Problem 2 - Aircraft Propulsion

Question

Write the chemical reaction for the combustion of hydrogen, \(\mathrm{H}_{2}\), and air then calculate the stoichiometric fuelto-air ratio \(f_{\text {stoich }}\).

Step-by-Step Solution

Answer

The combustion reaction for hydrogen is \(2H_{2} + O_{2} \rightarrow 2H_{2}O\), and the stoichiometric fuel-to-air ratio is 2.

Step 1: Combustion Reaction of Hydrogen

In the combustion of hydrogen, hydrogen gas (\(H_{2}\)) reacts with oxygen (\(O_{2}\)) in the air to create water (\(H_{2}O\)). Since the reaction needs to be balanced, it must have the same number of each type of atom on both sides. So, a balanced chemical equation is: \(2H_{2} + O_{2} \rightarrow 2H_{2}O\).

Step 2: Deduces Fuels and Airs in Chemical Reaction

From the balanced chemical reaction, it can be seen that two moles of hydrogen are needed for each mole of oxygen. Therefore, the molar ratio of hydrogen to oxygen is \(2:1\).

Step 3: Calculating the Stoichiometric Fuel to Air Ratio

The stoichiometric fuel-to-air ratio, \(f_{stoich}\), can be calculated by dividing the molar ratio of the fuel (hydrogen, \(H_{2}\)) by air (oxygen, \(O_{2}\)). Hence, \(f_{stoich} = \frac{2 mol H_{2}}{1 mol O_{2}} = 2\).

Key Concepts

Combustion reaction

Combustion reactions involve the process of a substance reacting rapidly with oxygen, resulting in the release of energy, usually in the form of heat and light. These reactions are crucial in various applications, such as powering engines and generating heat for homes. In the context of hydrogen combustion, the reaction is straightforward because hydrogen is a simple molecule.
In this specific reaction, hydrogen gas (\(H_2\)) combines with oxygen gas (\(O_2\)) to form water (\(H_2O\)). The purpose of this reaction goes beyond simple burning; it's about efficiently transforming chemical energy into thermal energy. In practical uses such as in rocket propulsion or fuel cells, this reaction helps convert stored hydrogen energy into a usable form.
Understanding combustion reactions is essential for optimizing fuel usage and minimizing emissions, making it a fundamental principle in environmental science and engineering fields.

Chemical equation balancing

Balancing a chemical equation ensures that the law of conservation of mass is respected, which states that matter is neither created nor destroyed in a chemical reaction. This means that the number of atoms for each element must remain equal on both sides of the equation.

• The combustion of hydrogen involves the equation: \(2H_2 + O_2 \rightarrow 2H_2O\).
• To balance this equation, each type of atom should be counted on both sides. We've got 4 hydrogen atoms and 2 oxygen atoms on both the reactants and products sides, satisfying the conservation law.
• The coefficients used—numbers placed before the chemical formulas—are important because they indicate the relative amounts of each substance involved.

Balancing chemical equations is a fundamental skill in chemistry because it allows the calculation of reactant and product quantities, which is vital for laboratory work and industrial applications.

Fuel-to-air ratio

The fuel-to-air ratio (F/A ratio) is a measure of how much fuel is mixed with air, and it is an essential parameter in combustion processes. Calculating this ratio correctly allows for better control of the combustion process, leading to more efficient energy usage and reduced emissions.
For the combustion of hydrogen, the stoichiometric fuel-to-air ratio, denoted as \(f_{stoich}\), is derived from the balanced equation: \(2H_2 + O_2 \rightarrow 2H_2O\). The ratio is calculated based on the molar relationship between the fuel and oxygen.

• In this instance, two moles of hydrogen react with one mole of oxygen, giving a stoichiometric ratio of 2:1.
• This ratio signifies that for every part of oxygen, two parts of hydrogen are required for complete combustion without leftover fuel or oxygen.

Controlling the fuel-to-air ratio is key in various applications—such as engines and industrial furnaces—because even slight variations can significantly affect performance and pollutant formation. Therefore, understanding and managing this ratio is crucial for optimizing combustion processes.