In a zero-order reaction,the reactant A disappeared with a rate of reaction k=0.04 Msec-1. The initial concentration of A is 1 M. What will be the concentration of A after 20 seconds?
In a zero-order reaction,the reactant A disappeared with a rate of reaction k=0.04 Msec-1. The initial concentration of A is 1 M. What will be the concentration of A after 20 seconds?
1.08 M
0.2 M
0.8 M
0.002 M
0.008 M
The Correct Option is B
Approach Solution - 1
Given parameters:
- Rate constant \( k = 0.04 \, \text{M sec}^{-1} \)
- Initial concentration \( [A]_0 = 1 \, \text{M} \)
- Time \( t = 20 \, \text{sec} \)
- Zero-order reaction kinetics
Zero-order rate equation: \[ [A]_t = [A]_0 - kt \] \[ [A]_t = 1 - (0.04 \times 20) \] \[ [A]_t = 1 - 0.8 = 0.2 \, \text{M} \]
Thus, the correct option is (B): 0.2 M.
Approach Solution -2
1. Zero-order reaction rate law:
For a zero-order reaction, the rate of reaction is independent of the concentration of the reactant. The integrated rate law for a zero-order reaction is:
\[[A]_t = [A]_0 - kt\]
where:
- \([A]_t\) is the concentration of A at time \(t\)
- \([A]_0\) is the initial concentration of A
- \(k\) is the rate constant
- \(t\) is the time elapsed
2. Substitute the given values:
\([A]_0 = 1 \, M\)
\(k = 0.04 \, M \, sec^{-1}\)
\(t = 20 \, sec\)
\[[A]_t = 1 - (0.04)(20)\]
3. Perform the calculation:
\[[A]_t = 1 - 0.8 = 0.2 \, M\]
4. Final answer:
The concentration of A after 20 seconds is 0.2 M.
Thus, the correct option is (B) 0.2 M.
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Concepts Used:
Rate of a Chemical Reaction
The rate of a chemical reaction is defined as the change in concentration of any one of the reactants or products per unit time.
Consider the reaction A → B,
Rate of the reaction is given by,
Rate = −d[A]/ dt=+d[B]/ dt
Where, [A] → concentration of reactant A
[B] → concentration of product B
(-) A negative sign indicates a decrease in the concentration of A with time.
(+) A positive sign indicates an increase in the concentration of B with time.
Factors Determining the Rate of a Reaction:
There are certain factors that determine the rate of a reaction:
- Temperature
- Catalyst
- Reactant Concentration
- Chemical nature of Reactant
- Reactant Subdivision rate