Balanced chemical reactions ( RXN ) represent reactions in which perfect ratios of reactants and products react. Let’s consider a photosynthetic RXN where glucose reacts with molecular oxygen to form carbon dioxide, water, and energy:
C6H12O6 + 6O2 → 6CO2 + 6H2O + energy
In the subatomic world, a single molecule of glucose reacts with six moles of molecular oxygen to form six molecules of carbon dioxide, six molecules of water, and energy. In a laboratory setting, it would be convenient to measure quantities of reactants that directly replicate the subatomic ratios of reactants needed to react completely with one another. In such a scenario, the quantities of products formed will be directly proportional to the quantities of molecules produced in a subatomic RXN. In order to see how this is done, let’s consider a circumstance in which 1 gram of hydrogen ions is used to represent a single hydrogen ion ( 1 amu ) within a laboratory.
Recall that a single hydrogen ion is a proton, and it is interchangeably referred to as an atomic mass unit ( 1 amu ). A single proton and neutron both have an approximate mass of 1/12 of a carbon-12 atom: 1 amu = ( 1.622 x 10-24 g ). The mass of 1 amu is sometimes referred to as a dalton ( Da ). Since a single amu is much smaller than a gram, some multiple of amu are contained in 1 g of hydrogen. This number of atoms is referred to as Avogadro’s Number, and it is derived in the following manner:
( 1 g / 1.622 x 10-24 g ) = 6.165 x 1023 molecules.
This quantity of molecules is referred to as being a “ mole “ of atoms, and the accepted value of the number of atoms contained within a mole of atoms is 6.022 x 1023. Therefore, 1 gram of hydrogen ( 1 mole ) will contain 6.022 x 1023 atoms.
Let’s now compare a hydrogen ion to a carbon atom. A hydrogen atom has a mass of 1 amu, and a carbon-12 atom has a mass of 12 amu ( protons and neutrons ). Since a mole of hydrogen has a mass of 1 g, a mole of carbon-12 atoms will be twelve times more massive. For this reason, a mole of carbon-12 has a mass of 12 g. A mole of any atom or molecule will have a mass ( in grams ) that is proportional to how many atomic mass units ( amu ) it contains:
Q: What is the mass of a mole of oxygen atoms? How many atoms are contained within a mole of oxygen atoms?
A: The mass of a mole of oxygen is 16 g, and there are 6.022 x 1023 atoms in a mole of oxygen.
Q: What is the mass of a mole of molecular oxygen? How many atoms are contained in a mole of molecular oxygen?
A: Recall that molecular oxygen is diatomic; therefore, a molecule of oxygen ( O2 ) contains 32 amu. As a consequence, a mole of O2 has a mass of 32 g. Furthermore, a mole of oxygen molecules contains 6.022 x 1023 molecules.
IN SI UNITS, THE MOLAR MASS IS EXPRESSED AS THE MASS IN KILOGRAMS ( kg ) OF AN ATOM OR MOLECULE CONTAINED WITHIN A MOLE ( kg / mol ). By convention, the molar mass is expressed in ( g / mol ) for a given atom or molecule. And a mole of any substance always contains 6.022 x 1023 molecules.
Within a laboratory, the coefficients that precede the atoms ( or molecules ) in a balanced reaction are represented as moles of each substance. In this way, measurements of reactants ( in grams ) in the laboratory can be made in proportion to the number of atoms ( or molecules ) in the reactants and products of a RXN sequence:
Q: How many moles of glucose, oxygen, carbon dioxide, and water are contained in a balanced RXN?
C6H12O6 + 6O2 → 6CO2 + 6H2O + energy
A: One mole of glucose and six moles of molecular oxygen react to form six moles of carbon dioxide and six moles of water.
Q: What is the mass of one mole of carbon dioxide? What quantity of molecules are contained in a mole of carbon dioxide? What quantity of atoms are contained in six moles of carbon dioxide? What is the mass of six moles of carbon dioxide?
A: One mole of carbon dioxide has the quantity of amu contained in its carbon and oxygen atoms. A carbon atom contains 12 amu in its nucleus. Two oxygen atoms contain 32 amu; therefore, a mole of carbon dioxide has a mass of ( 12 g + 32 g ) = 44 g / mol. A mole of carbon dioxide contains 6.022 x 1023 molecules. The quantity of molecules contained within six moles of carbon dioxide is ( 6 mol CO2 )( 6.022 x 1023 molecules CO2 / mol CO2 ) = 3.613 x 1033 molecules.
We are now ready to define the concentration of a substance in terms of molarity ( M ). The molarity ( M ) of a solution is defined as the moles of an atom or molecule contained in a liter ( L ) of solution:
Q: How can a 1M solution of sodium chloride in distilled water be prepared in a laboratory?
A: A mole of sodium chloride ( NaCl ) has a molar mass of 58.44 g / mol. A 1M solution of NaCl in distilled water can be prepared by dissolving 58.44g of NaCl in 1L of distilled water.
Q: What mass in grams ( g ) is contained in 5L of a 5M solution of NaCl?
A: A 5M solution of NaCl contains [ ( 5 )( 58.44 g ) ] / L = 292.2 g / L. Within 5L of a 5M solution of NaCl, there are ( 292.2 g / L )( 5L ) = 1,461 g or 1.461 kg of NaCl.
Q: How many atoms of NaCl are contained in a 5L of a 5M solution of NaCl?
A: 5L of a 5M solution of NaCl contains ( 5M )( 5L ) = 25 mol NaCl. Since a mole of any atom or molecule contains 6.022 x 1023 atoms, ( 25 mol NaCl )( 6.022 x 1023 atoms / mol ) = 1.5 x 1025 atoms.
There are many circumstances where the quantities of reactants needed to go to completion in a reaction are not balanced. In these circumstances, one of the reactants is in excess of what is needed to react with another reactant. For this reason, the reactant that is not in excess will limit the quantities of products that can be formed in a reaction. This reactant is referred to as being a limiting reagent. Once the quantity of a limiting reagent is consumed, an excess of the other reactant ( or reactants ) will remain. The first challenge is to determine which reactant in a given circumstance is the limiting reagent. This is accomplished using a balanced equation:
Q: What mass of carbon dioxide forms in a reaction between 25 grams of glucose and 40 grams of molecular oxygen?
C6H12O6 + 6O2 → 6CO2 + 6H2O + energy
A: One mole of glucose reacts with six moles of molecular oxygen to form six moles of carbon dioxide and six moles of water. Let’s first determine how many moles are in 25 grams of glucose and 40 grams of molecular oxygen:
( 25 g C6H12O6 )( 1 mol C6H12O6 / 180.06 g C6H12O6 ) = 0.1388 mol C6H12O6
( 40 g O2 )( 1 mol O2 / 32 g O2 ) = 1.25 mol O2
Let’s now use the balanced reaction to determine which of these two reactants is the limiting reagent. The reaction indicates that one mole of glucose reacts with six moles of oxygen:
C6H12O6 + 6O2 → 6CO2 + 6H2O + energy
Since there are 1.25 mol O2 available to react, we can use the molar relationship established by the balanced reaction to see how many moles C6H12O6 would be needed for a reaction to go to completion:
( 1.25 mol O2 )( 1 mol C6H12O6 / 6 mol O2 ) = 0.208 mol C6H12O6
0.208 moles of C6H12O6 will be consumed in a complete reaction with 1.25 mol O2 . This is greater than the 0.1388 mol C6H12O6 that is actually available to react with O2. Therefore, C6H12O6 is the limiting reagent.
Likewise, we can use the molar relationship established by the balanced reaction to see how moles of O2 would be needed for a reaction to go to completion:
( 0.1388 mol C6H12O6 )( 6 mol O2 / 1 mol C6H12O6 ) = 0.8328 mol O2
0.8328 moles of O2 will be consumed in a complete reaction with 0.1388 mol C6H12O6. This is less than the 1.25 mol O2 that is actually available to react with C6H12O6. Therefore, the O2 molecule is in excess.
We can also use the molar ratio of O2 and C6H12O6 available to determine which reactant is the limiting reagent. The balanced chemical reaction indicates that six moles of molecular oxygen are required to react with every mole of glucose present; therefore, there is a 6:1 molar ratio between oxygen and glucose in a balanced reaction:
C6H12O6 + 6O2 → 6CO2 + 6H2O + energy
As we have seen, there are 25 grams of glucose and 40 grams of molecular oxygen available to react. This corresponds to there being 0.1388 moles of glucose available to react, and there are 1.25 moles of molecular oxygen available to react. If the ratio of the moles oxygen and glucose available to react is less than the 6:1 ratio required in a balanced reaction, this will indicate that not enough oxygen is present to make the reaction go to completion ( the denominator is too large ). If the molar ratio of the moles of oxygen and glucose available to react is greater than 6:1, this will indicate that not enough glucose is available to make the reaction go to completion ( the denominator is too small ). The molar ratio of the moles of oxygen and glucose available to react is as follows:
( 1.25 mol O2 / 0.1388 mol C6H12O6 ) = 9:1 ratio ( ignoring significant figures ) of the oxygen to glucose moles available to react. This indicates that the amount of oxygen is in excess, and glucose is the limiting reagent:
Q: How many moles of excess oxygen remain after the reaction goes to completion?
A: 1.25 moles O2 – 0.8328 moles O2 = 0.417 moles O2 remain.
RENAISSANCE PHYSICS 