(a) Explain the following terms :
(i) Rate of a reaction
(ii) Activation energy of a reaction
(b) The decompositon of phosphine , PH3, proceeds according to the following equation :
`4 PH_(3) (g) to P_(4)(g) + 6 H_(2) (g)`
It is found that the reaction follows the following rate equation :
Rate = k [`PH_(3)]`.
The half-life of ` PH_(3)" is "37.9" s at "120^(@)C`.
(i) How much time is required for `3//4^("th") "of " PH_(3)` to decompose ?
(ii) What fraction of the original sample of `PH_(3)` remains behind after 1 minute ?

Explanation

### Step-by-Step Solution

#### (a) Explanation of Terms

**(i) Rate of a Reaction:**
The rate of a reaction is defined as the change in concentration of a reactant or product per unit time. Mathematically, it can be expressed as:
\[ \text{Rate} = -\frac{d[\text{Reactant}]}{dt} \quad \text{or} \quad \text{Rate} = \frac{d[\text{Product}]}{dt} \]
where \([\text{Reactant}]\) and \([\text{Product}]\) are the concentrations of the reactants and products, respectively.
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