fill up the following with suitable terms
(i) Activation energy = Threshold energy - _____
(ii) Half-life period of zero order reaction =____
(iii) Average rate of reaction = ___
(iv) Instantaneous rate of reaction

Options

A. Potential energy `(0.693)/(k), (dx)/(dt), (Delta[A])/(Delta t)`
B. Energy of reactants `(1)/(k), (Delta[A])/(Delta t), (dx)/(dt)`
C. Energy of reaction `(log x)/(t), (Delta[A])/(Delta t), (dx)/(dt)`
D. Average kinetic energy of reactants `(a)/(2k), (Delta[A])/(Delta t) , (dx)/(dt)`

Answer

Let's solve the question step by step:

### Step 1: Activation Energy
The activation energy (Ea) can be defined in relation to the threshold energy. The formula is:
\[ \text{Activation Energy} = \text{Threshold Energy} - \text{Average Energy of Reactants} \]
Thus, the blank can be filled with:
**Average Energy of Reactants**

### Step 2: Half-life Period of Zero Order Reaction
For a zero-order reaction, the half-life period (t½) can be derived from the rate law. The formula is:
\[ t_{1/2} = \frac{[A]_0}{2k} \]
where \([A]_0\) is the initial concentration and \(k\) is the rate constant. Therefore, the blank can be filled with:
**[A]₀/2k**

### Step 3: Average Rate of Reaction
The average rate of a reaction can be defined as the change in concentration of a reactant or product over a specified time interval. The formula is:
\[ \text{Average Rate} = \frac{\Delta [A]}{\Delta t} \]
Thus, the blank can be filled with:
**Δ[A]/Δt**

### Step 4: Instantaneous Rate of Reaction
The instantaneous rate of a reaction is defined as the rate at a specific moment in time. It is given by the derivative of concentration with respect to time:
\[ \text{Instantaneous Rate} = \frac{d[A]}{dt} \]
Thus, the blank can be filled with:
**d[A]/dt**

### Final Answers:
1. Activation energy = Threshold energy - **Average Energy of Reactants**
2. Half-life period of zero order reaction = **[A]₀/2k**
3. Average rate of reaction = **Δ[A]/Δt**
4. Instantaneous rate of reaction = **d[A]/dt**

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