The rate of the reaction:
`CH_(3)COOC_(2)H_(5) + NaOH to Ch_(3)COONa + C_(2)H_(5) OH` is given by the equation,
rate `= k [CH_(3) COOC_(2)H_(5)][NaOH]`
If concenration is expressed in mol/L the units of k are

Options

A. `mol^(-2) L^(2) s^(-1)`
B. `mol L^(-1) s^(-1)`
C. `L mol^(-1) s^(-1)`
D. `S^(-1)`

Explanation

To determine the units of the rate constant \( k \) for the given reaction, we start with the rate equation provided:

\[ \text{rate} = k [CH_3COOC_2H_5][NaOH] \]

### Step 1: Understand the Units of Rate
The rate of a reaction is typically expressed in terms of concentration change over time. In this case, the rate can be expressed in units of molarity per second (mol/L/s). Therefore, the units of rate are:

\[ \text{Units of Rate} = \frac{\text{mol}}{\text{L} \cdot \text{s}} = \text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \]

### Step 2: Identify the Concentration Terms
The concentrations of the reactants \( [CH_3COOC_2H_5] \) and \( [NaOH] \) are both expressed in molarity, which has units of mol/L. Thus, we can write:

\[ [CH_3COOC_2H_5] = \frac{\text{mol}}{\text{L}} \quad \text{and} \quad [NaOH] = \frac{\text{mol}}{\text{L}} \]

### Step 3: Substitute Concentration Units into the Rate Equation
Substituting the concentration units into the rate equation gives:

\[ \text{rate} = k \left(\frac{\text{mol}}{\text{L}}\right) \left(\frac{\text{mol}}{\text{L}}\right) = k \left(\frac{\text{mol}^2}{\text{L}^2}\right) \]

### Step 4: Rearrange to Solve for \( k \)
Now, we can rearrange the equation to solve for \( k \):

\[ k = \frac{\text{rate}}{[CH_3COOC_2H_5][NaOH]} = \frac{\text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1}}{\frac{\text{mol}^2}{\text{L}^2}} \]

### Step 5: Simplify the Expression
When we simplify the expression for \( k \):

\[ k = \frac{\text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \cdot \text{L}^2}{\text{mol}^2} = \frac{\text{L} \cdot \text{s}^{-1}}{\text{mol}} \]

Thus, the units of \( k \) can be expressed as:

\[ k = \frac{\text{L}}{\text{mol} \cdot \text{s}} = \text{L} \cdot \text{mol}^{-1} \cdot \text{s}^{-1} \]

### Conclusion
The correct units for the rate constant \( k \) in this reaction are:

\[ \text{L} \cdot \text{mol}^{-1} \cdot \text{s}^{-1} \]

This corresponds to option 3: **liter per mole per second**.

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