Respuesta :
Answer:
a) The rate law of the reaction is ;
[tex]=k[NH_4^{+}]^1[NO_2^{-}]^1[/tex]
b) The value of the rate constant : [tex]0.0003 M^{-1} s^{-1}[/tex]
c) [tex]6.084\times 10^{-6} M/s[/tex] is the reaction rate when the concentrations are [tex][NH_4^{+}][/tex] = 0.39 M and [tex][NO_2^{-}][/tex] = 0.052 M.
Explanation:
Rate of the reaction will be given by :
[tex]=k[NH_4^{+}]^x[NO_2^{-}]^y[/tex]
a) Rate of the reaction when[tex][NH_4^{+}][/tex] and [tex][NO_2^{-}][/tex] is 0.24 M and 0.1 M respectively = R
R = [tex]7.2\times 10^{-6} M/s[/tex]
[tex]R=k[0.24 M]^x[0.1 M]^y[/tex]...[1]
Rate of the reaction when[tex][NH_4^{+}][/tex] and [tex][NO_2^{-}][/tex] is 0.12 M and 0.1 M respectively = R'
R' = [tex]3.6\times 10^{-6} M/s[/tex]
[tex]R'=k[0.12 M]^x[0.1 M]^y[/tex]...[2]
Rate of the reaction when[tex][NH_4^{+}][/tex] and [tex][NO_2^{-}][/tex] is 0.12 M and 0.15 M respectively = R'
R'' = [tex]5.4\times 10^{-6} M/s[/tex]
[tex]R''=k[0.12 M]^x[0.15 M]^y[/tex]...[3]
Dividing [1] and [2]
[tex]\frac{R}{R'}=\frac{k[0.24 M]^x[0.1]^y}{k[0.12 M]^x[0.1]^y}[/tex]
[tex]\frac{7.2\times 10^{-6} M/s}{3.6\times 10^{-6} M/s}=\frac{k[0.24 M]^x[0.1 M]^y}{k[0.12 M]^x[0.1 M]^y}[/tex]
[tex]2=2^x[/tex]
x = 1
Dividing [2] and [3]
[tex]\frac{R'}{R''}=\frac{k[0.12 M]^x[0.1 M]^y}{k[0.12 M]^x[0.15]^y}[/tex]
[tex]\frac{3.6\times 10^{-6} M/s}{5.4\times 10^{-6} M/s}=\frac{k[0.12 M]^x[0.1 M]^y}{k[0.12 M]^x[0.15 M]^y}[/tex]
[tex]\frac{2}{3}=(\frac{2}{3})^y[/tex]
y = 1
The rate law of the reaction is ;
[tex]=k[NH_4^{+}]^1[NO_2^{-}]^1[/tex]
b) The value of the rate constant :
From [1]:
[tex]7.2\times 10^{-6} M/s=k[0.24 M]^1[0.1 M]^1[/tex]...[1]
[tex]k=\frac{7.2\times 10^{-6} M/s}{[0.24 M]^1[0.1 M]^1}=0.0003 M^{-1} s^{-1}[/tex]
The value of the rate constant : [tex]0.0003 M^{-1} s^{-1}[/tex]
c) Rate of the reaction when[tex][NH_4^{+}][/tex] and [tex][NO_2^{-}][/tex] is 0.39 M and 0.052 M respectively = R
[tex]R=0.0003 M^{-1} s^{-1}\times [0.39 M][0.052 M][/tex]
[tex]R=6.084\times 10^{-6} M/s[/tex]
[tex]6.084\times 10^{-6} M/s[/tex] is the reaction rate when the concentrations are [tex][NH_4^{+}][/tex] = 0.39 M and [tex][NO_2^{-}][/tex] = 0.052 M.
