When the number of atoms of each element on the reactants and products side are equal which law is followed?

Figure 3: A forest system

Because of conservation of mass, if inputs exceed outputs, the biomass of a compartment increases (such as in an early successional forest). Where inputs and outputs are equal, biomass maintains a steady level (as in a mature forest). When outputs exceed inputs, the biomass of a compartment decreases (e.g., a forest being harvested).

Each organism has a unique, relatively fixed, elemental formula, or composition determined by its form and function. For instance, large size or defensive structures create particular elemental demands. Other biological factors such as rapid growth can also influence elemental composition. Ribonucleic acid (RNA) is the biomolecular template used in protein synthesis. RNA has a high phosphorus content (~9% by mass), and in microbes and invertebrates RNA accounts for a large fraction of an organism's total phosphorus content. As a result, fast-growing organisms such as bacteria (which can double more than 6 times per day) have especially high phosphorus content and therefore demands. By contrast, among vertebrates structural materials such as bones (made of calcium phosphate) account for the majority of an organism's phosphorus content. Among mammals, black-tailed deer (Odocoileus columbianus; Figure 6) have a relatively high phosphorus demand due to their annual investment in calcium- and phosphorus-rich antlers. Failure to meet elemental demands can lead to poor health, limited reproduction, and even extinction. The extinction of the majestic Irish Elk (Megaloceros giganteus) is thought to have been caused by the shortened growing season that occurred during the last ice age, which reduced the availability of the calcium and phosphorus these animals needed to grow their enormous antlers.

Figure 4: All types of natural and even human-designed systems can be evaluated as ecosystems based on conservation of mass.

Individual organisms, watersheds, and cities receive materials (inputs), transform them, and export them (outputs) sometimes in the form of waste.

Obtaining the resources required for metabolism, growth, and reproduction is one of the central challenges of life. Animals, particularly those that feed on plants (herbivores) or detritus (detritivores), often consume diets that do not include enough of the nutrients they need. The struggle to obtain nutrients from poor quality diets influences feeding behavior and digestive physiology and has led to epic migrations and seemingly bizarre behavior such as geophagy (feeding on materials such as clay and chalk). For example, the seasonal mass migration of Mormon crickets (Anabrus simplex) across western North America in search of two nutrients: protein and salt. Researchers have shown that the crickets stop walking once their demand for protein is met (Figure 7).

Figure 5: Comparison between elemental composition of the Earth's crust and the human body

The flip side of the struggle to obtain scarce resources is the need to get rid of excess substances. Herbivores often consume a diet rich in carbon — think potato chips, few nutrients but lots of energy. Some of this material can be stored internally, but this is a limited option and excess carbon storage can be harmful, just as obesity is harmful to humans. Thus, animals have several mechanisms for getting rid of excess elements. Excess nutrients are released in feces or urine or sometimes it is respired (i.e., released as carbon dioxide). This release of excess nutrients can influence both food webs and nutrient cycles.

Figure 6: Components of an animal's mass balance

This black-tailed deer consumes plant material rich in carbon but poor in other necessary nutrients, such as nitrogen (N). The deer requires more N than is found in its food and must cope the surplus a surplus of carbon. As a result, it must act to retain N while releasing excess carbon to maintain mass balance. Carbon and N mass balances suggest that deer waste should be carbon rich and low in N. Boxes show the abundance of N (green boxes) relative to carbon (gray boxes) in the diet, deer, and deer waste products.

A chemical reaction expresses a chemical change. For example, one chemical property of hydrogen is that it will react with oxygen to make water. We can write that as follows:

We can represent this chemical change more succinctly as

where the + sign means that the two substances interact chemically with each other and the → symbol implies that a chemical reaction takes place. But substances can also be represented by chemical formulas. Remembering that hydrogen and oxygen both exist as diatomic molecules, we can rewrite our chemical change as

This is an example of a chemical equationA concise way of representing a chemical reaction., which is a concise way of representing a chemical reaction. The initial substances are called reactantsAn initial substance in a chemical equation., and the final substances are called productsA final substance in a chemical equation..

Unfortunately, it is also an incomplete chemical equation. The law of conservation of matter says that matter cannot be created or destroyed. In chemical equations, the number of atoms of each element in the reactants must be the same as the number of atoms of each element in the products. If we count the number of hydrogen atoms in the reactants and products, we find two hydrogen atoms. But if we count the number of oxygen atoms in the reactants and products, we find that there are two oxygen atoms in the reactants but only one oxygen atom in the products.

What can we do? Can we change the subscripts in the formula for water so that it has two oxygen atoms in it? No; you cannot change the formulas of individual substances because the chemical formula for a given substance is characteristic of that substance. What you can do, however, is to change the number of molecules that react or are produced. We do this one element at a time, going from one side of the reaction to the other, changing the number of molecules of a substance until all elements have the same number of atoms on each side.

To accommodate the two oxygen atoms as reactants, let us assume that we have two water molecules as products:

The 2 in front of the formula for water is called a coefficientA number in a chemical equation indicating more than one molecule of the substance.. Now there is the same number of oxygen atoms in the reactants as there are in the product. But in satisfying the need for the same number of oxygen atoms on both sides of the reaction, we have also changed the number of hydrogen atoms on the product side, so the number of hydrogen atoms is no longer equal. No problem—simply go back to the reactant side of the equation and add a coefficient in front of the H2. The coefficient that works is 2:

There are now four hydrogen atoms in the reactants and also four atoms of hydrogen in the product. There are two oxygen atoms in the reactants and two atoms of oxygen in the product. The law of conservation of matter has been satisfied. When the reactants and products of a chemical equation have the same number of atoms of all elements present, we say that an equation is balancedA condition when the reactants and products of a chemical equation have the same number of atoms of all elements present.. All proper chemical equations are balanced. If a substance does not have a coefficient written in front of it, it is assumed to be 1. Also, the convention is to use all whole numbers when balancing chemical equations. This sometimes makes us do a bit more “back and forth” work when balancing a chemical equation.

Write and balance the chemical equation for each given chemical reaction.

1. Hydrogen and chlorine react to make HCl.
2. Ethane, C2H6, reacts with oxygen to make carbon dioxide and water.

Solution

1. Let us start by simply writing a chemical equation in terms of the formulas of the substances, remembering that both elemental hydrogen and chlorine are diatomic:

   H2 + Cl2 → HCl

   There are two hydrogen atoms and two chlorine atoms in the reactants and one of each atom in the product. We can fix this by including the coefficient 2 on the product side:

   H2 + Cl2 → 2HCl

   Now there are two hydrogen atoms and two chlorine atoms on both sides of the chemical equation, so it is balanced.

2. Start by writing the chemical equation in terms of the substances involved:

   C2H6 + O2 → CO2 + H2O

   We have two carbon atoms on the left, so we need two carbon dioxide molecules on the product side, so that each side has two carbon atoms; that element is balanced. We have six hydrogen atoms in the reactants, so we need six hydrogen atoms in the products. We can get this by having three water molecules:

   C2H6 + O2 → 2CO2 + 3H2O

   Now we have seven oxygen atoms in the products (four from the CO2 and three from the H2O). That means we need seven oxygen atoms in the reactants. However, because oxygen is a diatomic molecule, we can only get an even number of oxygen atoms at a time. We can achieve this by multiplying the other coefficients by 2:

   2C2H6 + O2 → 4CO2 + 6H2O

   By multiplying everything else by 2, we don’t unbalance the other elements, and we now get an even number of oxygen atoms in the product—14. We can get 14 oxygen atoms on the reactant side by having 7 oxygen molecules:

   2C2H6 + 7O2 → 4CO2 + 6H2O

   As a check, recount everything to determine that each side has the same number of atoms of each element. This chemical equation is now balanced.

Test Yourself

Write and balance the chemical equation that represents nitrogen and hydrogen reacting to produce ammonia, NH3.

Answer

N2 + 3H2 → 2NH3

Many chemical equations also include phase labels for the substances: (s) for solid, (ℓ) for liquid, (g) for gas, and (aq) for aqueous (i.e., dissolved in water). Special conditions, such as temperature, may also be listed above the arrow. For example,

1. From the statement “nitrogen and hydrogen react to produce ammonia,” identify the reactants and the products.

2. From the statement “sodium metal reacts with water to produce sodium hydroxide and hydrogen,” identify the reactants and the products.

3. From the statement “magnesium hydroxide reacts with nitric acid to produce magnesium nitrate and water,” identify the reactants and the products.

4. From the statement “propane reacts with oxygen to produce carbon dioxide and water,” identify the reactants and the products.

5. Write and balance the chemical equation described by Exercise 1.

6. Write and balance the chemical equation described by Exercise 2.

7. Write and balance the chemical equation described by Exercise 3.

8. Write and balance the chemical equation described by Exercise 4. The formula for propane is C3H8.

9. Balance: ___NaClO3 → ___NaCl + ___O2

10. Balance: ___N2 + ___H2 → ___N2H4

11. Balance: ___Al + ___O2 → ___Al2O3

12. Balance: ___C2H4 + ___O2 → ___CO2 + ___H2O

13. How would you write the balanced chemical equation in Exercise 10 if all substances were gases?

14. How would you write the balanced chemical equation in Exercise 12 if all the substances except water were gases and water itself were a liquid?

1. reactants: nitrogen and hydrogen; product: ammonia

3. reactants: magnesium hydroxide and nitric acid; products: magnesium nitrate and water

7. Mg(OH)2 + 2HNO3 → Mg(NO3)2 + 2H2O