Natural gases are rarely pure methane; they usually also...

Natural gases are rarely pure methane; they usually also contain other light hydrocarbons and nitrogen. Determine an expression for the standard heat of combustion as a function of composition for a natural gas containing methane, ethane, propane, and nitrogen. Assume liquid water as a product of combustion. Which of the following natural gases has the highest heat of combustion? (a) $y_{\mathrm{CH}_4}=0.95, y_{C_2 \mathrm{H}_6}=0.02, y_{C_3 \mathrm{H}_3}=0.02, y_{N_2}=0.01$. (b) $y_{C_4 H_4}=0.90, y_{C_2 H_6}=0.05, y_{C_3 H_3}=0.03, y_{N_2}=0.02$. (c) $y_{C_{H_4}}=0.85, y_{C_2 H_6}=0.07, y_{C_3 H_8}=0.03, y_{N_2}=0.05$.

Natural gases are rarely pure methane; they usually also contain other light hydrocarbons and nitrogen. Determine an expression for the standard heat of combustion as a function of composition for a natural gas containing methane, ethane, propane, and nitrogen. Assume liquid water as a product of combustion. Which of the following natural gases has the highest heat of combustion?
(a) $y_{\mathrm{CH}_4}=0.95, y_{C_2 \mathrm{H}_6}=0.02, y_{C_3 \mathrm{H}_3}=0.02, y_{N_2}=0.01$.
(b) $y_{C_4 H_4}=0.90, y_{C_2 H_6}=0.05, y_{C_3 H_3}=0.03, y_{N_2}=0.02$.
(c) $y_{C_{H_4}}=0.85, y_{C_2 H_6}=0.07, y_{C_3 H_8}=0.03, y_{N_2}=0.05$.

Key Concepts

Effect of Inert Components

Non-combustible gases such as nitrogen are present in natural gas mixtures and influence the overall energy output by diluting the concentration of reactive hydrocarbons. While they do not contribute directly to the heat of combustion, their presence reduces the energy density of the fuel by lowering the overall fraction of fuel available to react, hence affecting the standard heat of combustion when computed on a per mole basis.

Stoichiometry of Combustion Reactions

Stoichiometry deals with the balancing of chemical equations for combustion processes, ensuring that atoms are conserved in the reaction between the fuel and an oxidant. For each hydrocarbon component, a specific balanced chemical reaction can be written to account for the combustion process where liquid water as a product indicates condensation. Understanding the stoichiometric coefficients is essential for determining the energy release per mole of fuel.

Energy Contributions of Light Hydrocarbons

Different hydrocarbons, such as methane, ethane, and propane, have distinct heats of combustion that reflect differences in their chemical structure and bond energies. Lighter hydrocarbons typically offer lower energy content per mole compared to heavier ones due to differences in carbon-carbon and carbon-hydrogen bonding. Therefore, the mixture’s heat of combustion depends on the specific energy contribution of each hydrocarbon weighted by its mole fraction.

Standard Heat of Combustion

This concept involves the calculation of the energy released when a substance undergoes complete combustion under standard conditions. The standard heat of combustion is typically expressed per mole of fuel, and it is determined by accounting for the bond energies that are broken and formed during the reaction. In the context of a fuel mixture, it is computed as a weighted sum of the heats of combustion of each individual component, where the weights are the mole fractions of the respective fuels.

Fuel Composition and Mole Fractions

In natural gas mixtures, the composition consists of various hydrocarbons along with inert gases like nitrogen. Mole fractions represent the relative amounts of these components present in the mixture. The overall energy content of the fuel mixture is significantly influenced by these mole fractions, as each hydrocarbon contributes a specific amount of energy per mole to the overall heat of combustion, while inert gases, which do not combust, dilute the energy content.

Transcript

00:01 For this question, we're looking at three different fuels.

00:04 We are looking at methane, octane, representing gasoline, and kerosene represented by c -10h -22.

00:15 And we want her first right balanced chemical reactions and then calculate delta -h standard for the reactions.

00:23 After that, we need to consider when burned under standard state conditions which of these three fuels would produce the most heat per mole and which would produce the most heat per gram.

00:38 So let's start with methane.

00:41 We'll write a balanced chemical reaction that includes a two coefficient on oxygen and a two coefficient on liquid water.

00:51 Delta h standard for the reaction will be one times the delta h of formation of carbon dioxide, plus two times the delta h formation of liquid water, minus two times delta h of formation of oxygen, which is zero and one times the delta h of formation of methane, giving us negative 890 .39 kilojoules per mole.

01:13 To calculate kilojoules per gram, we'll simply divide the kilojoules per mole by the molar mass of methane, then the moles will cancel and we'll get kilojoules per gram.

01:25 Negative 55 .5 kilojoules per gram.

01:29 The next one is gasoline represented as octane.

01:33 To balance this chemical reaction, for 1 .5.

01:36 1 mole of octane.

01:37 We need to put an 8 in front of the carbon, a carbon dioxide, so we have 8 carbons, a 9 in front of the water, so we have 18 hydrogens, and then we need to put 25 halves in front of the oxygen, so we have 25 oxygens on each side...

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