In the reaction A + 2B ⇌ 2C, if 2 moles of A, 3 moles of B and 2 moles of C are placed in a 2 L flask and
the equilibrium concentration of C is 0.5 mol/L. The equilibrium constant (KC) for the reaction is.....and please tell how you know that the reaction is going forward .. imean how to calculate the reaction quotient ???

To find the equilibrium constant (K_C) for the reaction A + 2B ⇌ 2C, we first need to determine the equilibrium concentrations of all species involved. Given that the equilibrium concentration of C is 0.5 mol/L, we can calculate the moles of C at equilibrium:

Calculating Moles at Equilibrium

Since the volume of the flask is 2 L, the moles of C at equilibrium are:

• Moles of C = Concentration × Volume = 0.5 mol/L × 2 L = 1 mole

Initial Moles

Initially, we have:

• A = 2 moles
• B = 3 moles
• C = 2 moles

Change in Moles

From the balanced equation, for every 2 moles of C produced, 1 mole of A and 2 moles of B are consumed. Since we have 1 mole of C at equilibrium, we can determine the changes:

• Change in C = +1 mole (from 2 to 1)
• Change in A = -0.5 moles (0.5 moles of A consumed)
• Change in B = -1 mole (1 mole of B consumed)

Equilibrium Moles

Now, we can find the equilibrium moles:

• A = 2 - 0.5 = 1.5 moles
• B = 3 - 1 = 2 moles
• C = 1 mole

Equilibrium Concentrations

Next, we calculate the equilibrium concentrations:

• [A] = 1.5 moles / 2 L = 0.75 mol/L
• [B] = 2 moles / 2 L = 1 mol/L
• [C] = 1 mole / 2 L = 0.5 mol/L

Calculating K_C

The equilibrium constant expression for the reaction is:

K_C = \(\frac{[C]^2}{[A][B]^2}\)

Substituting the equilibrium concentrations:

• K_C = \(\frac{(0.5)^2}{(0.75)(1)^2} = \frac{0.25}{0.75} = \frac{1}{3} \approx 0.33\)

Understanding Reaction Direction

To determine if the reaction is moving forward or backward, we calculate the reaction quotient (Q) using the initial concentrations:

Q = \(\frac{[C]^2}{[A][B]^2}\)

Using initial concentrations:

• [A] = 1 mol/L (2 moles in 2 L)
• [B] = 1.5 mol/L (3 moles in 2 L)
• [C] = 1 mol/L (2 moles in 2 L)

Thus, Q = \(\frac{(1)^2}{(1)(1.5)^2} = \frac{1}{2.25} \approx 0.44\)

Comparing Q and K_C

Since Q (0.44) is greater than K_C (0.33), the reaction will shift to the left to reach equilibrium, indicating that it is currently moving backward.

To find the equilibrium constant (K_C) for the reaction A + 2B ⇌ 2C, we first need to determine the equilibrium concentrations of all species involved. Given that the equilibrium concentration of C is 0.5 mol/L, we can calculate the concentrations of A and B at equilibrium.

Step 1: Calculate Initial Concentrations

Initially, we have:

• 2 moles of A in 2 L: [A]_initial = 2 moles / 2 L = 1 mol/L
• 3 moles of B in 2 L: [B]_initial = 3 moles / 2 L = 1.5 mol/L
• 2 moles of C in 2 L: [C]_initial = 2 moles / 2 L = 1 mol/L

Step 2: Change in Concentrations

At equilibrium, the concentration of C is 0.5 mol/L. The change in concentration for C is:

• Change in C: 1 mol/L - 0.5 mol/L = 0.5 mol/L

Since the reaction produces 2 moles of C for every mole of A and 2 moles of B consumed, the changes for A and B will be:

• Change in A: -0.25 mol/L
• Change in B: -0.5 mol/L

Step 3: Equilibrium Concentrations

Now we can find the equilibrium concentrations:

• [A]_equilibrium = 1 mol/L - 0.25 mol/L = 0.75 mol/L
• [B]_equilibrium = 1.5 mol/L - 0.5 mol/L = 1.0 mol/L
• [C]_equilibrium = 0.5 mol/L

Step 4: Calculate K_C

The equilibrium constant expression for the reaction is:

K_C = [C]² / ([A][B]²)

Substituting the equilibrium concentrations:

K_C = (0.5)² / (0.75)(1.0)² = 0.25 / 0.75 = 0.333

Determining the Direction of the Reaction

To find out if the reaction is moving forward or backward, we calculate the reaction quotient (Q) using the initial concentrations:

Q = [C]² / ([A][B]²)

Using initial concentrations:

Q = (1)² / (1)(1.5)² = 1 / 2.25 = 0.444

Comparison of Q and K_C

Since Q (0.444) is less than K_C (0.333), the reaction will proceed forward to reach equilibrium.

To find the equilibrium constant (K_C) for the reaction A + 2B ⇌ 2C, we first need to determine the equilibrium concentrations of all species involved. Given that the equilibrium concentration of C is 0.5 mol/L, we can calculate the moles of C at equilibrium.

Step 1: Calculate Moles of C

In a 2 L flask, the moles of C at equilibrium can be calculated as:

Moles of C = Concentration × Volume = 0.5 mol/L × 2 L = 1 mole

Step 2: Determine Changes in Concentrations

From the balanced equation, we know:

• 2 moles of C are produced for every mole of A consumed.
• 2 moles of C require 2 moles of B.

Since we have 1 mole of C at equilibrium, this means:

• 0.5 moles of A were consumed (since 1 mole of C corresponds to 0.5 moles of A).
• 1 mole of B was consumed (since 2 moles of B are needed for 1 mole of C).

Step 3: Calculate Equilibrium Concentrations

Now, we can find the equilibrium concentrations of A and B:

• Initial moles of A = 2 moles; at equilibrium = 2 - 0.5 = 1.5 moles.
• Initial moles of B = 3 moles; at equilibrium = 3 - 1 = 2 moles.

Now, convert these moles to concentrations:

• [A] = 1.5 moles / 2 L = 0.75 mol/L
• [B] = 2 moles / 2 L = 1 mol/L

Step 4: Calculate K_C

The equilibrium constant expression for the reaction is:

K_C = [C]² / ([A] × [B]²)

Substituting the equilibrium concentrations:

K_C = (0.5)² / (0.75 × (1)²) = 0.25 / 0.75 = 0.333

Understanding Reaction Direction

To determine if the reaction is moving forward or backward, we can calculate the reaction quotient (Q). The reaction quotient is calculated using the initial concentrations:

Q = [C]² / ([A] × [B]²)

Using initial concentrations:

• [A] = 1 mole / 2 L = 0.5 mol/L
• [B] = 1.5 moles / 2 L = 0.75 mol/L
• [C] = 0 moles / 2 L = 0 mol/L

Thus, Q = (0)² / (0.5 × (0.75)²) = 0. This indicates that the reaction will proceed forward to produce more products until equilibrium is reached.

Final Result

The equilibrium constant K_C for the reaction is approximately 0.333, and the reaction is moving forward based on the calculated reaction quotient.

To find the equilibrium constant (K_C) for the reaction A + 2B ⇌ 2C, we first need to determine the equilibrium concentrations of all species involved. Given that the equilibrium concentration of C is 0.5 mol/L, we can calculate the moles of C at equilibrium.

Step 1: Calculate Moles of C

In a 2 L flask, the moles of C at equilibrium are:

Moles of C = Concentration × Volume = 0.5 mol/L × 2 L = 1 mole

Step 2: Determine Changes in Concentration

From the balanced equation, for every 2 moles of C produced, 1 mole of A and 2 moles of B are consumed. Thus, if we have 1 mole of C at equilibrium:

• Change in A = -0.5 moles (since 2 moles of C require 1 mole of A)
• Change in B = -1 mole (since 2 moles of C require 2 moles of B)

Step 3: Initial Moles

Initially, we have:

• A = 2 moles
• B = 3 moles
• C = 2 moles

Step 4: Calculate Equilibrium Moles

At equilibrium, the moles of each substance are:

• A = 2 - 0.5 = 1.5 moles
• B = 3 - 1 = 2 moles
• C = 1 mole (as calculated earlier)

Step 5: Calculate Equilibrium Concentrations

Now, we convert moles to concentrations:

• [A] = 1.5 moles / 2 L = 0.75 mol/L
• [B] = 2 moles / 2 L = 1 mol/L
• [C] = 1 mole / 2 L = 0.5 mol/L

Step 6: Calculate K_C

The equilibrium constant expression for the reaction is:

K_C = [C]² / ([A] × [B]²)

Substituting the equilibrium concentrations:

K_C = (0.5)² / (0.75 × (1)²) = 0.25 / 0.75 = 0.333

Understanding Reaction Direction

To determine if the reaction is moving forward or backward, we calculate the reaction quotient (Q) using initial concentrations:

Q = [C]² / ([A] × [B]²)

Using initial concentrations:

• [A] = 2 moles / 2 L = 1 mol/L
• [B] = 3 moles / 2 L = 1.5 mol/L
• [C] = 2 moles / 2 L = 1 mol/L

Calculating Q:

Q = (1)² / (1 × (1.5)²) = 1 / 2.25 = 0.444

Final Comparison

Since Q (0.444) is less than K_C (0.333), the reaction will proceed forward to reach equilibrium.