In a certain reaction, `10%` of the reactant decomposes in one hour, `20%` in two hours, `30%` in theee hours, and so on. The dimenison of the velocity constant (rate constant) are

Options

A. `hr^(-1)`
B. `Mol L^(-1) hr^(-1)`
C. `L mol^(-1) s^(-1)`
D. `Mol s^(-1)`

Explanation

To solve the problem step by step, we will analyze the information given and apply the relevant concepts of chemical kinetics.

### Step 1: Identify the Order of the Reaction
The problem states that 10% of the reactant decomposes in 1 hour, 20% in 2 hours, and 30% in 3 hours. This consistent increase in the percentage decomposed suggests that the rate of reaction does not depend on the concentration of the reactant.

**Hint:** Look for patterns in the data to determine the order of the reaction.

### Step 2: Determine the Order of Reaction
Since the percentage decomposed increases linearly with time, we can conclude that the reaction is of zero order. In a zero-order reaction, the rate is constant and does not depend on the concentration of the reactant.

**Hint:** Recall that for zero-order reactions, the rate is independent of the concentration of the reactants.

### Step 3: Write the Rate Law for Zero-Order Reaction
For a zero-order reaction, the rate law can be expressed as:
\[ \text{Rate} = k \]
where \( k \) is the rate constant.

**Hint:** Remember that for zero-order reactions, the rate constant has a specific unit that we will derive next.

### Step 4: Determine the Units of the Rate Constant
The general formula for the units of the rate constant \( k \) is given by:
\[ k = \text{(concentration)}^{1-n} \cdot \text{(time)}^{-1} \]
where \( n \) is the order of the reaction. For a zero-order reaction, \( n = 0 \).

Substituting \( n = 0 \) into the formula:
\[ k = \text{(concentration)}^{1-0} \cdot \text{(time)}^{-1} \]
\[ k = \text{(concentration)}^{1} \cdot \text{(time)}^{-1} \]

### Step 5: Define Concentration and Time Units
Concentration is typically expressed in moles per liter (mol/L), and time is expressed in seconds (s). Therefore:
\[ k = \frac{\text{mol}}{\text{L} \cdot \text{s}} \]

**Hint:** Make sure to use consistent units for concentration and time when determining the units of the rate constant.

### Step 6: Final Units of the Rate Constant
Thus, the units of the rate constant \( k \) for a zero-order reaction are:
\[ k = \text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \]

### Conclusion
The dimensions of the velocity constant (rate constant) for this zero-order reaction are:
\[ \text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \]