Calculate the equivalence ratio for the combustion reaction of n-decane and hydrogen peroxide using the stoichiometric equation. Show your calculations and explain the results.

Question

Hint: Equivalence ratio, often denoted by the symbol φ (phi), is a term commonly used

in the field of combustion to describe the relative amount of fuel and oxidizer present in

a combustion process. It provides a quantitative measure of the mixture's composition

compared to the stoichiometric mixture required for complete combustion. The formula

for calculating the equivalence ratio is as follows: φ = (Fuel-to-Oxidizer Ratio) /

(Stoichiometric Fuel-to-Oxidizer Ratio)

Answer 1

To calculate the equivalence ratio for the combustion reaction of n-decane (C10H22) and hydrogen peroxide (H2O2), we need the balanced stoichiometric equation for the combustion reaction.

The balanced stoichiometric equation for the combustion of n-decane is: C10H22 + 13.5 O2 -> 10 CO2 + 11 H2O

The balanced stoichiometric equation for the decomposition of hydrogen peroxide is: 2 H2O2 -> 2 H2O + O2

Now, we can determine the stoichiometric fuel-to-oxidizer ratio for each reaction.

For the combustion of n-decane: Stoichiometric Fuel-to-Oxidizer Ratio (n-decane) = 1 (coefficient of C10H22) / 13.5 (coefficient of O2) = 1/13.5

For the decomposition of hydrogen peroxide: Stoichiometric Fuel-to-Oxidizer Ratio (H2O2) = 0.5 (coefficient of H2O2) / 1 (coefficient of O2) = 0.5

Now, we can calculate the equivalence ratio (φ) using the formula: φ = (Fuel-to-Oxidizer Ratio) / (Stoichiometric Fuel-to-Oxidizer Ratio)

For the combustion of n-decane: φ (n-decane) = (Fuel-to-Oxidizer Ratio) / (Stoichiometric Fuel-to-Oxidizer Ratio) = Fuel-to-Oxidizer Ratio / (1/13.5)

For the decomposition of hydrogen peroxide: φ (H2O2) = (Fuel-to-Oxidizer Ratio) / (Stoichiometric Fuel-to-Oxidizer Ratio) = Fuel-to-Oxidizer Ratio / 0.5

Without specific information about the initial quantities of n-decane and hydrogen peroxide, we cannot determine the actual fuel-to-oxidizer ratio in the mixture, and consequently, we cannot calculate the exact equivalence ratio.

The equivalence ratio (φ) provides a measure of how the actual mixture's composition compares to the stoichiometric mixture required for complete combustion or reaction. If φ is less than 1, it indicates that there is an excess of oxidizer relative to the fuel, and if φ is greater than 1, it suggests an excess of fuel relative to the oxidizer. When φ is exactly 1, it represents the stoichiometric mixture where the fuel and oxidizer are in the precise proportion for complete combustion.

In practical combustion applications, it is essential to carefully control the equivalence ratio to achieve efficient and clean combustion processes.