One mole of H2O and one mole of CO are taken in 10 L vessel and heated to 725 K. At equilibrium 40% of water (by mass) reacts with CO according to the equation,

To analyze the reaction between water (H2O) and carbon monoxide (CO) in a 10 L vessel at 725 K, we first need to establish the reaction taking place. The balanced equation for the reaction is:

Reaction Overview

2 H2O(g) + CO(g) ⇌ H2(g) + CO2(g)

In this scenario, we start with one mole of H2O and one mole of CO. Given that 40% of the water by mass reacts, we can calculate how much water is consumed and how this affects the equilibrium concentrations of all species involved.

Calculating Initial Conditions

• Mass of one mole of H2O = 18 g
• Mass of one mole of CO = 28 g
• Initial moles of H2O = 1 mole
• Initial moles of CO = 1 mole

Since 40% of the water reacts, we can find the mass of water that reacts:

• Mass of water reacting = 0.40 × 18 g = 7.2 g
• Moles of water reacting = 7.2 g / 18 g/mol = 0.4 moles

Determining Changes in Moles

According to the stoichiometry of the reaction, for every 2 moles of H2O that react, 1 mole of CO is consumed, producing 1 mole of H2 and 1 mole of CO2. Therefore, if 0.4 moles of H2O react:

• Moles of CO consumed = 0.4 moles H2O × (1 mole CO / 2 moles H2O) = 0.2 moles CO
• Moles of H2 produced = 0.4 moles H2O × (1 mole H2 / 2 moles H2O) = 0.2 moles H2
• Moles of CO2 produced = 0.4 moles H2O × (1 mole CO2 / 2 moles H2O) = 0.2 moles CO2

Final Moles at Equilibrium

Now, we can summarize the moles at equilibrium:

• Remaining moles of H2O = 1 - 0.4 = 0.6 moles
• Remaining moles of CO = 1 - 0.2 = 0.8 moles
• Moles of H2 = 0.2 moles
• Moles of CO2 = 0.2 moles

Calculating Concentrations

To find the concentrations of each species at equilibrium, we use the formula:

Concentration (C) = Moles / Volume (L)

Given the volume is 10 L, we can calculate:

• Concentration of H2O = 0.6 moles / 10 L = 0.06 M
• Concentration of CO = 0.8 moles / 10 L = 0.08 M
• Concentration of H2 = 0.2 moles / 10 L = 0.02 M
• Concentration of CO2 = 0.2 moles / 10 L = 0.02 M

Equilibrium Constant Expression

The equilibrium constant (K) for the reaction can be expressed as:

K = [H2][CO2] / ([H2O]^2[CO])

Substituting the equilibrium concentrations into this expression gives:

• K = (0.02)(0.02) / ((0.06)^2(0.08))

Final Calculation of K

Now, we can calculate K:

• K = 0.0004 / (0.0036 × 0.08)
• K = 0.0004 / 0.000288 = 1.39

This value of K indicates the extent to which the reaction favors the products at the given temperature of 725 K. In summary, by understanding the stoichiometry and applying the principles of equilibrium, we can effectively analyze the behavior of this reaction in a controlled environment.