A mixture of 2.0 mol of H₂(g) and 1.0 mol of O₂(g) is placed in a sealed evacuated container made of a perfect insulating material at 25 °C. The mixture is ignited with a spark and reacts to form liquid water. Determine the temperature of the water.

Verified step by step guidance

1. Write the balanced chemical equation for the reaction between hydrogen gas (H2) and oxygen gas (O2) to form liquid water (H2O). The balanced equation is: 2 H2(g) + O2(g) → 2 H2O(l).
2. Calculate the limiting reactant. Since the reaction consumes hydrogen and oxygen in a 2:1 ratio, compare the moles of H2 and O2 provided to determine which is the limiting reactant.
3. Use stoichiometry to determine the amount of water produced based on the limiting reactant. This involves using the mole ratio from the balanced equation.
4. Calculate the heat released during the reaction. Use the enthalpy change of the reaction (ΔH) for the formation of water from hydrogen and oxygen gases. The ΔH for the formation of liquid water from H2(g) and O2(g) is typically found in tables of standard enthalpies of formation.
5. Apply the concept of conservation of energy (the first law of thermodynamics) to determine the final temperature of the water. Since the container is insulated, all the heat released from the reaction will be used to increase the temperature of the water formed. Use the specific heat capacity of water and the mass of water formed to calculate the final temperature.

Key Concepts

Stoichiometry of Combustion Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions. In this case, the combustion of hydrogen (H2) with oxygen (O2) follows the balanced equation 2H2 + O2 → 2H2O. Understanding the mole ratios is essential to determine how much water is produced and the energy released during the reaction.

Thermodynamics and Heat Transfer

Thermodynamics studies the relationships between heat, work, and energy. In this scenario, the reaction is exothermic, meaning it releases heat. The temperature of the water formed will depend on the amount of heat released and the specific heat capacity of water, which dictates how much the temperature will rise based on the energy transferred.

Ideal Gas Law and Reaction Conditions

The Ideal Gas Law (PV=nRT) relates the pressure, volume, temperature, and number of moles of a gas. Although the gases are ignited in a sealed container, understanding the initial conditions (25 °C) and the behavior of gases during the reaction is crucial for predicting the final state of the products, including the temperature of the water formed.