Questions: Question 4 (1 point) "Given the Kc of the first reaction below, find the Kc of the second reaction. A(g)+B(g)=AB(g) 3A(g)+3B(g) ⇋ 3AB(g) Kc=9.101 × 10^3 Kc=?"

Transcript text: Question 4 (1 point) "Given the Kc of the first reaction below, find the Kc of the second reaction. \[ \begin{array}{l} A(g)+B(g)=A B(g) \\ 3 A(g)+3 B(g) \rightleftharpoons 3 A B(g) \end{array} \] \[ \begin{array}{c} \mathrm{Kc}=9.101 \times 10^{3} \\ K c=? " \end{array} \]

Solution

Solution Steps

Step 1: Understand the Relationship Between the Reactions

The first reaction is: \[ A(g) + B(g) \rightleftharpoons AB(g) \]

The second reaction is: \[ 3A(g) + 3B(g) \rightleftharpoons 3AB(g) \]

The second reaction is simply the first reaction multiplied by 3.

Step 2: Determine the Relationship Between Equilibrium Constants

When a chemical equation is multiplied by a factor \( n \), the equilibrium constant for the new reaction is the original equilibrium constant raised to the power of \( n \).

For the given reactions, the second reaction is the first reaction multiplied by 3. Therefore, the equilibrium constant for the second reaction, \( K_c \), is given by: \[ K_c = (K_c')^3 \]

where \( K_c' = 9.101 \times 10^3 \).

Step 3: Calculate the New Equilibrium Constant

Substitute the given \( K_c' \) into the equation: \[ K_c = (9.101 \times 10^3)^3 \]

Calculate: \[ K_c = (9.101 \times 10^3)^3 = 9.101^3 \times (10^3)^3 \]

\[ K_c = 753.6 \times 10^9 \]

\[ K_c = 7.536 \times 10^{11} \]