A chemical equation is a symbolic representation of a chemical reaction. It is a formula used to display different stages for chemical reactions, where chemical substances are changed into other substances. The elements and/or compounds to the left of the arrow in a chemical equation represent the reactants, the arrow represents the transition stage, and the species to the right of the arrow represent the products. The four basic chemical equations are:

A → B

A → B + C

A + B → C

A + B → C + D

For example, the combustion of methane (in oxygen) is depicted as:

CH₄ + 2 O₂ → CO₂ + 2 H₂O,

and the reversible reaction of the Haber process is shown as

N_2(g) + 3H_2(g) 2NH_3(g) + ΔH.

A chemical equation should represent the stoichiometry observed in the chemical reaction. When the net amount of atoms on both sides of the equation is identical the equation is said to be a balanced equation.

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Reading chemical equations

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When reading a chemical equation there are some points to consider.

• Each side of an equation represents a mixture of chemicals. The mixture is written as a set of molecular formulas, separated by + symbols.
• Each formula is preceded by an optional scalar number (if no scalar number is written, it is implied that the number is 1). The scalar numbers indicate the relative quantity of molecules in the reaction. For instance, the string 2H₂O + 3CH₄ represents a mixture containing 2 molecules of H₂O for every 3 molecules of CH₄.
• The two sides of the equation are separated by an arrow. If the reaction is non-reversible, a right-arrow (→) is used, indicating that the left side represents the mixture of chemicals before the reaction, and the right side indicates the mixture after the reaction. For a reversible reaction, a two-way arrow is used. For example the equation 4Na + O₂ → 2Na₂O represents a non-reversible reaction. In this reaction, sodium (Na) and oxygen (O₂) are converted to a single molecule, Na₂O (containing 2 sodium atoms and 1 oxygen atom). We can also see that for every 4 sodium atoms at the beginning of the reaction, a single O₂ molecule will participate, and 2 Na₂O molecules will result.
• A chemical equation does not imply that all reactants are consumed in a chemical process. For instance a limiting reagent determines how far a reaction can go.
• In an ionic equation balancing of charge also takes place. In a full equation all reactants are written as molecules.

Balancing chemical equations

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In a chemical reaction, the quantity of each element does not change. Thus, each side of the equation must represent the same quantity of any particular element. Also in case of net ionic reactions the same charge must be present on both sides of the equation. Then, and only then, the equation is balanced. Given an unbalanced equation, one may balance it by changing the scalar number for each molecular formula.

Simple chemical equations can be balanced by inspection, that is, by trial and error. Generally, it is best to balance the most complicated molecule first. Hydrogen and oxygen are usually balanced last.

Ex #1. Na + O₂ → Na₂O

In order for this equation to be balanced, there must be an equal amount of Na on the left hand side as on the right hand side. As it stands now, there is 1 Na on the left but 2 Na's on the right. This problem is solved by putting a 2 in front of the Na on the left hand side:

2Na + O₂ → Na₂O

In this equation there are 2 Na atoms on the left and 2 Na atoms on the right. In the next step the oxygen atoms are balanced as well. On the left hand side there are 2 O atoms and the right hand side only has one. This is still an unbalanced equation. To fix this a 2 is added in front of the Na₂O on the right hand side. Now the equation reads:

2Na + O₂ → 2Na₂O

Notice that the 2 on the right hand side is "distributed" to both the Na₂ and the O. Currently the left hand side of the equation has 2 Na atoms and 2 O atoms. The right hand side has 4 Na's total and 2 O's. Again, this is a problem, there must be an equal amount of each chemical on both sides. To fix this 2 more Na's are added on the left side. The equation will now look like this:

4Na + O₂ → 2Na₂O

This equation is a balanced equation because there is an equal number of atoms of each element on the left and right hand sides of the equation.

Ex #2. P₄ + O₂ → P₄O₁₀

This equation is not balanced because there is an unequal amount of O's on both sides of the equation. The left hand side has 4 P's and the right hand side has 4 P's. So the P atoms are balanced. The left hand side has 2 O's and the right hand side has 10 O's. To fix this unbalanced equation a 5 in front of the O₂ on the left hand side is added to make 10 O's on both sides resulting in

P₄ + 5O₂ → P₄O₁₀

The equation is now balanced because there is an equal amount of substances on the left and the right hand side of the equation.

Ex #3. C₂H₅OH + O₂ → CO₂ + H₂O

This equation is more complex than the previous examples and requires more steps. The most complicated molecule here is C₂H₅OH, so balancing begins by placing the coefficient 2 before the CO₂ to balance the carbon atoms.

C₂H₅OH + O₂ → 2CO₂ + H₂O

Since C₂H₅OH contains 6 hydrogen atoms, the hydrogen atoms can be balanced by placing 3 before the H₂O:

C₂H₅OH + O₂ → 2CO₂ + 3H₂O

Finally the oxygen atoms must be balanced. Since there are 7 oxygen atoms on the right and only 3 on the left, a 3 is placed before O₂, to produce the balanced equation:

C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O

Linear system balancing

In reactions involving many compounds, balancing may get harder, we can then try to balance equation using algebraic method, based on solving set of linear equations:

1. Assign variables to each coefficient:

• a K₄Fe(CN)₆ + b H₂SO₄ + c H₂O → d K₂SO₄ + e FeSO₄ + f (NH₄)₂SO₄ + g CO

2. We must have the same quantities of each atom in each side of the equation. So, for each element, count its atoms and equal both sides:

• K: 4a = 2d
• Fe: 1a = 1e
• C: 6a = g
• N: 6a = 2f
• H: 2b+2c = 8f
• S: b = d+e+f
• O: 4b+c = 4d+4e+4f+g

3. Solving the system (usually direct substitution is the best way)

• d=2a
• e=a
• g=6a
• f=3a
• b=6a
• c=6a

which means that we have all coefficients depending on a parameter a, just choose a=1 (a number that will make all of them small whole numbers) and you'll have:

• a=1 b=6 c=6 d=2 e=1 f=3 g=6

4. And the balanced equation at last:

• K₄Fe(CN)₆ + 6 H₂SO₄ + 6 H₂O → 2 K₂SO₄ + FeSO₄ + 3 (NH₄)₂SO₄ + 6 CO

To speed up the process, one can combine both methods to get a more practical algorithm:

1. Identify elements which occur in one compound in each member (this is very usual)

2. Start with the one among those which has a big index (this will help to keep working with integers), and assign a variable, let's say a.

• a K₄Fe(CN)₆ + H₂SO₄ + H₂O → K₂SO₄ + FeSO₄ + (NH₄)₂SO₄ + CO

3. Well, K₂SO₄ has to be 2a (because of K), and also, FeSO₄ has to be 1a (because of Fe), CO has to be 6a (because of C) and (NH₄)₂SO₄ has to be 3a (because of N). Well, this takes out the first four equations of the system! We already now that, whatever the coefficients are, those proportions must hold:

• a K₄Fe(CN)₆ + H₂SO₄ + H₂O → 2a K₂SO₄ + a FeSO₄ + 3a (NH₄)₂SO₄ + 6a CO

4. We can continue by writing the equations now (and having simpler problem to solve) or, in this particular case (although not so particular) we could continue by noticing that adding the Sulfurs we get 6a for H₂SO₄ and finally by adding the hydrogens (or the oxygens) we get the lasting 6a for H₂SO₄.

5. Again, having a convenient value for a (in this case 1 will do, but if a gets fractionary values in the other coefficients you will like to cancel the denominators) we get the result:

• K₄Fe(CN)₆ + 6 H₂SO₄ + 6 H₂O → 2 K₂SO₄ + FeSO₄ + 3 (NH₄)₂SO₄ + 6 CO

External links

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• Classic Chembalancer - Play Chembalancer, a free online game at FunBasedLearning.com, to learn how to balance equations by inspection
• Online calculator, determines of the coefficients of a chemical equation
• Free chemical equation balancer, solves chemical equation, works online, low bandwidth
• Chemical equation balancing program - works off-line, calculates stoichiometry and limiting reagents, balances charge.
• Online Chemical Equation Balancer Balances equation of any chemical reaction (full or half-cell) in one click.

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