Question

Consider the general reaction $\mathbf{aA}\mathbf{+}\mathbf{bB}\to \mathbf{cC}$and the following average rate data over a specific time period $\mathbf{\Delta t}$:

$\begin{array}{l}\mathbf{-}\frac{\mathbf{\Delta }\mathbf{A}}{\mathbf{\Delta }\mathbf{t}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0080}\mathbf{}{\mathbf{\text{molL}}}^{\mathbf{-}\mathbf{1}}{\mathbf{\text{s}}}^{\mathbf{-}\mathbf{1}}\\ \mathbf{-}\frac{\mathbf{\Delta }\mathbf{B}}{\mathbf{\Delta }\mathbf{t}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0120}\mathbf{}\mathbf{}{\mathbf{\text{molL}}}^{\mathbf{-}\mathbf{1}}{\mathbf{\text{s}}}^{\mathbf{-}\mathbf{1}}\\ \mathbf{-}\frac{\mathbf{\Delta }\mathbf{C}}{\mathbf{\Delta }\mathbf{t}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0160}\mathbf{}\mathbf{}{\mathbf{\text{molL}}}^{\mathbf{-}\mathbf{1}}{\mathbf{\text{s}}}^{\mathbf{-}\mathbf{1}}\end{array}$

Determine a set of possible coefficients to balance this general reaction

Short answer

The possible coefficients are $a=2,b=3$and $c=4$. Therefore, the general reaction is:

role="math" localid="1663754488303" $\text{2A+3B→4C}$

Step-by-step solution

Define the reaction rate of the chemical reaction.

The change of concentration of a reactant or product per unit of time is known as the reaction rate.

The reaction rate for the given general equation:

$\text{aA+bB→cC}$

$\text{Rate}=-\frac{1}{a}\frac{\Delta A}{\Delta t}=-\frac{1}{b}\frac{\Delta B}{\Delta t}=-\frac{1}{c}\frac{\Delta C}{\Delta t}......\left(1\right)$

Determine the coefficients for a given general reaction.

Substituting the above value in equation (i) and solve for $a,b$and $c$.

$\begin{array}{c}\frac{1}{a}\times 0.0080=\frac{1}{b}\times 0.0120=\frac{1}{c}\times 0.0160\\ a=\frac{0.0080}{0.0080}=1\\ b=\frac{0.120}{0.0080}=1.5\\ c=\frac{0.0160}{0.0080}=2\end{array}$

Now multiply every coefficient with 2 so the coefficients of reaction become whole numbers.

Hence, $a=2,b=3$and $c=4$.

Now the general reaction is written as:

$\text{2A+3B→4C}$