Chemical Equilibrium

$K_{a_1}$, $K_{a_2}$ and $K_{a_3}$ are the respective ionization constants for the following reactions (a), (b), and (c).

(a) $\mathrm{H_2C_2O_4\rightleftharpoons H^++HC_2O_4^-}$

(b) $\mathrm{HC_2O_4^-\rightleftharpoons H^++C_2O_4^{2-}}$

(c) $\mathrm{H_2C_2O_4\rightleftharpoons2H^++C_2O_4^{2-}}$

The relationship between $K_{a_1}$, $K_{a_2}$ and $K_{a_3}$ is given as

At 298 K, the equilibrium constant is $2\times10^{15}$ for the reaction :

$$\mathrm{Cu(s)+2Ag^+(aq)\rightleftharpoons Cu^{2+}(aq)+2Ag(s)}$$

The equilibrium constant for the reaction

$$\mathrm{\tfrac12Cu^{2+}(aq)+Ag(s)\rightleftharpoons\tfrac12Cu(s)+Ag^+(aq)}$$

is $x\times10^{-8}$. The value of $x$ is ______. (Nearest Integer)

At 600K, 2 mol of NO are mixed with 1 mol of $\mathrm{O_2}$.

$$\mathrm{2NO(g)+O_2(g)\rightleftharpoons2NO_2(g)}$$

The reaction occurring as above comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows that 0.6 mol of oxygen are present at equilibrium. The equilibrium constant for the reaction is ______. (Nearest integer)

The value of standard enthalpy, $\Delta H^\ominus$ (in kJ mol$^{-1}$) for the given reaction is ____.

The value of $\Delta S^\ominus$ (in J K$^{-1}$ mol$^{-1}$) for the given reaction, at 1000 K is ____.

For the reaction A$_{(g)}$ → B$_{(g)}$, the value of the equilibrium constant at 300 K and 1 atm is equal to 100.0. The value of Δ$_r$G for the reaction at 300 K and 1 atm in J mol$^{-1}$ is −xR, where x is _______. (Rounded off to the nearest integer)

[R = 8.31 J mol$^{-1}$K$^{-1}$ and ln 10 = 2.3]

At 1990 K and 1 atm pressure, there are equal number of Cl$_2$ molecules and Cl atoms in the reaction mixture. The value of K$_P$ for the reaction $\mathrm{Cl_{2(g)}\rightleftharpoons2Cl_{(g)}}$ under the above conditions is $x\times10^{-1}$. The value of $x$ is _______. (Rounded off to the nearest integer)

Consider the reaction $\ce{A <=> B}$ at 1000 K. At time $t'$, the temperature of the system was increased to 2000 K and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of A was maintained at 1 bar. Given below is the plot of the partial pressure of B with time. What is the ratio of the standard Gibbs energy of the reaction at 1000 K to that at 2000 K?

For the following reaction, the equilibrium constant $K_c$ at 298 K is $1.6\times10^{17}$.

$$\ce{Fe^{2+}(aq) + S^{2-}(aq) <=> FeS(s)}$$

When equal volumes of 0.06 M $\ce{Fe^{2+}}(aq)$ and 0.2 M $\ce{S^{2-}}(aq)$ solutions are mixed, the equilibrium concentration of $\ce{Fe^{2+}}(aq)$ is found to be $Y\times10^{-17}$ M. The value of $Y$ is ______

For a reaction, A ⇌ P, the plots of [A] and [P] with time at temperatures $T_1$ and $T_2$ are given below.

If $T_2 > T_1$, the correct statement(s) is (are)

(Assume $\Delta H^\ominus$ and $\Delta S^\ominus$ are independent of temperature and ratio of $\ln K$ at $T_1$ to $\ln K$ at $T_2$ is greater than $T_2/T_1$. Here $H$, $S$, $G$ and $K$ are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)

The surface of copper gets tarnished by the formation of copper oxide. $\mathrm{N_2}$ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the $\mathrm{N_2}$ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below:

$$\mathrm{2Cu(s) + H_2O(g) \rightarrow Cu_2O(s) + H_2(g)}$$

$p_{\mathrm{H_2}}$ is the minimum partial pressure of $\mathrm{H_2}$ (in bar) needed to prevent the oxidation at 1250 K. The value of $\ln(p_{\mathrm{H_2}})$ is ____.

(Given: total pressure = 1 bar, $R$ (universal gas constant) = 8 J K$^{-1}$ mol$^{-1}$, ln(10) = 2.3. Cu(s) and Cu$_2$O(s) are mutually immiscible.

At 1250 K: $\mathrm{2Cu(s) + \tfrac{1}{2}O_2(g) \rightarrow Cu_2O(s)}$; $\Delta G^\ominus = -78{,}000$ J mol$^{-1}$

$\mathrm{H_2(g) + \tfrac{1}{2}O_2(g) \rightarrow H_2O(g)}$; $\Delta G^\ominus = -1{,}78{,}000$ J mol$^{-1}$; $G$ is the Gibbs energy)

Consider the following reversible reaction,

$$\mathrm{A(g) + B(g) \rightleftharpoons AB(g)}.$$

The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$ (in J mol$^{-1}$). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of $\Delta G^\ominus$ (in J mol$^{-1}$) for the reaction at 300 K is ____.

(Given; ln(2) = 0.7, $RT$ = 2500 J mol$^{-1}$ at 300 K and $G$ is the Gibbs energy)

The standard state Gibbs free energies of formation of C(graphite) and C(diamond) at T = 298 K are

$$\Delta_f G^o[\mathrm{C(graphite)}] = 0\ \mathrm{kJ\,mol^{-1}}$$
$$\Delta_f G^o[\mathrm{C(diamond)}] = 2.9\ \mathrm{kJ\,mol^{-1}}.$$

The standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite [C(graphite)] to diamond [C(diamond)] reduces its volume by $2 \times 10^{-6}\ \mathrm{m^3\,mol^{-1}}$. If C(graphite) is converted to C(diamond) isothermally at T = 298 K, the pressure at which C(graphite) is in equilibrium with C(diamond), is

[Useful information: 1 J = 1 kg m$^2$ s$^{-2}$; 1 Pa = 1 kg m$^{-1}$ s$^{-2}$; 1 bar = $10^5$ Pa]

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant $K$ in terms of change in entropy is described by

The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal :
$$\ce{Fe2O3(s) + 3CO(g) <=> 2Fe(l) + 3CO2(g)}$$
Using the Le Chatelier's principle, predict which one of the following will not disturb the equilibrium ?

The equilibrium constant $K_P$ for this reaction at 298 K, in terms of $\beta_{equilibrium}$, is

The INCORRECT statement among the following, for this reaction, is

The equilibrium constant at 298 K for a reaction $\ce{A + B <=> C + D}$ is 100. If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in mol L$^{-1}$) will be :

For the reaction, $\ce{A(g) + B(g) -> C(g) + D(g)}$, ΔH° and ΔS° are, respectively, −29.8 kJ mol$^{-1}$ and −0.100 kJ K$^{-1}$ mol$^{-1}$ at 298 K. The equilibrium constant for the reaction at 298 K is :

A solid XY kept in an evacuated sealed container undergoes decomposition to form a mixture of gases X and Y at temperature T. The equilibrium pressure is 10 bar in this vessel. $K_p$ for this reaction is :