When a solution can be found, as in the case of a CTMC, the computation is usually much quicker than directly solving the global balance equations. In some situations, terms on either side of the global balance equations cancel.
The global balance equations can then be partitioned to give a set of local balance equations also known as partial balance equations ,  independent balance equations  or individual balance equations . During the s it was thought local balance was a requirement for a product-form equilibrium distribution ,   but Gelenbe 's G-network model showed this not to be the case. From Wikipedia, the free encyclopedia. This article is about balance equations in probability theory. For the concept of balanced equations in chemistry, see chemical equation.
See also: Detailed balance. Reversibility and stochastic networks. March Princeton, N. Computational probability. Queueing theory. Walter de Gruyter. Markov Chains.
Cambridge University Press. Retrieved Mani ; Muntz, R.
Finally with regard to balanced equations, recall that convention dictates use of the smallest whole-number coefficients. Although the equation for the reaction between molecular nitrogen and molecular hydrogen to produce ammonia is, indeed, balanced,.
Balancing Equations Help
Dividing each coefficient by the greatest common factor, 3, gives the preferred equation:. The physical states of reactants and products in chemical equations very often are indicated with a parenthetical abbreviation following the formulas. Common abbreviations include s for solids, l for liquids, g for gases, and aq for substances dissolved in water aqueous solutions , as introduced in the preceding chapter.
These notations are illustrated in the example equation here:. This equation represents the reaction that takes place when sodium metal is placed in water. The solid sodium reacts with liquid water to produce molecular hydrogen gas and the ionic compound sodium hydroxide a solid in pure form, but readily dissolved in water. Given the abundance of water on earth, it stands to reason that a great many chemical reactions take place in aqueous media.
When ions are involved in these reactions, the chemical equations may be written with various levels of detail appropriate to their intended use. To illustrate this, consider a reaction between ionic compounds taking place in an aqueous solution. When ionic compounds dissolve in water, they may dissociate into their constituent ions, which are subsequently dispersed homogenously throughout the resulting solution a thorough discussion of this important process is provided in the chapter on solutions. Ionic compounds dissolved in water are, therefore, more realistically represented as dissociated ions, in this case:.
Unlike these three ionic compounds, AgCl does not dissolve in water to a significant extent, as signified by its physical state notation, s.
General Chemistry/Balancing Equations
Explicitly representing all dissolved ions results in a complete ionic equation. In this particular case, the formulas for the dissolved ionic compounds are replaced by formulas for their dissociated ions:. These spectator ions —ions whose presence is required to maintain charge neutrality—are neither chemically nor physically changed by the process, and so they may be eliminated from the equation to yield a more succinct representation called a net ionic equation :.
Following the convention of using the smallest possible integers as coefficients, this equation is then written:.
This net ionic equation indicates that solid silver chloride may be produced from dissolved chloride and silver I ions, regardless of the source of these ions. When carbon dioxide is dissolved in an aqueous solution of sodium hydroxide, the mixture reacts to yield aqueous sodium carbonate and liquid water. Write balanced molecular, complete ionic, and net ionic equations for this process. Begin by identifying formulas for the reactants and products and arranging them properly in chemical equation form:.
Balance is achieved easily in this case by changing the coefficient for NaOH to 2, resulting in the molecular equation for this reaction:. The two dissolved ionic compounds, NaOH and Na 2 CO 3 , can be represented as dissociated ions to yield the complete ionic equation:.
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Diatomic chlorine and sodium hydroxide lye are commodity chemicals produced in large quantities, along with diatomic hydrogen, via the electrolysis of brine, according to the following unbalanced equation:. Chemical equations are symbolic representations of chemical and physical changes.
Formulas for the substances undergoing the change reactants and substances generated by the change products are separated by an arrow and preceded by integer coefficients indicating their relative numbers. Balanced equations are those whose coefficients result in equal numbers of atoms for each element in the reactants and products.
Chemical reactions in aqueous solution that involve ionic reactants or products may be represented more realistically by complete ionic equations and, more succinctly, by net ionic equations. An equation is balanced when the same number of each element is represented on the reactant and product sides.
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Equations must be balanced to accurately reflect the law of conservation of matter. Skip to main content.
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Writing and Balancing Chemical Equations Learning Objectives By the end of this section, you will be able to: Derive chemical equations from narrative descriptions of chemical reactions. Write and balance chemical equations in molecular, total ionic, and net ionic formats. Element Reactants Products Balanced? Key Concepts and Summary Chemical equations are symbolic representations of chemical and physical changes. Exercises What does it mean to say an equation is balanced? Why is it important for an equation to be balanced? Consider molecular, complete ionic, and net ionic equations.
What is the difference between these types of equations? In what circumstance would the complete and net ionic equations for a reaction be identical? Write a balanced molecular equation describing each of the following chemical reactions. Solid calcium carbonate is heated and decomposes to solid calcium oxide and carbon dioxide gas. Gaseous butane, C 4 H 10 , reacts with diatomic oxygen gas to yield gaseous carbon dioxide and water vapor. Aqueous solutions of magnesium chloride and sodium hydroxide react to produce solid magnesium hydroxide and aqueous sodium chloride.
Water vapor reacts with sodium metal to produce solid sodium hydroxide and hydrogen gas. Write a balanced equation describing each of the following chemical reactions. Solid potassium chlorate, KClO 3 , decomposes to form solid potassium chloride and diatomic oxygen gas. Solid aluminum metal reacts with solid diatomic iodine to form solid Al 2 I 6. When solid sodium chloride is added to aqueous sulfuric acid, hydrogen chloride gas and aqueous sodium sulfate are produced.
Aqueous solutions of phosphoric acid and potassium hydroxide react to produce aqueous potassium dihydrogen phosphate and liquid water. Colorful fireworks often involve the decomposition of barium nitrate and potassium chlorate and the reaction of the metals magnesium, aluminum, and iron with oxygen.
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