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Read the following paragraph and answer...

Read the following paragraph and answer the questions given below ,
Stable equilibrium is of various type . Mechanical equilibrium is achieved when all particles are at rest and total potential energy of the system is minimum . At any stage where particles are at rest but the system is not at stabel equilibrium as it can reduce its potential energy by reverting to another position, is called metastable equilibrium . Thermal equilibrium is result from the absence of temperature gradients in the system. chemical equilibrium is obtained when no further reaction occurs between reacting substances, i.e forward and reverse rates of reaction are equal. when steam with solid iron at high temperature `Fe_3O_4(s)` and hydrogen gas are produced . But the reaction never goes to completion. this is because as the products are formed the reaction proceeds in reverse direction and when rate of reverse reaction is equal to rate of forward reaction , the concentration of reactants and products become constant and equilibrium is reached.
The correct expression for equilibrium constant of the reaction, taken as an example of chemical equilibrium in the above passage is

A

a) `((pH_2)^2)/((pH_2O)^2)`

B

b) `((pH_2)^4)/((pH_2O)^4)`

C

c) `([H_2]^4 [Fe_3O_4]) / ([H_2O]^4[Fe]^3)`

D

d) `([Fe_3O_4])/([Fe])`

Text Solution

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The correct Answer is:
To find the correct expression for the equilibrium constant of the reaction described in the passage, we will follow these steps: ### Step 1: Identify the Reaction The passage mentions a reaction involving solid iron (Fe), steam (H2O), and the products are Fe3O4 (solid) and hydrogen gas (H2). The reaction can be written as: \[ 3 \text{Fe (s)} + 4 \text{H}_2\text{O (g)} \rightleftharpoons \text{Fe}_3\text{O}_4 \text{ (s)} + 4 \text{H}_2 \text{ (g)} \] ### Step 2: Balance the Chemical Equation The balanced equation is: \[ 3 \text{Fe (s)} + 4 \text{H}_2\text{O (g)} \rightleftharpoons \text{Fe}_3\text{O}_4 \text{ (s)} + 4 \text{H}_2 \text{ (g)} \] ### Step 3: Write the Expression for the Equilibrium Constant (K) The equilibrium constant expression (K) is based on the concentrations of the products and reactants. For a general reaction: \[ aA + bB \rightleftharpoons cC + dD \] The equilibrium constant (K) is given by: \[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \] ### Step 4: Apply the Expression to Our Reaction In our case: - Products: Fe3O4 (s) and H2 (g) - Reactants: Fe (s) and H2O (g) Since solids do not appear in the equilibrium expression, we only include the gaseous components: \[ K = \frac{[\text{H}_2]^4}{[\text{H}_2\text{O}]^4} \] ### Step 5: Finalize the Expression Thus, the correct expression for the equilibrium constant for the reaction is: \[ K = \frac{[\text{H}_2]^4}{[\text{H}_2\text{O}]^4} \]
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