Fill in the blanks by choosing the correct option. Order of the reaction is the `underline(X)` of the powers to which concentration terms are raised in experimentally determined rate equation. The unit of first order rate constant is `underline(Y)`. The unit of first order rate constant when concentration measured in terms of pressure and time in minutes is `underline(Z)`

Options

A. `X to` product, `Y to mol L^(-1) "time"^(-1), Z to "atm" "min"^(-1)`
B. `X to` sum `Y to L mol^(-1) "time"^(-1), Z to "atm" "min"^(-1)`
C. `X to` product, `Y to L mol^(-1), Z to "atm" "min"^(-1)`
D. `X to` sum, `Y to "tim"^(-1), Z to "min"^(-1)`

Answer

To solve the question, we need to fill in the blanks with the correct options based on our understanding of chemical kinetics.

### Step-by-Step Solution:

1. **Understanding the Order of Reaction (X)**:
- The order of a reaction is defined as the sum of the powers to which the concentration terms are raised in the experimentally determined rate equation.
- Therefore, the correct term to fill in for `underline(X)` is **"sum"**.

2. **Determining the Unit of First Order Rate Constant (Y)**:
- The unit of the rate constant (k) for a first-order reaction can be derived from the rate law.
- The rate of a reaction is typically expressed in terms of concentration over time. For a first-order reaction, the unit of k is derived as follows:
- Rate = k [A]^1 (where [A] is the concentration of reactant A)
- The unit of rate is mol L⁻¹ s⁻¹ (or mol L⁻¹ min⁻¹ if time is in minutes).
- Therefore, for a first-order reaction, the unit of k is **"time⁻¹"** or specifically **"min⁻¹"** when time is measured in minutes.
- Thus, for `underline(Y)`, we fill in **"min⁻¹"**.

3. **Unit of First Order Rate Constant with Pressure (Z)**:
- When the concentration is measured in terms of pressure (e.g., atm), the unit of pressure is atm, and the time is still in minutes.
- The unit of the rate constant k in this case would be:
- k = Rate / [Pressure] = (atm min⁻¹) / (atm) = min⁻¹.
- Therefore, for `underline(Z)`, we also fill in **"min⁻¹"**.

### Final Answers:
- X = **"sum"**
- Y = **"min⁻¹"**
- Z = **"min⁻¹"**