This is because during the reaction CO , H2 and H2O which were initially present as 1 mole will get consumed and the remaining concentration becomes less that 1 mole at equilibrium.

Introduction:
In this scenario, we have a 20L vessel initially containing 1 mole each of carbon monoxide (CO), water (H2O), and carbon dioxide (CO2). The reaction that occurs is:

CO + H2O ⇄ CO2 + H2

We need to determine whether the amount of CO, H2O, and H2 present at equilibrium is less than 1 mole.

Explanation:
To solve this problem, we can use the concept of the equilibrium constant (Kc). The equilibrium constant is a ratio of the concentrations of the products and reactants at equilibrium. In this case, the equilibrium constant expression is:

Kc = [H2] / [CO][H2O]

If the equilibrium constant (Kc) is less than 1, it means that the concentration of the products is lower than the concentration of the reactants at equilibrium. Conversely, if Kc is greater than 1, it means that the concentration of the products is higher than the concentration of the reactants at equilibrium.

Calculating the Equilibrium Constant:
To calculate the equilibrium constant, we need the concentrations of H2 and the reactants CO and H2O at equilibrium. Let's assume that at equilibrium, x moles of CO react to form x moles of CO2 and x moles of H2. Therefore, the concentrations at equilibrium are:

[CO] = (1 - x) moles / 20 L
[H2O] = (1 - x) moles / 20 L
[CO2] = x moles / 20 L
[H2] = x moles / 20 L

Substituting these values into the equilibrium constant expression, we get:

Kc = [H2] / [CO][H2O]
= (x / 20) / [(1 - x) / 20 * (1 - x) / 20]
= x / (1 - x)^2

Determining the Value of x:
To determine the value of x, we need to solve the equation for the equilibrium constant. Since we have equal initial moles of CO, H2O, and CO2, we can assume that the value of x is the same for all three species. Therefore, we can rewrite the equation as:

Kc = x / (1 - x)^2

Simplifying further, we have:

Kc(1 - x)^2 = x

Expanding and rearranging, we get:

Kc - 2Kcx + Kcx^2 = x

Rearranging again, we have:

Kcx^2 + (2Kc - 1)x - Kc = 0

This is a quadratic equation, and we can solve it using the quadratic formula. The value of x will depend on the specific value of the equilibrium constant, Kc.

Conclusion:
To determine whether the amount of CO, H2O, and H2 at equilibrium is less than 1 mole, we need to solve the quadratic equation derived from the equilibrium constant expression. Without a specific value for Kc, we cannot determine the exact amount of CO, H2O, and H2 at equilibrium. However, by solving the equation, we can find the value of x, which represents the mo