For a reaction : 2A(g) `rarr` B(g) + 3C(g), rate constant of disappearance of A is `10^(-3) "M sec"^(-1)`. If initially 2 M of A is taken then what will be concentration of C afterr 5 minutes?

Options

A. `0.3M`
B. `0.9M`
C. `0.45M`
D. `1.5xx10^(-2)M`

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the Reaction Order
The given reaction is:
\[ 2A(g) \rightarrow B(g) + 3C(g) \]

The rate constant for the disappearance of A is given as \( k = 10^{-3} \, \text{M s}^{-1} \). Since the rate constant has units of concentration per time, this indicates that the reaction is a zero-order reaction.

### Step 2: Determine the Initial Concentration of A
Initially, the concentration of A is given as:
\[ [A]_0 = 2 \, \text{M} \]

### Step 3: Calculate the Amount of A Disappeared After 5 Minutes
In a zero-order reaction, the rate of reaction is constant and can be expressed as:
\[ [A] = [A]_0 - kt \]

Where:
- \( [A] \) is the concentration of A at time \( t \)
- \( k \) is the rate constant
- \( t \) is the time in seconds

Convert 5 minutes to seconds:
\[ t = 5 \, \text{minutes} \times 60 \, \text{s/minute} = 300 \, \text{s} \]

Now, substituting the values into the equation:
\[ [A] = 2 \, \text{M} - (10^{-3} \, \text{M s}^{-1} \times 300 \, \text{s}) \]
\[ [A] = 2 \, \text{M} - 0.3 \, \text{M} \]
\[ [A] = 1.7 \, \text{M} \]

### Step 4: Calculate the Amount of A that has Disappeared
The amount of A that has reacted (disappeared) is:
\[ x = [A]_0 - [A] = 2 \, \text{M} - 1.7 \, \text{M} = 0.3 \, \text{M} \]

### Step 5: Determine the Concentration of C Produced
From the stoichiometry of the reaction, for every 2 moles of A that react, 3 moles of C are produced. Thus, the concentration of C produced is:
\[ [C] = \frac{3}{2} x = \frac{3}{2} \times 0.3 \, \text{M} = 0.45 \, \text{M} \]

### Final Answer
The concentration of C after 5 minutes is:
\[ [C] = 0.45 \, \text{M} \]

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