Derive an expression to calculate time required for completion of zero order reaction.

Options

A. `t = ([R_(0)])/(k)`
B. `t = [R] - [R_(0)]`
C. `t = (k)/([R_(0)])`
D. `t = ([R_(0)] - [R])/([R_(0)])`

Explanation

To derive the expression for the time required for the completion of a zero-order reaction, we can follow these steps:

### Step 1: Write the Rate Expression for a Zero-Order Reaction
For a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants. The rate expression can be written as:
\[ \text{Rate} = -\frac{d[R]}{dt} = k \]
where:
- \([R]\) is the concentration of the reactant,
- \(k\) is the rate constant.

### Step 2: Relate Concentration to Time
For a zero-order reaction, we can express the change in concentration over time as:
\[ [R] = [R_0] - kt \]
where:
- \([R_0]\) is the initial concentration of the reactant,
- \(t\) is the time.

### Step 3: Set the Concentration to Zero for Completion
At the completion of the reaction, the concentration of the reactant \([R]\) becomes zero:
\[ 0 = [R_0] - kt \]

### Step 4: Solve for Time \(t\)
Rearranging the equation gives us:
\[ kt = [R_0] \]
Now, solving for \(t\):
\[ t = \frac{[R_0]}{k} \]

### Final Expression
Thus, the expression for the time required for the completion of a zero-order reaction is:
\[ t = \frac{[R_0]}{k} \]