For a student who is pursuing his academic career in the stream of chemistry, the topic of how to balance chemical equations is taught in a very earlier stage. The topic of how to balance a chemical equation, not only fascinates the students of the chemistry stream but also the students of the mathematical stream. This is mainly because the major concepts of linear algebra are heavily used in balancing the chemical equations. It should be understood by the students that the topic on how to balance the chemical equations is a very basic concept in the stream of chemistry and without mastering it, the student would have to face various contextual difficulties in learning the chemical theories of considerably higher level. By the means of a chemical equation, the scholars majorly aim to portray a certain chemical reaction figuratively on a paper. There is no other such effective way to document or record down the chemical reaction and present it in front of the audience. Both in the academical stream and industrial level, the significance of chemistry and the knowledge regarding how to balance chemical reactions is very high. Although a new compound is formed in a chemical reaction, it should be understood that there is no destruction or generation of atoms in the reaction. It is the participant’s atoms in the chemical reactions that bring the way for the generation of a new compound. Hence in a chemical equation, only the atoms present on the left side of the equation would end up on the right side of the chemical equation. If any new atom would end up in the product list or the right side of the equation, the chemical equation would deem to be a false one. The process of removing this sort of discrepancy from the equation would be termed as balancing the chemical equation. The major theory on which the task of how to balance chemical reaction depends on is the law of conservation of matter. If the student doesn’t possess the skill to balance the equation, he would find it very hard to score decent marks in the academic evaluation since a majority of the theories in the stream of chemistry relies on the concept of how to balance chemical equations. The atoms on the left side of the equation or the atoms which enter into the reaction are majorly termed to be reactants. The compounds/elements listed at the right side of the chemical equation is termed to be the products. The products would have very different chemical properties when compared to the compounds or elements which take part in the chemical reaction. To declare a chemical reaction to be a balanced one, the number of the atoms of each type on the right side should be equal to those on the left side or vice versa.

The first section of the trial and error process is conducted to confirm whether the chemical equation is balanced or not. The method is only effective if the provided chemical reaction is not a complex one. Though it has been observed that the method of the trial and error process possess a lot of limitation and restrictions. The coefficients of each variable could not adjust by the mere approach of the trial and error process. Hence adopting the algebraic approach in the task of how to balance chemical equations is a much better one. The approach of algebraic theory would be much better since it considers each respective coefficient is considered to be a very unknown dimension. The concept of algebra would be very apt to solve and balance multiple chemical equations simultaneously. The simple inspection method is not used in balancing the compound chemical equations in the higher classes and for the efficient commencement of the balancing should be done by the algebraic process. If closely encountered it could be understood by the student that the balancing process has nothing to do with the theories in chemistry and is purely a linear algebraic operation. If only a vector space is created by the chemical reaction, then the process of balancing could be done in the chemical reactions from a scientific point of view.

Normally a chemical reaction which happens normally in nature is a balanced one and always maintains consistency. If there is an additional element or atom in the product list then it should be ascertained that a new atom has taken part in the reaction and you have been ignorant of its existence. The acknowledgment of this fact would reduce the discrepancy while portraying the chemical equations in front of the audience. If the reaction doesn’t take place then the coefficient for each particle taking part in the chemical reaction could be assumed as the numerical value of zero. If looking into balancing the chemical equations, it could be observed there are a lot of methods suggested by mathematics and chemistry to solve the same situation. Though the student needs to understand the higher degree of mathematical operations since it consists of the concepts like generalized matrix inverses.

Let us have a detailed look at the types of reactions before continuing to mention the content on how to balance chemical equations.

Decomposition Reactions
The reactions which would follow the format of

The variables represented provided here in the above section of how to balance chemical equations represent the atoms involved in a chemical reaction. You could observe this sort of decomposition reaction in compounds like Calcium Carbonate. Below is provided the chemical equation.

The major characteristics of the decomposition are that normally only a single compound takes part in the chemical reaction and then after disintegrates into consecutive compounds and elements.

Combination reaction
The ideology behind the combination reaction mentioned in this report on how to balance chemical equations is quite opposite the principle of a decomposition reaction. Despite disintegrating, the combination of various elements or compounds taking part in the chemical reaction takes place. The format of the chemical reaction would be s in the below-provided format.

The best example of this could be represented by the chemical process between the compound of ammonium sulfate and sulphuric acid. Below is provided the chemical formula of the reaction in between these two compounds.

It could be observed that in the combination reaction the number of products would be much lesser than the number of reactants.

Single replacement reactions
The replacement of one or more than one element is being replaced by other atoms in a chemical reaction that could be termed as a single replacement reaction. You could portray the single replacement reaction as mentioned in the below format of this report.

The format could be justified by the chemical reaction which takes place in between Iron and the copper sulfate compound.

Double replacement reactions
The reaction of the double replacement could also be termed or signified as metathesis and could be portrayed in the below-provided format.

In nature, a plethora of reactions could be pointed out which would come under the category of metathesis. Though the ideal reaction which would come under this category is the chemical reaction in between the compounds of ammonium nitrate and lithium nitride.

Precipitation Reaction The instance in which the reaction between different compounds would lead to the generation of insoluble salts could be classified under the category of a precipitation reaction. The precipitation reaction is another variant of the single or double replacement chemical reaction itself. The precipitation reaction could be best portrayed when depicting the chemical reaction between the compounds od aqueous silver nitrate and aqueous sodium chloride.

The sign (aq) in the chemical formula would signify that the compound is introduced as a solution in water. The compounds mark their presence as the cations and anions in the solution of silver nitrate, sodium nitrate, and sodium chloride. The sign (s) depicts that the salt is in the solid-state, indirectly portraying that the compound or salt is insoluble in the present solution. The presence of silver chloride could be demarked in the solution as the presence of chloride anions and the silver cations. In this instance, the compound accompanied by the sign of (S) could be ascertained as the precipitate.

The natural occurrence of the precipitate formation is very gradual and slow, the accelerated rate of the precipitation reaction could be observed exclusively in the laboratories. The instance of mixing two different colorless and odorless solution leading to the formation of the precipitate could be very fascinating for a chemistry student. The precipitate appears initially as a cloudy material and hence settles down slowly at the bottom of the container. It is upon the nature of the compounds entered in the reaction that the color of the precipitate would depend upon. The liquid or the solution which remains after the precipitation process would be termed as the supernatant liquid.

Combustion reaction
It is majorly the reaction of the chemical substance with that of the oxygen which is termed as the process of combustion. The resultant of the combustion chemical process would be major water accompanied by carbon dioxide gas. In the process of combustion, both light and heat energy are emitted into the surrounding or the system. Below is provided standard combustion of a hydrocarbon.

It would be depended upon the chemical substance which has undergone the combustion process that would determine to which compound the oxygen would merge with. If taking the instance of sulfur, it would generate sulfur dioxide after into a combustion chemical reaction with oxygen. Let’s have a look at the chemical equation of the combustion process of the sulfur.

The most common form of chemical reaction in nature is the combustion of the compounds. The process of the combustion could also be classified under the section of reduction or oxidation. The major principle behind the combustion process could be deduced from the redox theory. It should be understood by the student from the chemistry background that all the combustion reactions could be classified as the redox reaction, though all the redox reactions could not be classified related as a combustion chemical reaction.

What is a Balanced Equation?
The depiction of the chemical reaction by using appropriate coefficients to balance both sides of the arrow constitutes the major background of the balanced equation. The total of the particular type of atom in both the reactant side and the product side should be similar. The generic law if portraying a chemical reaction using a chemical equation is to portray the reactants on the left side of the arrow and the resulting products to the right side of the arrow. The arrow should be pointed towards the expression of products. The below patter would make the format of the chemical equation.

Let us take an instance of the combustion process of the methane.

The combustion process of methane with oxygen would lead to the production of carbon dioxide and water.

The major precaution should be taken while conducting the task of how to balance the chemical equation that only the manipulation should be done to the coefficients of the reactants or the products. The chemical formula of the compounds of the elements should not be tampered or manipulated with. Let us look at the strict notion of not manipulating the chemical formulas of the elements or the compounds.

Major factors to be considered on how to balance chemical equations
The guidelines mentioned in the below section of this article on how to balance chemical equations should be followed strictly to ascertain that the drafted chemical reaction is in balanced form.

• The first notion on how to balance chemical equations is that the same type of atoms should only be present at the product side of the chemical equation. Let us take the instance of the equation one provided in the above section of this article. In the oxidation process of the methane, atoms of carbon, hydrogen, and oxygen take part as reactants and thus the product should be comprised of carbon, oxygen, and hydrogen. There should be no new type of atom present in the product side of the chemical equation. For instance, a student has depicted the combustion process of the methane compound as in the below-provided format

  CH₄ + O₂ → CO₂ + H₂O + Fe

• The expression would be utterly false since the reaction signifies the generation of a new atom in the product side. The chemical equation could be balanced in two ways. Either the addition of a sodium atom in the reactant side or the deletion of the sodium atom from the product side would help in balancing the equation. If the equation would not be altered then the chemical expression would defy the law of conservation of matter.

• If the first criteria are being followed in the equation you have to check whether the number of the atoms of each element is the same on both the reactant and product side.

Considering again the equation 1 CH₄ + O₂ → CO₂ + H₂O

The number of carbon tom on both sides is the same and there is no problem with the imbalance arising from it. Though if checked the number of atoms of hydrogen on the reactant side is four whereas the number of hydrogen on the product side is only two. Checking the case of oxygen, it has two atoms on the reactant side and three atoms on the product side. Thus both the number of oxygen and hydrogen atoms are creating the issue of imbalance in the chemical equation. Let us check the portrayal of the number of atoms in the tabular form.

Element       C             H             O

Reactant      1             4             2

Product        1             2             3

The chemical equation could be stated to be in a balanced state if the atoms of both the hydrogen and the oxygen are the same at both the reactant and product side. Though we have observed in many of the students that while conducting the process of balancing they would change the compound by changing the number of atoms specifically. The possibility of this sort would be depicted as in the below equation.

CH₂ + O₂ → CO + H₂O

Here although the number of atoms is the same on both sides of the equation, the depiction has turned out to be entirely wrong. The chemical formula of methane is CH4 and hence if any variation in the expression is made, it could not be said that the methane mole has been entered in reaction. Similarly, CO2 and CO are entirely different compounds where the first one is called carbon dioxide and the latter is called carbon monoxide. Changing the chemical formula of the compounds would lead to the emergence of critical contextual errors. Hence it should be taken care of especially by the student that the chemical formula would never be tampered or manipulated while conducting the task of how to balance chemical equations. If mentioned in a very rough manner the numbers denoted as subscripts should be altered while doing the task on how to balance chemical equations.

So, what would be the best way to encounter the issue of how to balance chemical equations? Yes, the alteration in the numerical value of the coefficients is the best possible way to tackle the issue. If the coefficients are changed there is no possibility in tampering with the chemical equations of the compounds and each compound thus could be treated as a mere variable. Though it should be upon the condition or the type of provided in the reaction by which the coefficients should be adjusted. Hence there is no hard and fast rule to adjust the coefficient while tackling the task on how to balance chemical equations. Because of the uncertainty of the process and submission of various values to the variables, the method is termed to be trial and error procedure. To conduct the process efficiently, you should consider the variables with the same sort of atoms.

Let us consider the equation 1 again.

If looked at carefully, it could be observed that the number of carbon is in balanced condition on both sides of the equation. Hence the coefficient of carbon doesn’t seem to be altered with or needs any attention. Since the hydrogen atom is present in two different compounds on both side of the equations, it is the next discrepancy which should be attended. If the coefficient of the H2O would be turned out to be 2, the resultant number of the hydrogen in the product side would be equal to 4 which is as that of the count of the hydrogen atom in the reactant side. The resultant chemical reaction would be as portrayed in the below section.

Now the third factor which should be taken care of is the variable of oxygen. Since the coefficient of H2O, The number of oxygen in the product has raised the number of 4. This could be adjusted in the reactant side by making the coefficient of the O₂ as 2. Thus, the number of oxygen would get 4 on both sides of the equation.

Now the chemical equation is in the balanced situation since the number of the atoms is the same on both the reactant and product side. Though this process seems to be a very long and speculative method, this is the only genuine approach that would be efficient in the task on how to balance chemical equations.

We hope that you have understood the course of actions to be taken to commence the task of how to balance chemical equations in a very effective way. Let us summarize the major laws to be followed in the task on how to balance chemical equations

• The chemical formulas of the compound or the elements depicted in the reactant or the product side should not be manipulated. In short, never try to manipulate the numerical values provided as the subscript.
• The major manipulation of the adjustment should be done in the coefficient section of each chemical formula.
• In the absence of any coefficient, the number of molecules or atoms should be considered as one.
• The major parameter of a chemical equation being in a balanced state is the equal number of the same kind of atoms on both sides of the chemical equation.
• The number values f the coefficients should portray all the characteristics of a whole number.

Recommendation

• You may encounter the situation when the coefficient of a certain compound would turn out to be decimal after conducting the task on how to balance the chemical equation. The equation should not be left in this state and thus the whole equation should be multiplied with a suitable number to make all the coefficients a whole number.
• To make the procedure of balancing a much simpler one, the polyatomic ions could be considered as a separate group. This approach should be taken n the chemical equations which solely deal with ions.
• It would be more convenient to attend the molecules with a single type of atoms at the last while commencing the task on how to balance chemical equations. Since manipulating it at the last would be much convenient than adjusting the compounds.
• If the chemical reaction is in aqueous solution or in any way the water is present in the chemical reaction, they should be considered as hydroxide ions or hydrogen ions. This approach would simplify the process of how to balance chemical reactions.
• If the compound molecule with complex chemical formula is attended at the initial stage, the process would be much simplified. If the adjustment is coefficients is done in these compounds the equation would get affected on a great dimension.
• If the disintegration of the polyatomic ions would happen in the chemical equations, then those polyatomic groups could not be brought under the same group while solving the instance of how to balance chemical equations.
• The molecule with one as coefficient should also be considered earlier at the atom counting stage of the procedure.
• The tabular arrangement of the numerical values of each type of atom would over simply the whole effort on how to balance chemical equations.

Conclusion
From this article, it could be deduced that the procedure on how to balance chemical equations is not an ideology derived from the concept of the chemistry theories. If considered the chemical formulas merely as the variables, it could be observed that the process of how to balance chemical equations is purely derived from the algebraic theories. The chemical equations could be compared with the homogenous system of linear equations in the stream of mathematics. The student who is facing many difficulties in understanding the theories in chemistry could find a great scope in scoring decent marks if he would master the skill on how to balance chemical equations. The topic of balancing the equations would generate much interest among the students who would suffer much of boredom while studying the monotonous theories in the stream of chemistry. Whatever difficult chemical reaction a student would come up within his examinations, he would solve it easily by just engaging a little common sense and mathematical ability to it. We have tried to provide our students with the systematical way of how to balance the equation in the most simplified way possible. The methodology proposed in this article would help the student in balancing the equation with great accuracy and simplicity. The student could imply the proposed methodology in this paper with on any complex equation he encounters with. Although the scientists and various mathematical researchers have tried to propose some alternate methodologies on how to balance chemical equations, the algebraic method still is deemed to be the most accurate and efficient one in both the academic and industrial fields. It has been observed widely that the instances in which the coefficient turnouts to be decimal or unreal numbers, only the algebraic approach would turn out to be the most effective one.

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