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The combustion of acetylene (C\textsubscript{2}H\textsubscript{2}) is the chemical reaction between acetylene gas and oxygen to produce carbon dioxide and water as the main products. Here, acetylene reacts with oxygen in a controlled manner. The balanced chemical equation for complete combustion of acetylene is: \[ \text{2} \text{C}_2\text{H}_2 + \text{5} \text{O}_2 \rightarrow \text{4} \text{CO}_2 + \text{2} \text{H}_2\text{O} \]This equation means that for every 2 moles of C\textsubscript{2}H\textsubscript{2}, 5 moles of O\textsubscript{2} are required, and it results in 4 moles of CO\textsubscript{2} and 2 moles of H\textsubscript{2}O. Combustion reactions are exothermic, releasing energy in the form of heat and light.
Understanding this balanced equation helps predict the products and calculate the required reactant amounts, including adjusting for real-world conditions like excess air and humidity.

Excess air in combustion processes is used to ensure complete burning of the fuel. More air than theoretically needed is supplied to guarantee there is enough oxygen available. If the theoretical air required (stoichiometric air) for the given fuel is known, excess air can be calculated as follows:\[ \text{Excess Air} = \text {Theoretical Air } \times \frac{\text{Excess Amount}}{100} \]In our exercise, 40% excess air means we add 40% more than the stoichiometric air, which helps in practical scenarios where complete mixing and combustion should take place.
Providing excess air prevents harmful pollutants and soot formation. While it ensures thorough combustion, it can also lead to heat losses because extra nitrogen is heated but not used actively in the reaction. Thus, balancing becomes crucial for efficient combustion.

Relative humidity (RH) measures the amount of moisture in the air relative to the maximum amount of moisture the air can hold at a specific temperature. It is expressed as a percentage. In combustion calculations, RH affects the air composition because the air may carry water vapor that participates in the reaction.For instance, in the provided exercise:- Given 80% RH, the moisture in the entering air impacts the reactant quantities since the air is not dry.- Moisture content in air can be calculated or referred to using psychrometric charts or equations based on temperature and pressure.Humidity affects the combustion process by altering the initial gas composition and possibly the combustion efficiency and temperature.

Equilibrium constants define the ratio of concentrations of products and reactants at equilibrium for reversible chemical reactions. For combustion in a steady-state reactor, this helps in predicting the composition of the mixture at the exit.For a generic reaction:\[ \text{aA} + \text{bB} \rightleftharpoons \text{cC} + \text{dD} \]The equilibrium constant (\text{K}\textsubscript{eq}) is formulated as:\[ \text{K}_{eq} = \frac{\text{[C]}^c \text{[D]}^d}{\text{[A]}^a \text{[B]}^b} \]It involves the concentrations (or partial pressures for gases) of products and reactants. This is essential in combustion systems operating at high temperatures and varying pressures to determine the exact exit compositions.

A steady-state reactor maintains constant conditions over time, implying that the reactants entering the reactor and products leaving it don't change with time. For the given exercise, the reactor operates under steady-state conditions, ensuring that:- The input and output flow rates and compositions remain constant.- Energy balance remains steady with continuous heat generation or absorption.- Achieving equilibrium states, relevant parameters like temperature, pressure, and concentration are stable.The steady-state assumption simplifies analysis and design calculations since it removes the time dependency from the equations, making it easier to predict the output composition based on known input conditions and reactions happening inside.