How Many Grams of Oxygen Are Required to Completely React with Hydrogen Gas?
Hydrogen gas (H2) is a versatile and crucial molecule in many industrial and scientific applications. Understanding how much oxygen (O2) is required to completely react with a given amount of hydrogen gas is essential in chemistry, especially when considering the balances and efficiency of these reactions. In this article, we will break down the process of calculating how many grams of oxygen are required to react with 1.6 grams of hydrogen gas, using the principles of stoichiometry and thermodynamics.
Stoichiometric Calculation: The Balanced Equation
The first step in determining the amount of oxygen required to react with hydrogen is to write the balanced chemical equation for the combustion reaction. The combustion of hydrogen is a redox reaction, where hydrogen gas reacts with oxygen gas to produce water (H2O). The balanced chemical equation is:
Combustion Reaction:
[ 2H_2 O_2 rightarrow 2H_2O ]
By examining the equation, we can see that 2 moles of hydrogen gas (H2) react with 1 mole of oxygen gas (O2) to produce 2 moles of water (H2O).
Quantifying the Reaction: Grams to Moles
To determine the amount of oxygen required, we must first convert the mass of hydrogen gas (H2) to the number of moles. The molar mass of hydrogen gas (H2) is approximately 2 g/mol. Therefore, 1.6 grams of hydrogen gas is calculated as follows:
[ text{Moles of } H_2 frac{1.6 text{ g}}{2 text{ g/mol}} 0.8 text{ moles} ]
Since the molar ratio of H2 to O2 in the balanced equation is 2:1, 0.8 moles of hydrogen gas will require 0.4 moles of oxygen gas.
To find the mass of oxygen required, we use the molar mass of O2, which is approximately 32 g/mol:
[ text{Mass of } O_2 0.4 text{ moles} times 32 text{ g/mol} 12.8 text{ g} ]
Thermodynamics of the Reaction
Once we have determined the amount of oxygen required, we can explore the thermodynamics of the reaction. The change in Gibbs free energy (ΔG) and the change in enthalpy (ΔH) are important indicators of the spontaneity and energy release of the reaction. For the combustion of hydrogen gas at 3200C:
Change in Free Energy (ΔG):
[ Delta G_{3200C} -40.7 text{ kJ} ] (negative, indicating a spontaneous reaction)
Change in Enthalpy (ΔH):
[ Delta H_{3200C} -201.2 text{ kJ} ] (negative, indicating an exothermic reaction)
These thermodynamic values show that the reaction is both spontaneous and releases energy, making it a highly desirable process for energy production.
Product Formation and Volume Calculation
Finally, we can calculate the amount of water (H2O) produced and the volume at standard conditions (assuming 1 mole of gas occupies 22.4 liters at standard temperature and pressure, STP). According to the balanced equation, 0.8 moles of hydrogen gas produce 0.8 moles of water:
[ text{Mass of } H_2O 0.8 text{ moles} times 18 text{ g/mol} 14.4 text{ g} ]
The volume of 14.4 grams of water at STP can be calculated as:
[ text{Volume of } H_2O 0.8 text{ moles} times 22.4 text{ L/mol} 17.92 text{ L} approx 17.93 text{ L} ]
Conclusion: Understanding the Reaction Stoichiometry and Thermodynamics
In conclusion, 1.6 grams of hydrogen gas requires 12.8 grams of oxygen gas to undergo complete combustion at 3200C, producing 14.4 grams of water and releasing 201.2 kJ of heat. Understanding these principles is crucial for optimizing processes in chemistry and related fields, such as in fuel cells and energy production. By grasping the thermodynamics and stoichiometry, one can better predict and control the behavior of such reactions in real-world applications.