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For the reaction A +B+ C D E, the initial reaction rate was measured for various initial concentrations of reactants. The following data were collected Trial A Bl Cl Initial rate 0.30 0.30 0.30 9.0x10 o 2.7x10-4 0.30 0.30 0.90 3.6x10-4 0.60 0.30 0.30 3.6x10-4 0.60 0.60 0.30
What is the value of the rate constant k for this reaction? When entering compound units, indicate multiplication of units explicitly using a multiplication dot (multiplication dot in the menu). For example, M−1⋅s−1. Express your answer to two significant figures and include the appropriate units. Indicate the multiplication of units explicitly either with a multiplication dot or a dash.

Answer :

Answer:

Rate constant of the reaction is [tex]3.3\times 10^{-3} M^{-2} s^{-1}[/tex].

Explanation:

A + B + C → D + E

Let the balanced reaction be ;

aA + bB + cC → dD + eE

Expression of rate law of the reaction will be written as:

[tex]R=k[A]^a[B]^b[C]^c[/tex]

Rate(R) of the reaction in trail 1 ,when :

[tex][A]=0.30 M,[B]=0.30 M,[C]=0.30 M[/tex]

[tex]R=9.0\times 10^{-5} M/s[/tex]

[tex]9.0\times 10^{-5} M/s=k[0.30 M]^a[0.30 M]^b[0.30 M]^c[/tex]...[1]

Rate(R) of the reaction in trail 2 ,when :

[tex][A]=0.30 M,[B]=0.30 M,[C]=0.90 M[/tex]

[tex]R=2.7\times 10^{-4} M/s[/tex]

[tex]2.7\times 10^{-4} M/s=k[0.30 M]^a[0.30 M]^b[0.90 M]^c[/tex]...[2]

Rate(R) of the reaction in trail 3 ,when :

[tex][A]=0.60 M,[B]=0.30 M,[C]=0.30 M[/tex]

[tex]R=3.6\times 10^{-4} M/s[/tex]

[tex]3.6\times 10^{-4} M/s=k[0.60 M]^a[0.30 M]^b[0.30 M]^c[/tex]...[3]

Rate(R) of the reaction in trail 4 ,when :

[tex][A]=0.60 M,[B]=0.60 M,[C]=0.30 M[/tex]

[tex]R=3.6\times 10^{-4} M/s[/tex]

[tex]3.6\times 10^{-4} M/s=k[0.60 M]^a[0.60 M]^b[0.30 M]^c[/tex]...[4]

By [1] ÷ [2], we get value of c ;

c = 1

By [3] ÷ [4], we get value of b ;

b = 0

By [2] ÷ [3], we get value of a ;

a = 2

Rate law of reaction is :

[tex]R=k[A]^2[B]^0[C]^1[/tex]

Rate constant of the reaction = k

[tex]9.0\times 10^{-5} M/s=k[0.30 M]^2[0.30 M]^0[0.30 M]^1[/tex]

[tex]k=\frac{9.0\times 10^{-5} M/s}{[0.30 M]^2[0.30 M]^0[0.30 M]^1}[/tex]

[tex]k=3.3\times 10^{-3} M^{-2} s^{-1}[/tex]

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