For zero order reaction which is (are) true?

Options

A. The rate constant is dimenisonless.
B. Amount of the reactant remains the same theoughout.
C. `t_(1//2) prop` initial concentration of the reactant.
D. A plot of concentration of reactant vs time is a straight. line with slope equal to `-k`.

Answer

To determine which statements about zero-order reactions are true, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding Zero-Order Reactions**:
- A zero-order reaction is one where the rate of reaction is constant and does not depend on the concentration of the reactants.
- The rate law for a zero-order reaction can be expressed as:
\[ \text{Rate} = k \]
- Where \( k \) is the rate constant.

2. **Analyzing the First Statement**:
- **Statement**: The rate constant is dimensionless.
- **Analysis**: The units of the rate constant \( k \) for a zero-order reaction are \( \text{mol L}^{-1} \text{s}^{-1} \). This indicates that it has dimensions and is not dimensionless.
- **Conclusion**: This statement is **false**.

3. **Analyzing the Second Statement**:
- **Statement**: The amount of the reactant remains the same throughout.
- **Analysis**: In a zero-order reaction, as the reaction progresses, the concentration of the reactant decreases over time as it is converted into products. Therefore, the amount of reactant does not remain constant.
- **Conclusion**: This statement is **false**.

4. **Analyzing the Third Statement**:
- **Statement**: \( T_{1/2} \) for zero-order is directly proportional to the initial concentration of the reactant.
- **Analysis**: The half-life \( T_{1/2} \) for a zero-order reaction can be derived from the equation:
\[ T_{1/2} = \frac{[A]_0}{2k} \]
This shows that \( T_{1/2} \) is indeed directly proportional to the initial concentration \( [A]_0 \).
- **Conclusion**: This statement is **true**.

5. **Analyzing the Fourth Statement**:
- **Statement**: A plot of concentration of reactant versus time is a straight line with slope equal to \(-k\).
- **Analysis**: The integrated rate law for a zero-order reaction is:
\[ [A] = [A]_0 - kt \]
This can be rearranged to the form of a straight line \( y = mx + c \), where:
- \( y = [A] \)
- \( m = -k \)
- \( c = [A]_0 \)
Therefore, the plot of concentration versus time is indeed a straight line with a slope of \(-k\).
- **Conclusion**: This statement is **true**.

### Final Summary:
- The true statements about zero-order reactions are:
- Third statement: \( T_{1/2} \) is directly proportional to the initial concentration of the reactant.
- Fourth statement: A plot of concentration of reactant versus time is a straight line with slope equal to \(-k\).