Respuesta :
Answer:
B. First order, Order with respect to C = 1
Explanation:
The given kinetic data is as follows:
A + B + C → Products
[A]₀ [B]₀ [C]₀ Initial Rate (10⁻³ M/s)
1. 0.4 0.4 0.2 160
2. 0.2 0.4 0.4 80
3. 0.6 0.1 0.2 15
4. 0.2 0.1 0.2 5
5. 0.2 0.2 0.4 20
The rate of the above reaction is given as:
[tex]Rate = k[A]^{x}[B]^{y}[C]^{z}[/tex]
where x, y and z are the order with respect to A, B and C respectively.
k = rate constant
[A], [B], [C] are the concentrations
In the method of initial rates, the given reaction is run multiple times. The order with respect to a particular reactant is deduced by keeping the concentrations of the remaining reactants constant and measuring the rates. The ratio of the rates from the two runs gives the order relative to that reactant.
Order w.r.t A : Use trials 3 and 4
[tex]\frac{Rate3}{Rate4}= [\frac{[A(3)]}{[A(4)]}]^{x}[/tex]
[tex]\frac{15}{5}= [\frac{[0.6]}{[0.2]}]^{x}[/tex]
[tex]3 = 3^{x} \\\\x =1[/tex]
Order w.r.t B : Use trials 2 and 5
[tex]\frac{Rate2}{Rate5}= [\frac{[B(2)]}{[B(5)]}]^{y}[/tex]
[tex]\frac{80}{20}= [\frac{[0.4]}{[0.2]}]^{y}[/tex]
[tex]4 = 2^{y} \\\\y =2[/tex]
Order w.r.t C : Use trials 1 and 2
[tex]\frac{Rate1}{Rate2}= [\frac{[A(1)]}{[A(2)]}]^{x}[\frac{[B(1)]}{[B(2)]}]^{y}[\frac{[C(1)]}{[C(2)]}]^{z}[/tex]
we know that x = 1 and y = 2, substituting the appropriate values in the above equation gives:
[tex]\frac{160}{80}= [\frac{[0.4]}{[0.2]}]^{1}[\frac{[0.4]}{[0.4]}]^{2}[\frac{[0.2]}{[0.4]}]^{z}[/tex]
[tex]1 = (0.5)^{z}[/tex]
z = 1
Therefore, order w.r.t C = 1
The dependence of the power of the reaction rate on the concentration is called the order of the reaction. The order of the reaction is the first order.
What is the initial-rate method?
The initial rate method is the estimation of the order of the reaction by the initial rates of the reactants and products and by performing the reaction several times by measuring the rate.
The reaction is given as,
[tex]\rm A + B + C \rightarrow Products[/tex]
The rate of reaction can be given as:
[tex]\rm rate = k[A]^{x}[B]^{y}[C]^{z}[/tex]
Here the variables x, y and z are orders respective to the reactant concentration and k is the rate constant.
Value of x with respect to A:
[tex]\begin{aligned} \rm \dfrac {Rate 3}{Rate 4} &= \rm [\dfrac{[A(3)]}{[A(4)]}]^{\rm x}\\\\\dfrac{15}{5} &= [\dfrac{[0.6]}{[0.2]}]^{\rm x}\\\\\rm x &= 1\end{aligned}[/tex]
Value of y with respect to B:
[tex]\begin{aligned}\rm \dfrac {Rate 2}{Rate 5} &= \rm [\dfrac{[B(2)]}{[B(5)]}]^{\rm y}\\\\\dfrac{80}{20} &= [\dfrac{[0.4]}{[0.2]}]^{\rm y}\\\\\rm y &= 2\end{aligned}[/tex]
Value of z with respect to C:
[tex]\rm \dfrac {Rate 1}{Rate 2} &= [\dfrac{[A(1)]}{[A(2)]}]^{x} [\dfrac{[B(1)]}{[B(2)]}]^{y} [\dfrac{[C(1)]}{[C(2)]}]^{z}[/tex]
Substituting value of x = 1 and y = 2 in the above equation:
[tex]\begin{aligned}\dfrac{160}{80} &= [\dfrac{[0.4]}{[0.2]}]^{1}[\dfrac{[0.4]}{[0.4]}]^{2} [\dfrac{[0.2]}{[0.4]}]^{\rm z}\\\\1 &= (0.5)^{\rm z}\\\\&= 1\end{aligned}[/tex]
Therefore option b. with respect to C = 1, the order of the reaction is first-order.
Learn more about the order of reaction here:
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