Respuesta :
Answer : The correct rate law becomes:
[tex]\text{Rate}=k[A]^2[B]^1[/tex]
Explanation :
Rate law is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.
For the given chemical equation:
[tex]3A(g)+2B(g)\rightarrow 2C(g)+2D(g)[/tex]
Rate law expression for the reaction:
[tex]\text{Rate}=k[A]^a[B]^b[/tex]
where,
a = order with respect to A
b = order with respect to B
Expression for rate law for first observation:
[tex]6.00\times 10^{-2}=k(0.200)^a(0.100)^b[/tex] ....(1)
Expression for rate law for second observation:
[tex]1.50\times 10^{-2}=k(0.100)^a(0.100)^b[/tex] ....(2)
Expression for rate law for third observation:
[tex]1.20\times 10^{-1}=k(0.200)^a(0.200)^b[/tex] ....(3)
Expression for rate law for fourth observation:
[tex]2.70\times 10^{-1}=k(0.300)^a(0.200)^b[/tex] ....(4)
Dividing 1 by 2, we get:
[tex]\frac{6.00\times 10^{-2}}{1.50\times 10^{-2}}=\frac{k(0.200)^a(0.100)^b}{k(0.100)^a(0.100)^b}\\\\4=2^a\\a=2[/tex]
Dividing 3 by 1, we get:
[tex]\frac{1.20\times 10^{-1}}{6.00\times 10^{-2}}=\frac{k(0.200)^a(0.200)^b}{k(0.200)^a(0.100)^b}\\\\2=2^b\\b=1[/tex]
Thus, the rate law becomes:
[tex]\text{Rate}=k[A]^2[B]^1[/tex]
Rate law is defined as the rate of reaction of reactants in molar concentration with each term raised to the power of their stoichiometric coefficient, in a balanced chemical equation.
The rate law can be expressed as:
Rate = k [A]ᵃ [B]ᵇ
In the given chemical equation:
3A(g) + 2B(g) [tex]\rightarrow[/tex] 2C(g) + 2D(g)
The rate for the equation is:
Rate = k [A]ᵃ [B]ᵇ
where,
a = order with respect to A
b = order with respect to B
The rate law for the first given observation:
1) 6.00 x 10⁻² = k [0.200]ᵃ [0.100]ᵇ
Similarly, for the second observation:
2) 1.50 x 10⁻² = k [0.100]ᵃ [0.100]ᵇ
Now, for the third and fourth observations:
3) 1.20 x 10⁻² = k [0.200]ᵃ [0.200]ᵇ
4) 2.70 x 10⁻² = k [0.300]ᵃ [0.200]ᵇ
Dividing the 1 equation by 2, we get:
[tex]\dfrac{{6.00 \times 10}^{-2}}{1.50 \times 10^{-2}} &=\dfrac {k (0.200)^a (0.100)^b}{k (0.100)^a (0.100)^b}[/tex]
4 = 2ᵃ
a = 2
Similarly, dividing equation 3 by 1, we get:
[tex]\dfrac{{1.20 \times 10}^{-2}}{6.00 \times 10^{-2}} &=\dfrac {k (0.200)^a (0.200)^b}{k (0.200)^a (0.100)^b}[/tex]
2 = 2ᵇ
b = 1
Thus, the rate law can be given as:
Rate = k [A]² [B]¹
To know more about rate law, refer to the following link:
https://brainly.com/question/4222261
