Question

At a certain temperature, 0.338 mol CH₄ and 0.831 mol H₂O are placed in a 3.50 L container. CH₄(g) + 2H₂O(g) → CO₂(g) + 4H₂(g) At equilibrium, 6.51 g CO₂ is present. Calculate c

A. 0.025 M
B. 0.75 M
C. 0.15 M
D. 1.5 M

Answer 1

To assess if the given mixture is at equilibrium, the reaction quotient (Q) is compared to the equilibrium constant (K). With Q calculated at 900 and K given as 2.4 × 10⁴, Q < K, indicating the reaction will proceed to the right to produce more CO and H₂.

Step-by-step explanation:

Equilibrium Calculation

To determine if the reaction is at equilibrium, we must calculate the reaction quotient Q and compare it to the equilibrium constant K given for the reaction at 900 K:

CH4(g) + H2O(g) → CO(g) + 3H2(g)

The equilibrium constant K is 2.4 × 104 at 900 K.

The reaction quotient Q is calculated using the initial concentrations (remember to convert moles to molarity by dividing by the volume of the reactor, in this case, 2.0 L):

1. 
   
3. Calculate the initial concentrations of each species:
   
   • 
     
   • [CH4] = 1.2 × 10-2 mol / 2.0 L = 6.0 × 10-3 M
   • 
     
   • [H2O] = 8.0 × 10-3 mol / 2.0 L = 4.0 × 10-3 M
   • 
     
   • [CO] = 1.6 × 10-2 mol / 2.0 L = 8.0 × 10-3 M
   • 
     
   • [H2] = 6.0 × 10-2 mol / 2.0 L = 3.0 × 10-2 M
   • 
     
   
   
4. 
   
6. Calculate Q using the expression Q = [CO][H2]3 / [CH4][H2O]:
   
   • 
     
   • Q = (8.0 × 10-3)(3.0 × 10-2)3 / (6.0 × 10-3)(4.0 × 10-3) = 900
   • 
     
   
   
7. 
   
9. Compare Q to K to determine the direction the reaction will proceed to reach equilibrium.

Since Q (900) is less than K (2.4 × 104), the reaction will proceed to the right (towards CO and H2 formation) until equilibrium is established.