Chemical Kinetics

Unit of rate constant =

From the units, it is clear that the order of reaction is three.

If rate of reaction is doubled by increasing
temperature from K.

and
On applying,

When volume is reduced to one fourth, concentrations become four times. Hence, the rate of reaction becomes 16 times as compared to the initial rate.

The correct answer is option (E): Mol^-1Lsec^-1
Rate=k[A]^½[B]^3/2
Rate = M/s =k [mol/L]^½ [mol/L]^3/2
On simplifying, k= (mol/L)^-1/s k=Mol^-1Lsec-¹

The correct answer is option (A): 4-Times
According to the question, the reaction is rate= k[A][B]² The concentration of B is doubled, so according to the rate law expression. Initial is B and later it is 2B. rate= k[A][2B]² As the concentration of B is increased by 2 times, the rate of the reaction will increase by four times.

Step 1: Understanding the Given Information.
We are given the rate constant and the time for the reaction to reach 100% completion. We can use the formula for the reaction time for a first-order reaction: Where is the rate constant and the time is in minutes.
Step 2: Calculation.
Thus, the time it will take to reach 100% completion is approximately 20 minutes.
Step 3: Conclusion.
The correct answer is (D) 20 min.

Step 1: Understanding the Relationship.
The relationship between the cell potential and the equilibrium constant is given by the Nernst equation: Where is the number of electrons involved in the reaction.
Step 2: Calculation.
Given that and , we can solve for :
Step 3: Conclusion.
The correct answer is (D) .

Step 1: Understand the condition for liberation of hydrogen gas.
A metal can liberate hydrogen gas from dilute hydrochloric acid only if it is more reactive than hydrogen. Metals placed above hydrogen in the activity series can displace hydrogen from acids, while metals placed below hydrogen cannot do so.
Step 2: Compare the given metals with hydrogen in the activity series.
Among the given metals, cobalt , nickel , and zinc are above hydrogen in the reactivity series. Therefore, these metals react with hydrochloric acid and liberate hydrogen gas.
Copper , however, lies below hydrogen in the activity series. Hence, it cannot displace hydrogen from dilute hydrochloric acid.
Step 3: Write the reasoning through reactions.
For reactive metals:
Similarly, cobalt and nickel also react with HCl to release . But copper does not show such a reaction with dilute HCl because it is less reactive than hydrogen.
Step 4: Conclusion.
Therefore, the metal which does not liberate hydrogen gas on reaction with hydrochloric acid is copper.
Final Answer:Cu.

Step 1: Use Arrhenius equation in logarithmic form.
When the temperature changes from to , the Arrhenius equation is written as:
Since the rate doubles, we take:
Also,
Step 2: Substitute the values in the formula.
We know that:
and
So,
Step 3: Calculate the activation energy.
Rearranging,
Step 4: Conclusion.
Therefore, the activation energy of the reaction is . Hence, the correct option is .
Final Answer: .

Step 1: Identify the order of reaction from the unit of rate constant.
The unit of the rate constant is given as . This unit corresponds to a first-order reaction. For a first-order reaction, the half-life is independent of the initial concentration and is given by a fixed formula.
Step 2: Write the formula for half-life of first-order reaction.
For a first-order reaction,
Here,
So,
Step 3: Convert the time into seconds.
Since,
therefore,
Step 4: Conclusion.
Hence, the half-life of the reaction is seconds. Therefore, the correct option is .
Final Answer:20.8 s.

Step 1: Recall the unit of rate constant for -th order reaction.
For an -th order reaction, the unit of rate constant is given by
If concentration is expressed in , then the unit becomes
Step 2: Compare with the given unit.
Given unit of rate constant is
Now compare this with the general form
So,
Also,
which again gives
Step 3: Conclusion.
Therefore, the reaction is of third order.
Final Answer:3.

Step 1: Write the Arrhenius equation.
The Arrhenius equation is
where is rate constant, is Arrhenius factor, is activation energy, is gas constant, and is absolute temperature.
Step 2: Convert into logarithmic form.
Taking common logarithm on both sides, we get
This is in the form of a straight line equation
where
Step 3: Identify the slope.
Comparing with the straight line form, the slope is
Step 4: Conclusion.
Hence, in the graph of versus , the slope is .
Final Answer: .