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Balancing Chemical Equations Using Algebra Given this equation: ___C2H7N + ___O2 ___CO2 + ___H2O + ___NO2 Step 1. Assign a variable to each unknown coefficient. _a_C2H7N + _b_O2 _c_CO2 + _d_H2O + _e_NO2 Step 2. Write an MASS BALANCE equation for each element in the overall reaction using subscripts and coefficients to represent the number of atoms of each element in reactants and in products. The arrow () is the equals sign of the equation. These are the mass balance equations. Carbon Hydrogen Nitrogen Oxygen C H N O 2a 7a a 2b = = = = c 2d e 2c + d + 2e Note: You have just created a set of simultaneous algebraic equations the solution of which is the set of whole number coefficients that satisfy this chemical equation. Step 3. Examine the mass balance equations. Which variable is the most common, that is, the variable that appears in the most equations? “a” Right! Well, you will substitute 1 into all of the equations for “a” and solve the equations. C H N O 2a 7a a 2b Now we know that: a b c d e = = = = c 2d e 2c + d + 2e = = = = = 1 ? 2 7/2 1 If then a 2(1) 7(1) (1) 2b = = = = = 1 c 2d e 2c + d + 2e Step 4. Make secondary substitutions into the Oxygen equation to solve for “b” using the values you now have for “c”, “d”, and “e”. 2b 2b b = = = 2(2) + 7/2 + 2(1) 19/2 19/4 Step 5. Multiply the set of coefficients by the largest denominator of any fractional solutions to generate a set of whole numbers as the coefficients for the balanced equation. a b c d e = = = = = 1 19/4 2 7/2 1 x4 a b c d e = = = = = 4 19 8 14 4 Step 6. Substitute the solution into the chemical equation: _4_C2H7N + _19_O2 _8_CO2 + _14_H2O + _4_NO2