(a) Explain the following terms : (i) Rate of a reaction. (ii) Activation energy of a reaction.
(b) The decomposition of phosphine, `PH_(3)`, 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//4th` of `PH_(3)` to decompose.
(ii) What fractional 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. It can be expressed mathematically as:
- For a reactant: Rate = -d[A]/dt (where [A] is the concentration of the reactant)
- For a product: Rate = d[B]/dt (where [B] is the concentration of the product)
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