Question

Consider the general reaction below and the following average rate data over some time period, Δt. Determine a set of possible coefficients to balance this general reaction. (Use the lowest possible coefficients.)
a A + b B → c C

- delta A\delta t= 0.0065 mol/L · s
- delta B\delta t= 0.0130 mol/L · s
- delta C\delta t= 0.0065 mol/L · s
a =
b =
c =

Answer 1

Answer:

The values of stoichiometric coefficients of the reaction are :

a = 1, b = 2, c = 1

Explanation:

$aA+bB\rightarrow cC$

Rate of the reaction will given as:

$R=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=\frac{1}{c}\frac{d[C]}{dt}$

Given :

Rate of decrease in concentration of A = $-\frac{d[A]}{dt}=0.0065 mol/L s$

Rate of decrease in concentration of B = $-\frac{d[B]}{dt}=0.0130 mol/L s$

$-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}$

$\frac{1}{a}\times 0.0065 mol/L s=\frac{1}{b}\times 0.0130 mol/L s$

$a=0.5b$

b = 2a

Rate of increase in concentration of C = $-\frac{d[C]}{dt}=0.0065 mol/L s$

$-\frac{1}{a}\frac{d[A]}{dt}=\frac{1}{c}\frac{d[C]}{dt}$

$\frac{1}{a}\times 0.0065 mol/L s=\frac{1}{c}\times 0.0065mol/L s$

a = c

$aA+2aB\rightarrow aC$

$A+2B\rightarrow C$

The values of stoichiometric coefficients of the reaction are :

a = 1, b = 2, c = 1

Answer 2

The value of coefficient in the balanced chemical equation has been, a=2, b=1, and c=1.

The general reaction for the rate has been given with the stoichiometric coefficient for the reaction.

The rate for the given reaction has been given as:

$\rm Rate=\dfrac{1}{a} \dfrac{dA}{dt} \;=\;\dfrac{1}{b} \dfrac{dB}{dt} \;=\;\dfrac{1}{c} \dfrac{dC}{dt}$

Computation of the coefficient of the reaction

The value of $\rm \dfrac{dA}{dt}=0.0065\;mol/L.s$

The values of $\rm \dfrac{dB}{dt}=0.0130\;mol/L.s$

Substituting the values for rate:

$\rm \dfrac{1}{a} \dfrac{dA}{dt}=\dfrac{1}{b} \dfrac{dB}{dt}\\\\ \dfrac{1}{a} \;\times\;0.0065= \dfrac{1}{b} \;\times\;0.0130\\\\a=0.5b\\2a=b$

Substituting b for $\rm \dfrac{dC}{dt}=0.0065\;mol/L.s$

$\rm- \dfrac{1}{a} \dfrac{dA}{dt}=\dfrac{1}{c} \dfrac{dC}{dt}\\\\ -\dfrac{1}{a} \;\times\;0.0065= \dfrac{1}{c} \;\times\;0.0065\\\\a=c$

From the stoichiometric:

2a = b = c

Thus, the value of coefficient in the balanced chemical equation has been, a=2, b=1, and c=1.

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