A + B⟶P
Rate = k[A] [B]²
(i) When concentration of B is doubled it means conc. of B becomes 2 times.
Thus:   Rate = k[A]¹ [B]² 
 = k[A] [4B²]
So, the rate becomes 4 times.
(ii) Order of reaction is the no. of molecules whose conc. alters after the reaction. If A is present in excess i.e., its conc. is un-effected.
So, rate is depending only on the conc. of B. As 
= k[B]²
Thus the reaction is of second order.
(b) For the 1^st order reaction
\(k=\frac{2.303}{t}\log \frac{a}{a-x}\)
\(t=30 \times 60=1800\ sec\)
\(k=\frac{2.303}{1800}\log \frac{100}{100-50}\)
\(=\frac{2.303}{1800}\log 2\)
\(=\frac{2.303}{1800}\times0.3010\)
\(t=\frac{2.303}{k}\log \frac{a}{a-x}\)
\(=\frac{2.303}{k}\log \frac{100}{100-90}\)
\(=\frac{2.303}{k}\log 10=\frac{2.303}{k}\)
By putting the value of k here, we get
\(\Rightarrow \ t=\frac{2.303\times 1800}{2.303\times0.3010}\)
\(=5.98\times 10^3 sec\)

(i) The dissolution of sugar will increase on heating the mixture.
(ii) The rate of reaction increases with the rate of reaction.  
(iii) On increasing the temperature by 10'C, the molecules possessing activation energy becomes double. Therefore, the rate of reaction doubles.
(iv) Presence of mind and ability to give advice

(i) Due to lower temperature, less vapours are formed which cause less tears.
(ii) Meat should be stored in the coldest part of the refrigerator. This slows down the growth of microorganisms which are responsible for causing spoilage.
(iii) This statement is not correct as conversion of diamond to graphite is spontaneous thermodynamically. But process is so slow that this will take thousands of years.

Temperature has a great effect on reaction rates or reaction rate constants. In general, an increase in temperature increases the rates of almost all reactions. For homogeneous chemical reactions, the rate of the reaction or rate constant (k) becomes almost double for every 10° rises in temperature.According to collision theory, the rate of reaction depends upon,
(i) the collision frequency of the reacting molecules.
(ii) the fraction of effective collisions.
The frequency of collisions between reacting molecules depends upon the average velocity of the molecules. With the increase in temperature, the average velocity of the molecules increases which results into increase in collision frequency. However, an increase of 10° rise of temperature increases the number of collisions by only 1.016 times. Further, we know that all the collisions are not effective. For molecules to undergo effective collisions, they must possess a certain minimum amount of energy called threshold energy. The molecules which possess energy equal to or greater than threshold energy will result in the formation of products. However, the fraction of such molecules capable of effective collisions is very small. As the temperature has increased the fraction of molecules possessing energies greater than threshold energy increases and so the rate of the reaction increases.
Let us consider the effect of increase of temperature on the number of effective collisions (having energies greater than threshold energy). The energy. distribution, of molecules at two temperatures \({ T }_{ 1 }\) and \({ T }_{ 2 }\) (where \({ T }_{ 2 }={ T }_{ 1 }+10°\)) is shown in figure. It is clear from the figure that the curve at higher temperature gets shifted towards the right indicating that at higher temperature, the molecules have higher energies. Further, the curve at higher temperature is flatter than that at lower temperature which also indicates that the number of molecules with higher energy content have increased.
The minimum energy required for the effective collisions also shown in the diagram and the number of molecules possessing energies equal to or greater than E, is proportional to area abed at temperature \({ T }_{ 1 }\) and area above at temperature \({ T }_{ 2 }\). In the figure, the area abef is roughly twice as large as abcd. Since the rate of reaction depends upon the number of molecules which possess energies larger than activation energy (for effective collisions), it may be interpreted that the fraction of molecules possessing activation energy has increased approximately two times and thereby, increases the rate of reaction by two times for a rise of 10 degrees.
Thus, we may conclude that increase in the rate of reaction with the rise in temperature is mainly due to the increase in number of effective collisions.

From the given data, we have

Graph of 10 k vs lIT. The plot obtained is as shown in the Fig.
Slope of the line = \({y_2-y_1\over x_2-x_1}=-20.62\times10^3K\)
From Arrhenius eqn., Slope = -\({E_a\over R}\)(for plot of In k of Iff)
E_a = - Slope x R
= 20·62 x 10³ K x (8·314 JK^-I mol^-1)
= 171.4 kJ mol^-1
Further, In k = In A -\({E_a\over RT}\) or In A = in k+\({E_a\over RT}\)
Substituting T = 633 K, k = 0·19 x 10^-4 s^-1,
i.e. In k = - 10·87, we get
In \(A=-10.87+{171400\over8.314\times633}=-10.87+32.57=21.70\)
or A = 2·65 x 10⁹M^-1 s^-1.

\(t_1={2.303\over k_1}log{a\over 0.10a}=t_1={2.303\over k_2}log{a\over a-0.25a}\)
As t₁ = t₂ \({2.303\over k_1}log{a\over 0.90a}={2.303\over k_2}log{a\over 0.7a};\ {k_2\over k_1}={log(100/75)\over log(100/90)}=2.73\)
But \(log{k_2\over k_1}={E_a\over 2.303R}\left(T_2-T_1\over T_1T_2\right)\)
Putting k₂/k₁) = 2.73, R = 8.314 J K^-1 mol^-1, T₁ = 298 K, T₂ = 308 K, we get E_a = 76.6 kJ mol^-1
Further, k - Ae^{-E_a / RT} or log k = log A -\({E_a\over 2.303RT}\)
Putting A = 3.56 x 10⁹s^-1, R = 8.314 x 10^-3 kJ K^-1 mol^-1, E_a = 76.6 kJ mol^-1, T = 318 K, we get
k = 9.3 x 10^-4 S^-1.

 \({ t }_{ { 1 }/{ 2 } }=5730 \ years\)
\({ t }_{ { 1 }/{ 2 } }=\frac { 0.693 }{ k } \)
\(k=\frac { 0.693 }{ 5730 } { years }^{ -1 }\)
\(k=\frac { 2.303 }{ t } \log { \frac { { \left[ N \right] }_{ 0 } }{ \left[ N \right] } }\)
\(t=\frac { 2.303 }{ k } \log { \frac { 100 }{ 80 } }\)
\(=\frac { 2.303 }{ 0.693 } \times 5730\left[ \log { 5 } -\log { 4 } \right] \)
\(=\frac { 5730 }{ 0.3010 } \times \left[ 0.6990-0.6021 \right] \)
\(=\frac { 5730 }{ 0.3010 } \times 0.0969=\frac { 55.237 }{ 0.3010 } \)
\(=1844.64 \ years\approx 1845 \ years\)

(a) (i) Order of a reaction. The sum of the exponents (powers) of the concentration of reactants in the rate law is termed as order of the reaction. It can be in fraction. It can be zero also.
(ii) Molecularity: Total number of atoms, ions or molecules of the reactants involved in the reaction is termed as its molecularity. It is always in whole number. It is never more than three. It cannot be zero.
(b)
\(\log { \frac { { k }_{ 2 } }{ { k }_{ 1 } } } =\frac { { E }_{ a } }{ 2.303R } \left( \frac { 1 }{ { T }_{ 1 } } -\frac { 1 }{ { T }_{ 2 } } \right)\)
\(\log { 4 } =\frac { { E }_{ a } }{ 2.303\times 8.314 } \left( \frac { 1 }{ 300 } -\frac { 1 }{ 320 } \right) \)
\({ E }_{ a }=\frac { 19.147\times 0.6021\times 300\times 320 }{ 20 }\)
\(=55.336\quad kJ\ { mol }^{ -1 }\)

(a) (i) It is sum of powers to which cone. terms are raised in rate law or rate equation.
(ii) Each step of complex reaction (which takes place in more than one step) is called elementary, step in a reaction.
\((b) \ k=0.00510 \ { min }^{ -1 }\)
\(t=\frac { 2.303 }{ k } \log { \frac { { \left[ R \right] }_{ 0 } }{ \left[ R \right] } }\)
\(3\times 60\times 60=\frac { 2.303 }{ 0.00510 } \log { \frac { 0.1 }{ \left[ R \right] } }\)
\(\log { \frac { 0.1 }{ \left[ R \right] } } =\frac { 10800\times 0.00510 }{ 2.303 } \)
\(=23.94\)
\(\frac { 0.1 }{ \left[ R \right] } =Antilog \ 23.94\)
\(\frac { 0.1 }{ \left[ R \right] } =8.71\times { 10 }^{ 23 }\)
\(\left[ R \right] =\frac { 0.1 }{ 8.71\times { 10 }^{ 23 } }\)
\(\left[ R \right] =0.1148\times { 10 }^{ -24 }\)
\(\left[ R \right] =1.148\times { 10 }^{ -25 }M\)

(a) Rate of reaction is defined as change in cone. of reactants or products per unit time.Its unit is mol L^-1 S^-1.
Average rate: The rate of reaction measured over a long time interval is called average
rate of reaction: It is equal to Δx/Δt, e.g.
H₂(g) + Cl₂ (g) ⇾ 2HCI(g);
Rate of reaction = \(-{Δ[H_2]\over Δt}=-{Δ[Cl_2]\over Δt}=+{1\over 2}{Δ[HCl]\over Δt}\)
2HI (g) ⇾ H₂ (g) + I₂ (g)
Rate of reaction = \(-{Δ[HI]\over Δt}=+{Δ[H_2]\over Δt}=+{Δ[I_2]\over Δt}\)
Instantaneous rate: It is the rate of reaction when the average rate is taken over a very small interval of time. It is equal to dx/dt.
Instantaneous rate = Average rate as ∆t approaches zero.
(b) (t) Average rate = \(-\left(C_2-C_1\over t_2-t_1\right)=\left(0.17-0.31\over 60-30\right)=+{0.14\over 30}={10\over 100}\times{1\over 30}\)
= \({14\over 3}\) x 10^-3 moI L^-1 s^-1
=  4.67 x 10^-3 mol L^-1 s¹
(ii) \(k={2.303\over t}log{[A]_0\over [A]}={2.303\over 30}log{0.55\over 0.31}={2.303\over 30}[log 55-log 3]\)
\(={2.303\over 30}[1.7404 - 1.4914]={2.303\over 30}\times0.2490\)
= 1.91 x 10^-2 s^-1