Chemical Equilibrium

For a reversible reaction $\mathbf R\rightleftharpoons\mathbf P$, at constant temperature, both the forward and the backward reactions are first order elementary reactions with rate constants $k_f$ and $k_b$, respectively. At time zero, the concentration of $\mathbf R$ is $[\mathbf R]_0$ and the concentration of $\mathbf P$ is zero. At any given time, $[\mathbf R]$ and $[\mathbf P]$ are the concentrations of $\mathbf R$ and $\mathbf P$, respectively. If $k_b=4k_f$, the correct graphical representation of the reaction is

At T(K), the equilibrium constant of $\ce{A2(g) + B2(g) <=> C(g)}$ is $2.7\times10^{-5}$. What is the equilibrium constant for $\ce{1/3A2(g) + 1/3B2(g) <=> 1/3C(g)}$ at the same temperature?

For the following reaction at 50 °C and at 2 atm pressure,
$$\ce{2N2O5(g) <=> 2N2O4(g) + O2(g)}$$
$\ce{N2O5}$ is 50% dissociated.

The magnitude of standard free energy change at this temperature is $x$.

$x$ = ________ J mol$^{-1}$ [Nearest integer].

Given : R = 8.314 J mol$^{-1}$ K$^{-1}$, log 2 = 0.30, log 3 = 0.48, ln10 = 2.303, °C + 273 = K

The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below

$\ce{A(g) <=> B(g) + C(g)}$

$\frac{1}{T}$ (K$^{-1}$)	$\log_{10} K_p$
0.05	3.5
0.06	2.5
0.07	1.5

The magnitude of $\frac{\Delta H^\circ}{R}$ calculated from the above data is ________. (Nearest integer)

The reaction $\ce{A(g) <=> B(g) + C(g)}$ was initiated with the amount '$a$' of A(g). At equilibrium it is found that the amount of A(g) remaining is $(a-x)$ at a total pressure of p.

The equilibrium constant Kp of the reaction can be calculated from the expression :

One mole each of He and A(g) are taken in a 10 L closed flask and heated to 400 K to establish the following equilibrium.

$\ce{A(g) <=> B(g)}$

$K_c$ for this reaction at 400 K is 4.0. The partial pressures (in atm) of He and B(g) are respectively (at equilibrium)

(Assume He, A(g) and B(g) behave as ideal gases)

(Given : R = 0.082 L atm K$^{-1}$ mol$^{-1}$)

Consider the reaction $\ce{X <=> Y}$ at 300 K. If $\Delta H^\circ$ and K are 28.40 kJ mol$^{-1}$ and $1.8\times10^{-7}$ at the same temperature, then the magnitude of $\Delta S^\circ$ for the reaction in J K$^{-1}$ mol$^{-1}$ is ________. (Nearest integer)

(Given : R = 8.3 J K$^{-1}$ mol$^{-1}$, ln 10 = 2.3, log 3 = 0.48, log 2 = 0.30)

In a closed flask at 600 K, one mole of $\ce{X2Y4(g)}$ attains equilibrium as given below :

$\ce{X2Y4(g) <=> 2XY2(g)}$

At equilibrium, 75% $\ce{X2Y4(g)}$ was dissociated and the total pressure is 1 atm. The magnitude of $\Delta_rG^\ominus$ (in kJ mol$^{-1}$) at this temperature is ________. (Nearest Integer)

(Given : R = 8.3 J mol$^{-1}$ K$^{-1}$; ln 10 = 2.3, log 2 = 0.3, log 3 = 0.48, log 5 = 0.69, log 7 = 0.84)

Consider the following reactions in which all the reactants and products are present in gaseous state

$2xy\rightleftharpoons x_2+y_2$, $K_1=2.5\times10^5$

$xy+\frac12z_2\rightleftharpoons xyz$, $K_2=5\times10^{-3}$

The value of $K_3$ for the equilibrium $\frac12x_2+\frac12y_2+\frac12z_2\rightleftharpoons xyz$ is :

Solid carbon, CaO and $\ce{CaCO3}$ are mixed and allowed to attain equilibrium at T K.

$\ce{CaCO3(s) <=> CaO(s) + CO2(g)}$, $K_{p_1}=0.08$ atm

$\ce{C(s) + CO2(g) <=> 2CO(g)}$, $K_{p_2}=2$ atm

The partial pressure of CO is ________ $\times10^{-1}$ atm

The plot of $\log k_f$ versus $1/T$ for a reversible reaction $\ce{A(g) <=> P(g)}$ is shown.

Pre-exponential factors for the forward and backward reactions are $10^{15}\,\mathrm{s^{-1}}$ and $10^{11}\,\mathrm{s^{-1}}$, respectively. If the value of $\log K$ for the reaction at 500 K is 6, the value of $|\log k_b|$ at 250 K is _____.

[$K$ = equilibrium constant of the reaction; $k_f$ = rate constant of forward reaction; $k_b$ = rate constant of backward reaction]

In a one-litre flask, 6 moles of A undergoes the reaction $\ce{A(g) <=> P(g)}$. The progress of product formation at two temperatures (in Kelvin), $T_1$ and $T_2$, is shown in the figure:

If $T_1 = 2T_2$ and $\left(\Delta G_2^\ominus - \Delta G_1^\ominus\right) = RT_2\ln x$, then the value of x is _____.

[$\Delta G_1^\ominus$ and $\Delta G_2^\ominus$ are standard Gibb's free energy change for the reaction at temperatures $T_1$ and $T_2$, respectively.]

For a reaction at equilibrium
$$\mathrm{A(g)\rightleftharpoons B(g)+\tfrac12C(g)}$$
the relation between dissociation constant ($K$), degree of dissociation ($\alpha$) and equilibrium pressure ($p$) is given by :

$$\mathrm{2O_3(g)\rightleftharpoons3O_2(g)}$$
At 300 K, ozone is fifty percent dissociated. The standard free energy change at this temperature and 1 atm pressure is $(-)$ ______ J mol$^{-1}$. (Nearest integer)

[Given : $\ln1.35=0.3$ and $R=8.3\ \mathrm{J\,K^{-1}mol^{-1}}$]

$\mathrm{PCl_5}$ dissociates as
$$\mathrm{PCl_5(g)\rightleftharpoons PCl_3(g)+Cl_2(g)}$$
5 moles of $\mathrm{PCl_5}$ are placed in a 200 litre vessel which contains 2 moles of $\mathrm{N_2}$ and is maintained at 600 K. The equilibrium pressure is 2.46 atm. The equilibrium constant $K_p$ for the dissociation of $\mathrm{PCl_5}$ is ______ $\times10^{-3}$. (nearest integer)

(Given: $R=0.082\ \mathrm{L\,atm\,K^{-1}mol^{-1}}$; Assume ideal gas behaviour)

The standard free energy change ($\Delta G^\circ$) for 50% dissociation of $\mathrm{N_2O_4}$ into $\mathrm{NO_2}$ at 27°C and 1 atm pressure is $-x$ J mol$^{-1}$. The value of $x$ is ______. (Nearest Integer)

[Given : $R=8.31\ \mathrm{J\,K^{-1}mol^{-1}}$, $\log1.33=0.1239$, $\ln10=2.3$]

40% of HI undergoes decomposition to $\mathrm{H_2}$ and $\mathrm{I_2}$ at 300 K. $\Delta G^\ominus$ for this decompostion reaction at one atmopsphere pressure is ______ J mol$^{-1}$. [nearest integer]

(Use $R=8.31$ J K$^{-1}$ mol$^{-1}$; $\log2=0.3010$, $\ln10=2.3$, $\log3=0.477$)

$$\mathrm{2NOCl(g)\rightleftharpoons2NO(g)+Cl_2(g)}$$
In an experiment, 2.0 moles of NOCl was placed in a one-litre flask and the concentration of NO after equilibrium established, was found to be 0.4 mol/L. The equilibrium constant at 30°C is ______ $\times10^{-4}$.

4.0 moles of argon and 5.0 moles of $\mathrm{PCl_5}$ are introduced into an evacuated flask of 100 litre capacity at 610 K. The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be 6.0 atm. The $K_p$ for the reaction is

[Given: R = 0.082 L atm K$^{-1}$ mol$^{-1}$]

The equilibrium constant for the reversible reaction $\mathrm{2A(g)\rightleftharpoons2B(g)+C(g)}$ is $K_1$ and for the reaction $\mathrm{\frac32A(g)\rightleftharpoons\frac32B(g)+\frac34C(g)}$ is $K_2$. $K_1$ and $K_2$ are related as :