Question

For the reaction \(A(g)+3 B(g) \rightleftharpoons 2 C(g)\) at \(27^{\circ} \mathrm{C}, 2\) moles of \(A, 4\) moles of \(B\) and 6 moles of \(C\) are present in 2 litre vessel. If \(K_{c}\) for the reaction is \(1.2\), the reaction will proceed in : (a) forward direction (b) backward direction (c) neither direction (d) none of these

Short answer

The reaction will proceed in the forward direction.

Step-by-step solution

Write the Expression for the Equilibrium Constant

For the given reaction, the equilibrium constant expression in terms of concentrations (Kc) is given by the formula: \[K_c = \frac{[C]^2}{[A][B]^3}\], where [X] denotes the concentration of substance X in moles per liter (M).

Calculate the Initial Concentrations

Calculate the initial concentrations of A, B, and C by dividing the given moles by the volume of the vessel. For A, the concentration is \(\frac{2 \text{ moles}}{2 \text{ liters}} = 1M\), for B, it is \(\frac{4 \text{ moles}}{2 \text{ liters}} = 2M\), and for C, it is \(\frac{6 \text{ moles}}{2 \text{ liters}} = 3M\).

Plug the Concentrations into the Equilibrium Expression

Substitute the initial concentrations into the Kc expression: \[K_c = \frac{[3M]^2}{[1M][2M]^3} = \frac{9}{8} = 1.125\].

Compare Calculated Kc with Given Kc

Compare the calculated Kc value with the given Kc of the reaction. If the calculated Kc is less than the given Kc, the reaction will proceed in the forward direction to reach equilibrium. If the calculated Kc is more than the given Kc, the reaction will proceed in the backward direction.

Determine the Direction of the Reaction

Since the calculated Kc (1.125) is less than the given Kc (1.2), the reaction will proceed in the forward direction to achieve the given Kc at equilibrium.

Key concepts

Equilibrium Constant Expression

Understanding the equilibrium constant expression is crucial for predicting the behavior of reactions at equilibrium. It's a way to quantify the relative concentration of reactants and products in a reaction that has reached equilibrium. In the given exercise, the equilibrium constant (\( K_c \)) for the reaction between gases A, B, and C is defined by the formula:
\begin{align*}K_c = \frac{\left[ C \right]^2}{\left[A\right]\left[B\right]^3}\end{align*}
The square brackets represent concentrations in moles per liter (M). This expression shows that the concentration of the product C, raised to the power of 2, affects the equilibrium substantially more than the concentration of A and B. The exponents correspond to the coefficients in the balanced chemical equation.
For students to visualize how this concept applies to the exercise, imagine equilibrium as a see-saw balanced between reactants (A and B) and products (C). The equilibrium constant expression gives us a formula to ensure both sides of the see-saw are balanced. When you input the concentrations into the expression, you can find out which direction the see-saw will tilt to reach balance again.

Reaction Quotient

The reaction quotient (\( Q \)) is a pivotal concept in understanding how a reaction will proceed before it reaches equilibrium. Similar in form to the equilibrium constant expression, it uses the initial concentrations instead of those at equilibrium. Here's the key: if the reaction quotient doesn't match the equilibrium constant, the reaction will shift to restore balance.
In this exercise, using the same formula, we calculated the reaction quotient with the initial concentrations of A, B, and C. The resulting value was 1.125. Comparing this to the equilibrium constant (\( K_c = 1.2 \)), it's apparent that the reaction is not yet at equilibrium. Since the reaction quotient is lower than the equilibrium constant, the system will react by moving in the forward direction, increasing the concentration of C, until the reaction quotient equals the equilibrium constant.
Remember, the actual value of the reaction quotient tells us whether the forward or backward reaction is favored at any given moment. Think of it as a snapshot of where the reaction stands and an indicator of where it's headed next!

Le Chatelier's Principle

Le Chatelier's principle is an elegant rule of thumb that predicts how a system at equilibrium reacts to changes in conditions. It states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. This principle gives us a way to control chemical reactions and refine product yields.
For instance, if more of reactant A were added to the system in our exercise, the principle suggests the reaction would shift to produce more of product C to re-establish equilibrium. Conversely, increasing the concentration of product C would drive the reaction to favor the reactants.
In practical terms, Le Chatelier's principle is akin to adjusting the pressure on one side of a balloon to maintain its shape. If you squeeze one side (change conditions), the air pushes out (reaction shifts) to try to retain its original form (equilibrium). This principle is indispensable for predicting how changes in temperature, pressure, or concentration affect the direction of a reaction.