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Chemistry Question on Chemical Kinetics

The experimental data for the reaction 2A+B2⟶2AB2 A + B_2 \longrightarrow 2 AB is The rate equation for the above data is

Exp.[A][B2][B_2]Rate (M s−1)(M\,s^{-1})
10.500.501.6×10−41.6 \times 10^{-4}
2.0.051.003.2×10−43.2 \times 10^{-4}
3.1.001.003.2×10−43.2 \times 10^{-4}
A

rate = k [B2][B_2]

B

rate = k [B2]2[B_2]^2

C

rate = k [A]2[B]2[A]^2[B]^2

D

rate = k [A]2[B][A]^2[B]

Answer

rate = k [B2][B_2]

Explanation

Solution

Consider the following rate law equation,
\hspace15mm \frac{dx}{dt}=k [A]^m [B_2]^n
\, \, \, \, \, \, \, 1.6 \times 10^{-4}=k [0.50]^m [0.50]^n \hspace20mm ...(i)
\, \, \, \, \, \, \, 3.2 \times 10^{-4}=k [0.50]^m [1.0]^n \hspace20mm ...(ii)
\, \, \, \, \, \, \, 3.2 \times 10^{-4}=k [1.00]^m [1.0]^n \hspace20mm ...(iii)
From Eqs. (ii) and (iii)
        3.2×10−43.2×10−4=k[1.00]m[1.0]nk[0.50]m[1.0]n\, \, \, \, \, \, \, \, \frac{3.2 \times 10^{-4}}{3.2 \times 10^{-4}}=\frac{k [1.00]^m [1.0]^n}{k [0.50]^m [1.0]^n}
            1=2m    or    20=2m\, \, \, \, \, \, \, \, \, \, \, \, 1 =2^m \, \, \, \, or \, \, \, \, 2^0=2^m
∴                 m=0\therefore \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, m=0
From Eqs. (i) and (ii)
        3.2×10−41.6×10−4=k[0.50]m[1.0]nk[0.50]m[0.50]n\, \, \, \, \, \, \, \, \frac{3.2 \times 10^{-4}}{1.6 \times 10^{-4}}=\frac{k [0.50]^m [1.0]^n}{k [0.50]^m [0.50]^n}
               2=2n\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, 2= 2^n
or              21=2n\, \, \, \, \, \, \, \, \, \, \, \, \, 2^1=2^n
∴          n=1\therefore \, \, \, \, \, \, \, \, \, \, n=1
Hence, rate
\hspace15mm \big(\frac{dx}{dt}\big)=k [A]^0 [B_2]^1
\hspace25mm =k [B_2]

The pace at which reactants are changed into products is known as the reaction rate or rate of reaction. The rate at which chemical reactions take place varies greatly. While some chemical processes achieve their ultimate equilibrium very instantly, others take longer.

A broad meaning of the term "reaction rate" is the pace at which a reaction occurs. For instance, the oxidation of iron has a low response rate because the process is long, but burning wood has a high reaction rate because the process is quick.

Consider a chemical reaction.

aA + bB → cC + dD

Here, A and B denote reactants and C and D denote products

a, b, d, d denotes stoichiometric coefficients.

According to the IUPAC, the reaction rate r, which takes place in a closed system without the formation of reaction intermediates under isochoric conditions, is defined as: