In the first order thermal decomposition of $C _{2} H _{5} I (g) \longrightarrow C _{2} H _{4}(g)+ HI (g)$, the reactant in
the beginning exerts a pressure of $2$ bar in a closed vessel at $600 \,K$. If the partial pressure of the reactant is $0.1$ bar after $1000$ minutes at the same temperature the rate constant in $\min ^{-1}$ is $(\log 2=0.3010)$
- $6.0 \times 10^{-4}$
- $6.0 \times 10^{- 3}$
- $3 .0 \times 10^{- 3}$
- $3.0 \times 10^{-4}$
The Correct Option is C
Solution and Explanation
Since, the reaction is first order,
$k= \frac{2.303}{t} \log \frac{p}{p_{0}-x} $
$k =\frac{2.303}{1000} \log \frac{2}{2-1.9} $
$=\frac{2303}{1000} \log 20$
$k =3 \times 10^{-3} \min ^{-1}$
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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