Formulating and Balancing Chemical Equations: The Haber Process and Acetylene Combustion

Principles of Chemical Equation Writing and Balancing

A chemical equation represents a chemical reaction by showing the chemical formulas of the reactants on the left side and the products on the right side, separated by a reaction arrow ($\rightarrow$). To correctly translate a verbal description of a chemical reaction into a balanced chemical equation, fundamental chemical laws and conventions must be applied.

The Law of Conservation of Mass states that matter cannot be created or destroyed in an isolated system during a chemical reaction. Consequently, the total number of atoms of each element present in the reactants must equal the total number of atoms of that element in the products. Balancing an equation is the process of adjusting stoichiometric coefficients—the whole numbers placed in front of chemical formulas—to satisfy this conservation law. Subscripts within chemical formulas must never be changed during balancing, as altering subscripts changes the chemical identity of the substance.

When identifying gaseous reactants and products, it is essential to account for natural diatomic elements. Seven elements exist as homonuclear diatomic molecules in their pure elemental form under standard conditions: hydrogen ($H_2$), nitrogen ($N_2$), oxygen ($O_2$), fluorine ($F_2$), chlorine ($Cl_2$), bromine ($Br_2$), and iodine ($I_2$). When any of these elements appear as uncombined elemental gases in a reaction, their chemical formulas must be written with a subscript of 2$.\n\n# Synthesis of Ammonia via the Haber Process\n\nThe Haber process (also known as the Haber-Bosch process) is an industrial chemical reaction in which ammonia gas (NH_3) is synthesized directly from hydrogen gas and nitrogen gas.\n\nTo construct the balanced chemical equation for the Haber process, the chemical formulas of all participating reactants and products must first be determined:\n- Reactant 1: Hydrogen gas, represented in its elemental diatomic form as H_2(g).\n- Reactant 2: Nitrogen gas, represented in its elemental diatomic form as N_2(g).\n- Product: Ammonia gas, represented by the chemical formula NH_3(g).\n\nThe initial unbalanced skeleton chemical equation is written as:\nN_2(g) + H_2(g) \rightarrow NH_3(g)\n\nBalancing proceeds by auditing the atom count for each element across the reaction arrow:\n- On the reactant side, there are 2$nitrogen atoms (from$N_2$) and$2$hydrogen atoms (from$H_2).\n- On the product side, there is 1$nitrogen atom and$3$hydrogen atoms in a single molecule of$NH_3\n- To balance the nitrogen atoms, place a coefficient of 2$in front of$NH_3(g) on the product side:\nN_2(g) + H_2(g) \rightarrow 2NH_3(g)\n- Recalculating the atom inventory shows 2$nitrogen atoms on both sides. However, the product side now contains$2 \times 3 = 6$hydrogen atoms, whereas the reactant side contains only$2 hydrogen atoms.\n- To balance the hydrogen atoms, place a coefficient of 3$in front of$H_2(g)$on the reactant side to provide$3 \times 2 = 6 hydrogen atoms:\nN_2(g) + 3H_2(g) \rightarrow 2NH_3(g)\n\nVerifying the final balanced equation:\n- Nitrogen atoms: Reactants have 2 \times 1 = 2$; Products have$2 \times 1 = 2.\n- Hydrogen atoms: Reactants have 3 \times 2 = 6$; Products have$2 \times 3 = 6.\n\nThe stoichiometric ratio for this reaction is 1$mole of nitrogen gas reacting with$3$moles of hydrogen gas to yield$2 moles of ammonia gas. The complete balanced chemical equation is:\nN_2(g) + 3H_2(g) \rightarrow 2NH_3(g)\n\n# Hydrocarbon Combustion: Combustion of Acetylene\n\nAcetylene (systematic IUPAC name: ethyne) is an alkyne hydrocarbon with the chemical formula C_2H_2. When acetylene burns in air, it undergoes a combustion reaction.\n\nCombustion is an exothermic chemical reaction between a fuel and an oxidizing gas. The elemental gas present in atmospheric air that acts as the required oxidant for hydrocarbon combustion is oxygen gas (O_2$). Complete combustion of a hydrocarbon fuel in oxygen yields carbon dioxide ($CO_2$) and water ($H_2O).\n\nTo construct the balanced chemical equation for the combustion of acetylene:\n- Reactant 1: Acetylene (C_2H_2(g)).\n- Reactant 2: Oxygen gas, the elemental reactant supplied by air (O_2(g)).\n- Product 1: Carbon dioxide (CO_2(g)).\n- Product 2: Water (H_2O(g)).\n\nThe initial unbalanced skeleton chemical equation is written as:\nC_2H_2(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)\n\nBalancing proceeds step by step, addressing carbon first, hydrogen second, and oxygen last:\n- Balance Carbon: The reactant acetylene molecule C_2H_2$contains$2$carbon atoms. The product side initially contains$1$carbon atom in$CO_2$. Place a coefficient of$2$in front of$CO_2(g):\nC_2H_2(g) + O_2(g) \rightarrow 2CO_2(g) + H_2O(g)\n- Balance Hydrogen: The reactant side contains 2$hydrogen atoms in$C_2H_2$, and the product side contains$2$hydrogen atoms in$H_2O$. Hydrogen is balanced with a coefficient of$1$for$H_2O.\n- Count Oxygen Atoms on the Product Side: The product side contains 2 \times 2 = 4$oxygen atoms from$2CO_2(g)$plus$1 \times 1 = 1$oxygen atom from$H_2O(g)$, giving a total of$5 oxygen atoms on the product side.\n- Balance Oxygen using a Fractional Coefficient: To obtain 5$oxygen atoms from diatomic oxygen ($O_2$) on the reactant side, assign a coefficient of$\frac{5}{2}$to$O_2(g):\nC_2H_2(g) + \frac{5}{2}O_2(g) \rightarrow 2CO_2(g) + H_2O(g)\n- Convert to Whole-Number Coefficients: Chemical equations are conventionally written using the smallest whole-number coefficients. To eliminate the fraction \frac{5}{2}$, multiply every coefficient in the equation by$2:\n2C_2H_2(g) + 5O_2(g) \rightarrow 4CO_2(g) + 2H_2O(g)\n\nVerifying the final balanced atom inventory:\n- Carbon atoms: Reactants have 2 \times 2 = 4$; Products have$4 \times 1 = 4.\n- Hydrogen atoms: Reactants have 2 \times 2 = 4$; Products have$2 \times 2 = 4.\n- Oxygen atoms: Reactants have 5 \times 2 = 10$; Products have$(4 \times 2) + (2 \times 1) = 8 + 2 = 10.\n\nThe stoichiometric ratio shows that 2$moles of acetylene gas react with$5$moles of oxygen gas to produce$4$moles of carbon dioxide gas and$2 moles of water vapor. The complete balanced chemical equation is:\n2C_2H_2(g) + 5O_2(g) \rightarrow 4CO_2(g) + 2H_2O(g)$$