In a closed vessel of 15 litres, 5.6 litres of water gas at STP (containing equimolar amount of both the constituent gases) is ignited with 5.6 L of O₂ at STP. What will be the (approximate) final pressure of the vessel at 300 K?

To determine the final pressure in a closed vessel after igniting water gas with oxygen, we need to analyze the reaction and apply the ideal gas law. Let's break this down step by step.

Understanding the Reaction

Water gas is a mixture of hydrogen (H₂) and carbon monoxide (CO) in equimolar amounts. When it is ignited with oxygen (O₂), it undergoes combustion to produce water (H₂O) and carbon dioxide (CO₂). The balanced chemical equation for this reaction is:

• 2 H₂ + 2 O₂ → 2 H₂O + 2 CO₂

In this case, we have 5.6 liters of water gas, which means we have 2.8 liters of H₂ and 2.8 liters of CO. We also have 5.6 liters of O₂ available for the reaction.

Calculating Moles of Reactants

At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.4 liters. Therefore, we can calculate the number of moles of each gas:

• For water gas (5.6 L):
  Moles of H₂ = Moles of CO = 5.6 L / 22.4 L/mol = 0.25 moles each.
• For O₂ (5.6 L):
  Moles of O₂ = 5.6 L / 22.4 L/mol = 0.25 moles.

Identifying Limiting Reactants

From the balanced equation, we see that 2 moles of H₂ react with 2 moles of O₂. This means that 1 mole of H₂ reacts with 1 mole of O₂. Since we have equal moles of H₂ and O₂ (0.25 moles each), both will completely react with each other.

Products of the Reaction

After the reaction, the products formed are water (H₂O) and carbon dioxide (CO₂). Since water is in liquid form at room temperature, it will not contribute to the gas pressure in the vessel. Therefore, we only need to consider the carbon dioxide produced.

According to the stoichiometry of the reaction, for every 2 moles of H₂ and 2 moles of O₂, we produce 2 moles of CO₂. Thus, from 0.25 moles of H₂ and O₂, we will produce:

• 0.25 moles of CO₂.

Calculating Final Pressure

Now, we can use the ideal gas law to find the final pressure in the vessel. The ideal gas law is given by:

P = nRT/V

Where:

• P = pressure (in atm)
• n = number of moles of gas (0.25 moles of CO₂)
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature in Kelvin (300 K)
• V = volume of the vessel (15 L)

Substituting the values into the equation:

P = (0.25 moles) × (0.0821 L·atm/(K·mol)) × (300 K) / (15 L)

P = (6.1575) / (15) = 0.4105 atm

Final Thoughts

Therefore, the approximate final pressure of the vessel at 300 K after the reaction is about 0.41 atm. This calculation assumes ideal behavior of gases and that all water produced remains in liquid form, which is a reasonable approximation under these conditions.