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प्रश्न
Read the following passage and answer the questions that follow:
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The rate of reaction is concerned with decrease in the concentration of reactants or increase in the concentration of products per unit of time. It can be expressed as instantaneous rate at a particular instant of time and average rate over a large interval of time. A number of factors such as temperature, concentration of reactants, catalyst affect the rate of reaction. Mathematical representation of rate of a reaction is given by rate law: Rate = k[A]x [B]y x and y indicate how sensitive the rate is to change in concentration of A and B. Sum of x + y gives the overall order of a reaction. |
- What is the effect of temperature on the rate constant of a reason? [1]
- For a reaction \[\ce{A + B → Product}\], the rate law is given by, Rate = k[A]2 [B]1/2. What is the order of the reaction? [1]
- How order and molecularity are different for complex reactions? [1]
- A first-order reaction has a rate constant 2 × 10–3 s–1. How long will 6 g of this reactant take to reduce to 2 g? [2]
OR
The half-life for radioactive decay of 14C is 6930 years. An archaeological artifact containing wood had only 75% of the 14C found in a living tree. Find the age of the sample.
[log 4 = 0.6021, log 3 = 0.4771, log 2 = 0.3010, log 10 = 1] [2]
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उत्तर
a. The rate constant (k) for a reaction increases with an increase in temperature and becomes almost double with every 10° rise in temperature. This effect is expressed by the Arrhenius equation:
k = `Ae^(-E_a//RT)`
b. According to the equation, r = k[A]2[B]1/2
Order of the reaction = `2 + 1/2 = 5/2`
c. Order of reaction is defined as the sum of the powers of the molar concentration of the reaction species in the rate equation of the reaction. It is applicable to both elementary and complex reactions.
Molecularity of a reaction is defined as the total number of reacting species participating in an elementary reaction. It has no significance for complex reactions as applicable only to elementary reactions.
d. k = 2 × 10–3 s–1
t = `2.303/k log [R]_0/[R]`
t = `2.303/(2 xx 10^-3) log 6/2`
t = 1151.5 × 0.4771
t = 549.3 s
OR
According to first-order reaction,
Half-life (t1/2) = `0.693/k`
t1/2 = 6980 years
k = `0.693/6980`
However, the time taken can be calculated using the first-order rate of reaction when wood contains only 75% of 14C.
Initial concentration of C14, [R]0 = 100
Amount at time t s, [R] = 75
t = `2.303/k log [R]_0/([R])`
t = `2.303/(0.693/6980) log 100/75`
t = 2898 years
Thus, the age of the sample is approximately 2898 years.
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संबंधित प्रश्न
From the rate expression for the following reaction, determine the order of reaction and the dimension of the rate constant.
\[\ce{3NO_{(g)} -> N2O_{(g)}}\] Rate = k[NO]2
For the reaction:
\[\ce{2A + B -> A2B}\]
the rate = k[A][B]2 with k = 2.0 × 10−6 mol−2 L2 s−1. Calculate the initial rate of the reaction when [A] = 0.1 mol L−1, [B] = 0.2 mol L−1. Calculate the rate of reaction after [A] is reduced to 0.06 mol L−1.
Rate of reaction for the combustion of propane is equal to:
\[\ce{C3H8_{(g)} + 5O2_{(g)} -> 3CO2_{(g)} + 4H2O_{(g)}}\]
Consider a first order gas phase decomposition reaction given below :
\[\ce{A(g) -> B(g) + C(g)}\]
The initial pressure of the system before decomposition of A was pi. After lapse of time ‘t’, total pressure of the system increased by x units and became ‘pt’ The rate constant k for the reaction is given as ______.
For a complex reaction:
(i) order of overall reaction is same as molecularity of the slowest step.
(ii) order of overall reaction is less than the molecularity of the slowest step.
(iii) order of overall reaction is greater than molecularity of the slowest step.
(iv) molecularity of the slowest step is never zero or non interger.
Why is the probability of reaction with molecularity higher than three very rare?
Assertion: Rate constants determined from Arrhenius equation are fairly accurate for simple as well as complex molecules.
Reason: Reactant molecules undergo chemical change irrespective of their orientation during collision.
For a reaction \[\ce{Cl2l(g) + 2No(g) -> 2NaCl(g)}\] the rate law is expressed as rate= K[Cl2] [No]2 what is the order of the reaction?
The rate of a chemical reaction double for every 10° rise in temperature. If the temperature is raised. by 50°C, the rate of relation by about:-
A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is reduced to half?
