Question

In the nuclear industry, chlorine trifluoride is used to prepare uranium hexafluoride, a volatile compound of uranium used in the separation of uranium isotopes. Chlorine trifluoride is prepared by the reaction \({\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{(g) + 3}}{{\bf{F}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2Cl}}{{\bf{F}}_{\bf{3}}}{\bf{(g)}}\). Write the equation that relates the rate expressions for this reaction in terms of the disappearance of \({\bf{C}}{{\bf{l}}_{\bf{2}}}\) and \({{\bf{F}}_{\bf{2}}}\) and the formation of \({\bf{Cl}}{{\bf{F}}_{\bf{3}}}\).

Short answer

The equation that relates to in terms of the disappearance of \({\bf{C}}{{\bf{l}}_{\bf{2}}}\) and \({{\bf{F}}_{\bf{2}}}\)and the formation of \({\bf{Cl}}{{\bf{F}}_{\bf{3}}}\) given by the following equation:

Rate of disappearance of\({\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{ = }} - \frac{{{\bf{\Delta }}\left( {{\bf{C}}{{\bf{l}}_{\bf{2}}}} \right)}}{{{\bf{\Delta t}}}}{\bf{ = }} - \frac{{\bf{1}}}{{\bf{3}}}\frac{{{\bf{\Delta }}\left( {{{\bf{F}}_{\bf{2}}}} \right)}}{{{\bf{\Delta t}}}}{\bf{ = }}\frac{{\bf{1}}}{{\bf{2}}}\frac{{{\bf{\Delta }}\left( {{\bf{Cl}}{{\bf{F}}_{\bf{3}}}} \right)}}{{{\bf{\Delta t}}}}\)

Rate of disappearance of\({{\bf{F}}_{\bf{2}}}{\bf{ = }} - \frac{{\bf{1}}}{{\bf{3}}}\frac{{{\bf{\Delta }}\left( {{{\bf{F}}_{\bf{2}}}} \right)}}{{{\bf{\Delta t}}}}\)

Rate of appearance of \({\bf{Cl}}{{\bf{F}}_{\bf{3}}}{\bf{ = }}\frac{{\bf{1}}}{{\bf{2}}}\frac{{{\bf{\Delta }}\left( {{\bf{Cl}}{{\bf{F}}_{\bf{3}}}} \right)}}{{{\bf{\Delta t}}}}\)

Step-by-step solution

Understand the term rate and rate of disappearance.  

Rate is defined as the change in the concentration of reactant or product per unit of time and is given by the following formula:

\({\bf{Rate of reaction = }}\frac{{{\bf{Change in concentration of reactant or product}}}}{{{\bf{Time taken}}}}\)

When the reactant is being used up in the reaction, it tends to disappear as given by the following formula.

\({\bf{Rate of disappearance/appearance = - }}\frac{{{\bf{Disappearance of reactant}}}}{{{\bf{Time taken}}}}{\bf{ = }}\frac{{{\bf{appearance of product}}}}{{{\bf{Time taken}}}}\)

Understand the meaning of negative signs for the disappearance of reactants.

A negative sign denotes that the substance is used up in the reaction. Thus, while writing the rate of disappearance, negative sign is used. No negative sign is seen in the appearance of the product.

Determine how to write the rates disappearance of reactant for a general equation.

Let us consider the following reaction: \({\bf{aA}} \to {\bf{bB}}\)

While writing the reaction with coefficients, the stoichiometric factor is considered. The rate of disappearance is written as follows for the given reaction:

\({\bf{Rate = }} - \frac{{\bf{1}}}{{\bf{a}}}\frac{{{\bf{\Delta }}\left( {\bf{A}} \right)}}{{{\bf{\Delta t}}}}{\bf{ = }}\frac{{\bf{1}}}{{\bf{b}}}\frac{{{\bf{\Delta }}\left( {\bf{B}} \right)}}{{{\bf{\Delta t}}}}\)

Determine the rate of disappearance/formation.

The following reaction is given:

\({\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{(g) + 3}}{{\bf{F}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2Cl}}{{\bf{F}}_{\bf{3}}}{\bf{(g)}}\)

The rate of disappearance or appearance is as follows:

\({\bf{Rate of disappearance/}}{\rm{formation}}{\bf{ = }} - \frac{{{\bf{\Delta }}\left( {{\bf{C}}{{\bf{l}}_{\bf{2}}}} \right)}}{{{\bf{\Delta t}}}}{\bf{ = }} - \frac{{\bf{1}}}{{\bf{3}}}\frac{{{\bf{\Delta }}\left( {{{\bf{F}}_{\bf{2}}}} \right)}}{{{\bf{\Delta t}}}}{\bf{ = }}\frac{{\bf{1}}}{{\bf{2}}}\frac{{{\bf{\Delta }}\left( {{\bf{Cl}}{{\bf{F}}_{\bf{3}}}} \right)}}{{{\bf{\Delta t}}}}\)