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All questions of Rate Processes – Kinetics and Equilibrium (GC) for MCAT Exam

Ca(HCO3)2 is strongly heated and after equilibrium is attained, temperature changed to 25° C.

Kp = 36 (pressure taken in atm)
Thus, pressure set up due to CO2 is
  • a)
    36 atm
  • b)
    18 atm
  • c)
    12 atm
  • d)
    6 atm
Correct answer is 'D'. Can you explain this answer?

Mira Joshi answered
The reaction is as follow:-
Ca(HCO3)2(s)⇌CaO(s) + 2CO2 (g) + H2O(g)
At 25° C H2O goes in liquid state
Kp = (PCaO)1×(PCO2)2
(PCa(HCO3)2)
Since, Ca(HCO3)2, CaO and H2O are not in gaseous state, so their partial pressure is taken 1.
Putting all values, we have
36 = (PCO2)2 
Or PCO2 = 6 atm

Following equilibrium is set up at 298 K in a 1 L flask.

If one starts with 2 moles of A and 1 mole of B, it is found that moles of B and D are equal.Thus Kc is 
  • a)
    9.0
  • b)
    15.0
  • c)
    3.0
  • d)
    0.0667
Correct answer is option 'B'. Can you explain this answer?

Sushil Kumar answered
For the equilibrium reaction:
A+2B ⇌ 2C+D
volume of flask = 1L
Initial moles of A = 2 mol
initial concentration of A=[A]i = 2 M
initial mole of B = 1 mol 
[B]i = 1 M
[A]eq = 2-x, [B]eq = 1-2x, [C]eq = x, [D]eq = 3x
Given [D]eq = 1 * 1L
= 1 M
Thus x = 1M
[A]eq = 1, [B]eq = -1, [C]eq = 1, [D] = 3
Kc = {([D]eq)3 * ([C]eq)}/{[A]eq * ([B]eq)2
= Kc = {(3)3*1}/{1*(-1)2}
= 27/1
= 27

Following equilibrium is set up at 1000 K and 1 bar in a 5 L flask,

At equilibrium, NO2 is 50% o f the total volume. Thus, equilibrium constant Kc is 
  • a)
    0.133
  • b)
    0.266
  • c)
    0.200
  • d)
    0.400
Correct answer is option 'A'. Can you explain this answer?

The correct answer is Option A.    
                N2O4  ⇌  2NO2
Initial            1                 0           
Equilibrium  1−x             2x
Total moles = 1 - x + 2x 
NO2 is 50% of the total volume when equilibrium is set up.
Thus, the volume fraction (at equilibrium) of NO2 = 50/100 = 0.5 = ½
So,    2x / (1+x) = ½
     => x = ⅓
For 1 litre;
Kc = [NO2] / [N2O4]
    = [4*(1/9)] / [⅔]
    = 0.66; 
For 5 litres; 
Kc = 0.66 / 5
= 0.133
Thus, option A is correct.
 

Assume following equilibria when total pressure set up in each are equal to 1 atm, and equilibrium constant (Kp) as K1; K2 and K3


Thus,
  • a)
     K1 = K2 = K3
  • b)
    K1 < K2 < K3
  • c)
    K3 < K2 < K1
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

The correct answer is option C
CaCO3 ​→ CaO + CO2​
Kp​ = k1 ​= Pco2​​
total pressure of container P
k1​ = p
NH4​HS → NH3 ​+ H2​S
PNH3​​ = PH2​S ​= P0​
P0​ + P0​ = p (total pressure)
P0 ​= p/2
k2​ = kp ​= [PNH3​​][PH2​s​] p24
NH2​CoNH2 ​→ 2NH3 ​+ CO2​
PNH3​​ = 2P0​        PCO2​ ​= P0​
2P0​ + P0 ​= P

Which of the following is an example of a zero-order reaction?
  • a)
    Radioactive decay
  • b)
    First-order decay
  • c)
    Second-order reaction
  • d)
    Photochemical reaction
Correct answer is option 'A'. Can you explain this answer?

Harper White answered
Zero-Order Reaction
A zero-order reaction is a type of chemical reaction in which the rate of the reaction is independent of the concentrations of the reactants. This means that the reaction proceeds at a constant rate, regardless of how much reactant is present. The rate equation for a zero-order reaction is given by:

Rate = k

where k is the rate constant.

Radioactive Decay
Radioactive decay is an example of a zero-order reaction. It is the process by which unstable atomic nuclei spontaneously break apart, releasing radiation and transforming into a different element. The rate of radioactive decay is determined solely by the decay constant, which is a characteristic property of the radioactive material.

Explanation
In a zero-order reaction, the rate of the reaction does not depend on the concentration of the reactants. This means that even if the concentration of the reactant is doubled or halved, the rate of the reaction will remain the same.

Radioactive decay follows this behavior because it is a first-order reaction with respect to the radioactive material. The rate of decay is determined solely by the decay constant, which is a property of the specific radioactive isotope. The decay constant represents the probability of a radioactive atom decaying per unit time and is independent of the concentration of the radioactive material.

For example, if we have a sample of radioactive material with an initial concentration of 1 mol/L, the rate of decay will be a constant value determined by the decay constant. If we double the concentration of the radioactive material to 2 mol/L, the rate of decay will still be the same constant value. Similarly, if we halve the concentration to 0.5 mol/L, the rate of decay will remain unchanged.

Conclusion
Radioactive decay is an example of a zero-order reaction because the rate of decay is independent of the concentration of the radioactive material. The rate of decay is determined solely by the decay constant, which is a characteristic property of the radioactive isotope.

Kc forthe decomposition of NH4HS(s) is 1.8x 10-4 at 25°C.

If the system already contains [NH3] = 0.020 M, then when equilibrium is reached, molar concentration are
  • a)
    a
  • b)
    b
  • c)
    c
  • d)
    d
Correct answer is option 'B'. Can you explain this answer?

Sushil Kumar answered
 NH4HS (s)  ⇋ NH3 (g) + H2S (g)
Initial    1                   -               -
At eqm     1-x                 x+0.02     x
Kc = [NH3][H2S]   (Since NH4HS is solid, we ignore it.)
1.8×10-4    = (x+0.02)(x)
x2+0.02x-1.8×10-4 = 0
Applying quadratic formula; x = -0.02+√{(0.02)2-4×1.8×10-4}
= 0.033-0.020/2 = 0.0065
Therefore, concn of NH3 at equilibrium = x+0.020 = 0.0265
concn of H2S at equilibrium = x = 0.0065
So, option b is correct

The unit of rate constant for a first order reaction is
  • a)
    Mol/L
  • b)
    Mol2 / L2 / S2
  • c)
    S-1
  • d)
    Mol/L/S
Correct answer is option 'C'. Can you explain this answer?

Nikita Singh answered
The correct answer is Option C.
Let R be the rate of reaction.
For first order reaction,
R=K[A]1
⇒K=R[A]-1
Whereas, K and [A] are rate constant and initial concentration of reactant respectively.
Therefore,
Unit of rate constant =(mol L-1)1-nsec-1
For first order reaction, n=1
Unit of rate constant = sec-1
Hence the unit of rate constant for first order reaction is sec-1.

Passage I
Solid ammonium chloride is in equilibrium with ammonia and hydrogen chloride gases

0.980 g of solid NH4CI is taken in a closed vessel of 1 L capacity and heated to 275° C.
Q. Percentage decomposition of the original sample is
  • a)
    24.81%
  • b)
    6.24%
  • c)
    3.12%
  • d)
    12.13%
Correct answer is option 'D'. Can you explain this answer?

Knowledge Hub answered
The state of HCl is given wrong. It will be in gaseous state.
So, the reaction be like;-
NH4Cl(s)  ⇌  NH3(g) + HCl(g)        kp = 1.00×10-2 at 275° C
Kp = kc(RT)2
1.00×10-2 = kc(0.0821×548)2
Or kc = 4.94×10-6
                          NH4Cl(s)  ⇌  NH3(g) + HCl(g)
Initial  1                     -             -
At eqm 1-x                  x            x 
Kc = x2
x = √(4.94×10-6)
=  2.22×10-3
Therefore, NH4Cl dissociated at eqm = 2.22×10-3 × 53.5 = 0.118
%age decomposition = 0.118/0.980×100 = 12.13%

For the equilibrium,

at 1000 K. If at equilibrium pCO = 10 then total pressure at equilibrium is 
  • a)
    6.30 atm
  • b)
    0.63 atm
  • c)
    6.93 atm
  • d)
    69.3 atm
Correct answer is option 'C'. Can you explain this answer?

Lavanya Menon answered
C(s) + CO2(g) <=========> 2CO(g)
Kp = pCO2/pCO2
GIven Kp = 63 and pCO = 10pCO2
Putting the value of pCO in above equation,
63 = 100(pCO2)2/pCO2
Or pCO2 = 0.63
pCO = 6.3
Therefore, total pressure = 6.3+0.63 = 6.93 atm

Direction (Q. Nos. 21) This section contains 2 questions. when worked out will result in an integer from 0 to 9 (both inclusive)
Q. For the equilibrium in gaseous phase in 2 L flask we start with 2 moles of SO2 and 1 mole of O2 at 3 atm, 
When equilibrium is attained, pressure changes to 2.5 atm. Hence, equilibrium constant Kc is
    Correct answer is '4'. Can you explain this answer?

    Om Desai answered
    The correct answer is 4
    2SO2(g) + O2(g) ⇋ 2SO3
    Initial moles      2            1
    At equilibrium 2 - 2x     1 - x    2x
    Net moles at equilibrium  =  2 - 2x + 1 - x + 2x
    =(3 - x)moles
    Initial:
             moles = 3, 
        Pressure = 3 atm,
          Volume = 2L,
                 PV = nRT
              3 x 2 = 3RT  -------- 1
    At equilibrium
         Moles = 3 - x,
    Pressure = 2.5 atm
      Volume = 2L
            P‘V = n’RT ---------- 2
    Divide eqn  2 by 1

    ⇒2.5 = 3 - x
    ⇒x = 0.5

    If a reaction proceeds with a uniform rate throughout, the reaction is
    • a)
      Third order
    • b)
      Second order
    • c)
      First order
    • d)
      Zero order
    Correct answer is option 'D'. Can you explain this answer?

    Roshni Chavan answered
    Reaction Rate and Order:

    The rate of a chemical reaction refers to how quickly reactants are consumed and products are formed. It is determined by the rate equation, which shows how the concentration of reactants influences the rate of the reaction. The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate equation.

    Uniform Rate throughout the Reaction:

    When a reaction proceeds with a uniform rate throughout, it means that the rate of the reaction remains constant over time. This implies that the concentration of the reactants does not affect the reaction rate. In other words, the reaction is not dependent on the concentration of the reactants.

    Zero Order Reaction:

    When the reaction rate is independent of the concentration of the reactants, it is referred to as a zero order reaction. In this case, the rate equation is expressed as:

    Rate = k

    where k is the rate constant. The rate of the reaction is solely determined by the value of the rate constant, and it does not change with changes in reactant concentrations.

    Explanation:

    In the given question, if the reaction proceeds with a uniform rate throughout, it indicates that the rate of the reaction does not depend on the concentration of the reactants. This is a characteristic of a zero order reaction.

    The rate equation for a zero order reaction is Rate = k, where k is the rate constant. It means that the reaction proceeds at a constant rate, regardless of the initial concentrations of the reactants. The rate constant determines the speed of the reaction, and it remains constant throughout the reaction.

    Therefore, the correct answer is option 'D' - Zero order.

    Molecularity of a reaction
    • a)
      Cannot be less than 2
    • b)
      Can be zero
    • c)
      Is always a natural number
    • d)
      Can have a fractional values
    Correct answer is option 'C'. Can you explain this answer?

    Nandini Nair answered
    Molecularity is defined as the number of molecules, atoms, or radicals that must collide simultaneously in order for the reaction to take place. It is always a natural number and cannot be negative.

    At 700 K and 350 bar, a 1 : 3 mixture of N2(g) and H2(g) reacts to form an equilibrium mixture containing X (NH3)= 0.50. Assuming ideal behaviour Kp for the equilibrium reaction, 
    • a)
      2.03x 10-4
    • b)
      3.55x 10-3
    • c)
      1.02 x 10-4
    • d)
      3.1 x 10-4
    Correct answer is option 'D'. Can you explain this answer?

    Knowledge Hub answered
    The correct answer is option A
    2.03x 10-4
    The given equation is :-
     N2​(g)+3H2​(g) ⇌ 2NH3​(g)
    Initial moles : 1             3         0
    At eqm ;       (1−x)    (3−3x)   (2x)               
    (let)
    Total moles of equation
     =1 − x + 3 − 3x + 2x = (4−2x)
    Now, X(NH3​) = 
    ⇒ 2x = 2 − x
    ⇒ 3x = 2 ⇒ x = 0.66 = 
    32​
    Now, at equation, moles of N2​= 1/3, moles of NH3​ = 4/3
                 moles of H2 ​ =3 − 2 = 1

     

    A first order reaction is 50% completed in 1.26 × 1014 s. How much time would it take for 100% completion?
    • a)
      1.26 × 1015 s
    • b)
      2.52 × 1014 s
    • c)
      2.52 × 1028 s
    • d)
       infinite
    Correct answer is option 'D'. Can you explain this answer?

    Neha Chauhan answered
    The time taken for half the reaction to complete, i.e., the time in which the concentration of a reactant is reduced to half of its original value is called half-life period of the reaction. But it is impossible to perform 100% of the reaction. Whole of the substance never reacts because in every half-life, 50% of the substance reacts. Hence, time taken for 100% completion of a reaction is infinite. 

    At 273 K and 1 atm, 1 L of N2O4 (g) decomposes to NO2(g)a s given,
    At equilibrium, original volume is 25% less than the existing volume. Percentage decomposition of N2O4 (g) is thus, 
    • a)
      25%
    • b)
      50%
    • c)
      66.66%
    • d)
      33.33%
    Correct answer is option 'D'. Can you explain this answer?

    Suresh Reddy answered
    Let the initial volume of N2O4 be x and initial volume of NO2 is 0
    If the degree of dissociation is a, then the final volume of N2O4 is x(1−a) and NO2 is 2ax.
    Initial
    It equilibrium
    N2O4            ⟶              2NO2
    x                                       0
    x(1−a)                               2ax
    Total initial volume =x+0=x
    Final volume =x(1−a)+2ax=x+ax=x(1+a)
    It is given that the initial volume is 25% less than the final volume
    x=0.75×(1+a)
    1+a=1.33
    a=0.33
    So %age dissociation = 33.33%

    The effect of temperature on reaction rate is given by
    • a)
      Gibb’s Helmholtz equation
    • b)
      Clausius Claperon equation
    • c)
      Arrhenius equation
    • d)
      Kirchoff’s equation
    Correct answer is option 'C'. Can you explain this answer?

    Manoj Chauhan answered
    Arrhenius equation describes the effect of temperature on the rate constant of a chemical reaction. It is given by:

    k = Ae^(-Ea/RT)

    where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

    Explanation:

    Temperature is a measure of the average kinetic energy of the molecules in a substance. When the temperature is increased, the molecules move faster and collide more frequently. This increases the chance of successful collisions between reactant molecules, leading to an increase in the reaction rate.

    Arrhenius equation explains this relationship between temperature and reaction rate by stating that the rate constant (k) of a reaction increases exponentially with increasing temperature. The activation energy (Ea) is the minimum energy required for a reaction to occur, and it determines the rate at which the reaction proceeds.

    The pre-exponential factor (A) takes into account the frequency of collisions between reactant molecules. It is a constant that depends on the nature of the reaction and the reactants involved.

    The Arrhenius equation is widely used to describe the temperature dependence of chemical reactions in various fields, including chemistry, biology, and materials science.

    Conclusion:

    In summary, the Arrhenius equation is used to describe the effect of temperature on the rate constant of a chemical reaction. It explains that the rate constant increases exponentially with increasing temperature, due to an increase in the frequency and energy of collisions between reactant molecules.

    Passage II
    A 15 L flask at 300 K contains 64.4 g of a mixture of NO2 and N2O4 in equilibrium. Given,
    Q. Kc for the above equilibrium is 
    • a)
      164.28
    • b)
       6.087x 10-3
    • c)
      0.2708
    • d)
      3.693
    Correct answer is option 'A'. Can you explain this answer?

    Pooja Shah answered
    Kp = Kc(RT)n
    Kp = 6.67 ,
    ∆n = moles of products - moles of reactants = 1-2 = -1
    R = 0.0821 L atm mol-¹K-¹
    T = 300K
    Substitute these values in the formula,
    => Kc = 6.67×0.0821×300
    Kc = 164.28.
     

    The half life of a reaction is halved as the initial concentration of the reactant is doubled. The order of the reaction is
    • a)
      2
    • b)
      0
    • c)
      1
    • d)
      3
    Correct answer is option 'A'. Can you explain this answer?

    Snehal Iyer answered
    Explanation:

    The half-life of a reaction is defined as the time required for the concentration of a reactant to decrease by half.

    Let's assume that the initial concentration of a reactant is [A] and its half-life is t1/2.

    When the initial concentration of the reactant is doubled, the new concentration becomes 2[A]. Let's assume that the new half-life is t1/2'.

    Now, we know that the rate of a reaction is directly proportional to the concentration of the reactant raised to the power of the order of the reaction.

    Thus, we can write the following equation for the rate constant (k) of the reaction:

    k = A*[A]^n

    where A is a proportionality constant and n is the order of the reaction.

    Now, let's compare the rate constants of the reaction at two different concentrations.

    When the initial concentration of the reactant is [A], the rate constant is:

    k = A*[A]^n

    When the initial concentration of the reactant is 2[A], the rate constant is:

    k' = A*[2A]^n = 2^n*A*[A]^n

    We know that the half-life of the reaction is inversely proportional to the rate constant. Thus, we can write the following equation for the half-life of the reaction:

    t1/2 = ln(2)/(k*[A]^n)

    t1/2' = ln(2)/(k'*[2A]^n) = ln(2)/(2^n*A*[A]^n)

    Now, let's compare the two half-lives.

    t1/2' = ln(2)/(2^n*A*[A]^n) = (1/2)*ln(2)/(A*[A]^n)

    We know that t1/2' is half of t1/2.

    Thus, we can write the following equation:

    t1/2'/t1/2 = 1/2

    (1/2)*ln(2)/(A*[A]^n)/(ln(2)/(A*[A]^n)) = 1/2

    2^n = 2

    n = 2

    Thus, the order of the reaction is 2.

    H2S (g) initially at a pressure of 10.0 atm and a temperature of 800 K, dissociates as
    At equilibrium, the partial pressure of S2 vapour is 0.020 atm . Thus, Kp is 
    • a)
      3.23x 10-7
    • b)
      6.45x 10-7
    • c)
      1.55x 106
    • d)
      6.20x 107
    Correct answer is option 'A'. Can you explain this answer?

    Geetika Shah answered
    The correct answer is Option A.
        
                     2H2S(g) ⇌ 2H2(g) + S2(g)

    Pressure
    at t=0           Pi                −           −
    at eqm       Pi−P            2P          P
    as P=0.02    thus Pi−P=10−0.02
         Pi=10                     2P=0.04

    Kp = 3.23×10−7 atm.

    Once the equilibrium is reached under given condition:
    • a)
      Cone, remains the same in spite of the change in temperature
    • b)
      Cone, of all the substances presents do not change
    • c)
      Cone, of reactants remairfs same
    • d)
      Cone, of products remains same
    Correct answer is option 'B'. Can you explain this answer?

    Raghav Bansal answered
    In a chemical reaction, chemical equilibrium is the state in which the forward reaction rate and the reverse reaction rate are equal. The result of this equilibrium is that the concentrations of the reactants and the products do not change. However, just because concentrations aren’t changing does not mean that all chemical reaction has ceased. Just the opposite is true; chemical equilibrium is a dynamic state in which reactants are being converted into products at all times, but at the exact rate that products are being converted back into reactants. The result of such a situation is analogous to a bridge between two cities, where the rate of cars going over the bridge in each direction is exactly equal. The result is that the net number of cars on either side of the bridge does not change.

    The constant k used in rate equation is known as
    • a)
      Distance constant
    • b)
      Velocity constant
    • c)
      Reaction constant
    • d)
      Order constant
    Correct answer is option 'B'. Can you explain this answer?

    Nisha Kulkarni answered
    Rate Equation and Velocity Constant

    Rate equation

    The rate equation is an equation that describes the relationship between the rate of a chemical reaction and the concentration of the reactants. The rate of a reaction is the speed at which the reactants are converted into products.

    The rate equation is expressed in the following form:

    Rate = k[A]^m[B]^n

    Where,

    k = velocity constant or rate constant
    [A] = concentration of reactant A
    [B] = concentration of reactant B
    m and n = order of the reaction with respect to A and B respectively.

    Velocity constant

    The velocity constant (k) is a proportionality constant that relates the rate of a reaction to the concentration of the reactants. It is also known as the rate constant.

    The velocity constant is specific to a particular chemical reaction and is determined experimentally. It is a measure of the intrinsic tendency of the reactants to react and the efficiency of the reaction.

    The value of the velocity constant depends on the temperature, pressure, and other conditions of the reaction. It is expressed in units of concentration per unit time.

    Importance of velocity constant

    The velocity constant is important in understanding the kinetics of a chemical reaction. It provides information about the rate of the reaction and the mechanism by which it occurs.

    The value of the velocity constant can be used to predict the rate of the reaction at different concentrations of the reactants. It can also be used to compare the rates of different reactions and to optimize reaction conditions.

    Conclusion

    In conclusion, the velocity constant (k) is an important parameter in the rate equation that relates the rate of a chemical reaction to the concentration of the reactants. It is specific to a particular reaction and is determined experimentally. The value of the velocity constant provides information about the kinetics of the reaction and can be used to predict the rate of the reaction at different concentrations of the reactants.

    The minimum amount of energy required by the reacting molecules at the time of collisions in order to produce effective collisions is called
    • a)
      Threshold energy
    • b)
      Potential energy
    • c)
      Internal energy
    • d)
      Activation energy
    Correct answer is option 'D'. Can you explain this answer?

    Ciel Knowledge answered

    The minimum energy that the colliding molecules must possess for the chemical reaction to occur is known as threshold energy.
    The extra energy required by a reactant to participate in a reaction is called activation energy.

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