(i) First order reaction
(ii) First order reaction
(iii) \(\frac{1}{2}+2=2 \frac{1}{2}\); Pseudo first order reaction

Arrhenius equation is,
\(k=Ae^\left ({ \frac { -Ea }{ RT } } \right )\)
Here,
A \(\rightarrow\) Frequency factor
E_a \(\rightarrow\) Activation energy of the reaction
R \(\rightarrow\) Gas constant
T \(\rightarrow\) Absolute temperature (in K)

Reaction rate = k[x]^3/2[y]^1/2
(i) Over all order of reaction = (3/2 + 1/2)=2 
i.e., second order reaction.
(ii) Since the rate expression does not contain the concentration of z, the reaction is zero order with respect to z.

Reaction Rate = k[x]ⁿ [y]ⁿ
0.15 = k[0.2]ⁿ [0.02]^m   ...(1)
0.30 = k[0.4]ⁿ [0.02]^m  ...(2)
1.20 = k[0.4]ⁿ [0.08]^m  ...(3)
eqn(3) \(\div\) eqn(2) 
\(\Rightarrow\)\(\frac { 1.2 }{ 0.3 } =\frac { k{ \left[ 0.4 \right] }^{ n }{ \left[ 0.08 \right] }^{ m } }{ k{ \left[ 0.4 \right] }^{ n }{ \left[ 0.02 \right] }^{ m } } \)
\(4={ \left( \frac { \left[ 0.08 \right] }{ \left[ 0.02 \right] } \right) }^{ m }\)
\(4^1={ \left( 4 \right) }^{ m }\)
\(m=1\)
eqn(2) \(\div\) eqn(1), \(\frac{0.30}{0.15}=\frac{\mathrm{k}[0.4]^{\mathrm{n}}[0.02]^{\mathrm{m}}}{\mathrm{k}[0.2]^{\mathrm{n}}[0.02]^{\mathrm{m}}}\)
\( 2={ \left( \frac { \left[ 0.4 \right] }{ \left[ 0.2 \right] } \right) }^{ n}\)
\(2^1= 2 ^{ n }\)
\(\therefore n=1\)
Rate = \(k{ \left[ x \right] }^{ 1 }{ \left[ y \right] }^{ 1 }\)
\(0.15=k{ \left[ 0.1 \right] }^{ 1 }{ \left[ 0.02 \right] }^{ 1 }\)
\(\frac { 0.15 }{ { \left[ 0.2 \right] }^{ 1 }{ \left[ 0.02 \right] }^{ 1 } } =k\)
k = 37.5 mol⁻¹L s⁻¹

\(k=\frac { 2.303 }{ t } \log\frac { \left( { V }_{ \infty }-{ V }_{ 0 } \right) }{ \left( { V }_{ \infty }-{ V }_{ 0 } \right) } \)
\(k=\frac { 2.303 }{ 20 } \log\frac { 50.4-20.2 }{ 50.4-25.6 } \)
\(=0.1151 \log\frac { 30.2 }{ 24.8 } \)
= 0.1151 log 1.2479
= 0.1151 x 0.0959
= 11.03 x10^-3 min^-1
When t = 40 mts
\(k=\frac { 2.303 }{ 40 } \log\frac { 50.4-20.2 }{ 50.4-25.6 } \)
\(=0.0576\times \log\frac { 30.2 }{ 20.9 } \)
= 9.19 x 10^-3 min^-1
When t = 60 mts
\(k=\frac { 2.303 }{ 60 } \log\frac { 50.4-20.2 }{ 50.4-25.6 } \)
\(=0.03838\times \log\frac { 30.2 }{ 17.6 } \)
= 0.03838 x 0.2343
= 8.99 x 10^-3 min^-1
The constant values of K show that the reaction is of first order.