The equilibrium constant for the reaction `CO(g)+H_(2)O(g)hArrCO_(2)(g)+H_(2)(g) is 5` how many moles of `CO_(2)` must be added to 1 litre container alrady containing 3 moles each of CO and `H_(2)O` to make 2 M equilibrium conentration of CO?

Options

A. 15
B. 19
C. 5
D. 20

Answer

To solve the problem, we will follow these steps:

### Step 1: Write the balanced chemical equation
The reaction given is:
\[ \text{CO(g)} + \text{H}_2\text{O(g)} \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g) \]

### Step 2: Identify initial conditions
We are given that initially, there are:
- 3 moles of CO
- 3 moles of H2O
- Let \( x \) be the number of moles of CO2 added.

### Step 3: Set up the equilibrium concentrations
At equilibrium, we want the concentration of CO to be 2 M in a 1 L container. Therefore, the number of moles of CO at equilibrium will be:
\[ \text{Moles of CO at equilibrium} = 2 \text{ moles} \]

Since we started with 3 moles of CO, the change in moles of CO will be:
\[ \text{Change in moles of CO} = 3 - 2 = 1 \text{ mole} \]

### Step 4: Determine changes in other species
From the stoichiometry of the reaction:
- 1 mole of CO is consumed, which means 1 mole of CO2 is produced.
- Therefore, the moles of CO2 at equilibrium will be:
\[ \text{Moles of CO}_2 = x + 1 \]

### Step 5: Write the expression for the equilibrium constant (Kc)
The equilibrium constant \( K_c \) is given by:
\[ K_c = \frac{[\text{CO}_2][\text{H}_2]}{[\text{CO}][\text{H}_2\text{O}]} \]

Substituting the equilibrium concentrations:
- Concentration of CO at equilibrium = 2 M
- Concentration of H2O at equilibrium = \( 3 - 1 = 2 \) M (since 1 mole of H2O is consumed)
- Concentration of CO2 at equilibrium = \( x + 1 \) M
- Concentration of H2 at equilibrium = 1 M (since 1 mole of H2 is produced)

Thus, we have:
\[ K_c = \frac{(x + 1)(1)}{(2)(2)} = 5 \]

### Step 6: Solve for x
From the equation:
\[ \frac{x + 1}{4} = 5 \]

Multiplying both sides by 4:
\[ x + 1 = 20 \]

Subtracting 1 from both sides:
\[ x = 19 \]

### Conclusion
The number of moles of CO2 that must be added is **19 moles**.

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