In 140days ⇒ initial concentration reduced to (1/2) g
In 280 days ⇒ initial concentration reduced to (1/4) g
In 420 days ⇒ initial concentration reduced to (1/8) g
In 560 days ⇒ initial concentration reduced to (1/16) g

t_1/2 α \(\frac{1}{[A_{0}]^{n-1}}\)...(1)
If [A₀ = 2[A₀]; then t_1/2 = 2t_1/2
2t_1/2 α \(\frac{1}{[2A_{0}]^{n-1}}\)...(2)
(2)/(1) = \(2= \frac{1}{[2A_{0}]^{n-1}} \times \frac{1}{[A_{0}]^{n-1}}\)
\(2= \frac {[2A_{0}]^{n-1}} {[A_{0}]^{n-1}}\)
\(2= \frac {1} {2}^{n-1}\)
2 = (2^-1)^n-1
2¹ = (2^-n+1)
n = 0

A catalyst provides a new path to the reaction with low activation energy. i.e., it lowers the activation energy.

\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow 12 \mathrm{C}+\mathrm{H}_{2} \mathrm{SO}_{4} \cdot 11 \mathrm{H}_{2} \mathrm{O} \\ \text { Sucrose } \)
\(\underset{\text { Formic acid }}{\mathrm{HCOOH}}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{CO}+\mathrm{H}_{2} \mathrm{SO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\)
\(\underset{\text { Oxalic acid }}{\mathrm{(COOH)}_{2}}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{CO}+\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{SO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\)

Integrated rate equation for zero order reaction:
\(k=\frac{[A]_{0}-[A]}{t} ; t_{\frac{1}{2}}=\frac{[A]_{0}}{2 k}\)
Integrated rate equation for first order reaction.
\(k=\frac{2.303}{t} \log \frac{a}{a-x} ; t_{\frac{1}{2}}=\frac{0.693}{k}\)

(i) Many micro organisms (bacteria, fungi and moulds) produce certain chemicals which inhibit the growth or metabolism of some other micro organism. Such chemicals are called antibiotics.
(ii) Eg: Penicillin from the mould penicillium notatum

(a) OF₂
+ 2 + 2(x) = 0 
+2 = -2x 
2 x = -2 ⇒ x = -1
(b) O₂F₂
2(+1) + 2x = 0 
2x = -2 
x = -1
(c) Cl₂O₃
2(x) + 3(-2) = 0 
2x = +6 
x = +3
(d) I₂O₄
2(x) + 4(-2) = 0 
2x = +8 
x = +4

The dehydrating property can also be illustrated by its reaction with organic compounds such as sugar, oxalic acid and formic acid.
\(\underset{\substack{ \\ \text { Sucrose }}}{\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow 12 \mathrm{C}+\mathrm{H}_{2} \mathrm{SO}_{4} \cdot 11 \mathrm{H}_{2} \mathrm{O}\)
\(\underset{\text { Formic acid }}{\mathrm{HCOOH}}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{CO}+\mathrm{H}_{2} \mathrm{SO}_4 \cdot \mathrm{H}_{2} \mathrm{O}\)
\(\underset{\text { Oxalic acid }}{(\mathrm{COOH})_{2}}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{CO}+\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{SO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\)

(i) Preservatives are chemicals added to food which are capable of inhibiting, retarding or arresting the process of fermentation, acidification or other decomposition of food by the growth of micro organisms (or)
(ii) Chemical substances which are added to food that prevents the spoilage of food materials by destroying the food - spoiling micro-organisms are called food preservatives.
(iii) Eg: sodium benzoate, NaCl, Acetic acid Sodium metabisulphite, potassium meta bisulphite etc.

(i) Helium is used to provide inert atmosphere in electric-arc welding of metals.
(ii) Helium has lowest boiling point hence used in cryogenics.
(iii) It is much less denser than air and hence used for filling air balloons.

A reaction whose rate depends on the reactant concentration raised to the first power is called a first order reaction. Let us consider the following Cl₂ first order reaction,
A → product
Rate law can be expressed as
Rate = k[A]¹
Where, k is the first order rate constant
\(\frac{-\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\mathrm{k}[\mathrm{A}]^{1}  \)
\(\Rightarrow \frac{-\mathrm{d}[\mathrm{A}]}{[\mathrm{A}]}=\mathrm{kdt}\)  .....(1)
Integrate the above equation between the limits of time t = 0 and time equal to t, while the concentration varies from the initial concentration [A₀] to [A] at the later time.
\(\int_{\left[A_{0}\right]}^{[A]} \frac{-d[A]}{[A]}=k \int_{0}^{t} d t  \)
\((-\ln [A])_{\left[A_{0}\right]}^{[A]}=k(t)_{0}^{t}  \)
\(-\ln [A]-\left(-\ln \left[A_{0}\right]\right)=k(t-0) \)
\(-\ln [\mathrm{A}]+\ln \left[\mathrm{A}_{0}\right]=\mathrm{kt}  \)
\(\ln \left(\frac{\left[\mathrm{A}_{0}\right]}{[\mathrm{A}]}\right)=\mathrm{kt}\)  .....(2)
This equation is in natural logarithm. To convert it into usual logarithm with base 10, we have to multiply the term by 2.303.
\(2.303 \log \left(\frac{\left[A_{0}\right]}{[A]}\right)=k t  \)
\(k=\frac{2.303}{t} \log \left(\frac{\left[A_{0}\right]}{[A]}\right)\)   .....(3)

(i) To understand how a soap works as a cleansing agent, let us consider sodium palmitate an example of a soap. The cleansing action of soap is directly related to the structure of carboxylate ions (palmitate ion) present in soap. The structure of palmitate exhibit dual polarity. The hydrocarbon portion is non polar and the carboxyl portion is polar.

(ii) The nonpolar portion is hydrophobic while the polar end is hydrophilic. The hydrophobic hydro carbon portion is soluble in oils and greases, but not in water. The hydrophilic carboxylate group is soluble in water.
(iii) The dirt in the cloth is due to the presence of dust particles intact or grease which stick. When the soap is added to an oily or greasy part of the cloth, the hydrocarbon part of the soap dissolve in the grease, leaving the negatively charged carboxylate end exposed on the grease surface.
(iv) At the same time the negatively charged carboxylate groups are strongly attracted by water, thus leading to the formation of small droplets called micelles and grease is floated away from the solid object. When the water is rinsed away, the grease goes with it. As a result, the cloth gets free from dirt and the droplets are washed away with water. The micelles do not combine into large drops because their surfaces are all negatively charged and repel each other. The cleansing ability of a soap depends upon its tendency to act as a emulsifying agent between water and water insoluble greases.

The cleansing action of detergents are similar to cleansing action of soap. Eg: the structure of a cationic detergents is:

(a) Elementary reaction
Each and Every single step in a reaction mechanism is called an elementary reaction.
Rate = k[A] [B]
(b)