{\bf{2}}}{{\left( {{{\bf{I}}^{\bf{ - }}}} \right)}^{\bf{1}}}}\\{{\bf{0}}{\bf{.00184 = k}}{{\left( {{\bf{0}}{\bf{.0040}}} \right)}^{\bf{2}}}{{\left( {{\bf{0}}{\bf{.0020}}} \right)}^{\bf{1}}}}\end{aligned}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\bf{k = 5}}{\bf{.75 \times 1}}{{\bf{0}}^{\bf{4}}}{\bf{mo}}{{\bf{l}}^{{\bf{ - 2}}}}{{\bf{L}}^{\bf{2}}}{{\bf{s}}^{{\bf{ - 1}}}}\end{aligned}\)