Formulating Chemical Formulae Using Physical Quantities

Avogadro Constant.Avogadro Constant is the proportionality factor that relates the number of constituent particles with the amount of substance in the sample. It is the number of units in one mole of any substance. This is equal to 6.02214076 ×10²³.The units in a substance can be electrons, atoms, ions, or molecules. It depends on the nature of the substance and reaction characteristics. What else can we learn about the Avogadro number?.

Its SI unit is the multiplicative inverse of mole. That is mol⁻¹. It is named after the Italian scientist Amedeo Avogadro. Avogadro constant is denoted by NA. this means one mole of any substance contains 6.02214076 × 10²³ elementary particles.It is a dimensionless quantity. It is commonly used as a conversion factor shown here.

Faraday Constant.One Faraday represents the magnitude of the electric charge of one mole of electrons. It is equivalent to the Faraday constant. It is denoted by the symbol F. It has a universally accepted value of Faraday constant.This constant can be expressed in the merge of two other constants as F=eNA. Here, e is the charge of the electron in coulombs. NA is the Avogadro constant. Faraday constant is commonly used in electrolysis. By dividing the amount of charge in coulombs by the Faraday constant, we get the number of elements in moles that have been oxidized.

Mass Fraction.Mass fraction of species is the mass of the specie per unit mass of the mixture. An example is one gram of specie in one kilogram of a mixture. Expressed differently, in a mixture, a mass fraction is the amount of mass of one substance, divided by the mass of the total mixture. The sum of all these mass fractions is equal to 1. Therefore, mass fraction is does not have a unit. Its formula is shown here as Wᵢ.Mass percentage is the mass of the chemical, divided by the total mass and multiplied by 100.

Let’s calculate the mass fraction of CO₂ in a mixture of CO₂, O₂, N₂, and CH₄. The mass of carbon dioxide is 88.02g. We write it on top. Then in the bottom we write the masses of all of the compounds. The mass of oxygen is 319.98g. The mass of nitrogen is 1456.73g. The mass of methane is 20.86g. Therefore the mass fraction of CO₂ is 0.05. Examples of mass fraction of other specie is given in the figure. In this same way that we calculated the mass fraction of ,CO₂ the mass fraction of nitrogen, oxygen, and methane can be calculated.

Volume fraction.The volume fraction is the volume of the constituent divided by the volume of all the constituents in the mixture before mixing. It is dimensionless. It is expressed in numbers. Its unit is 1.Volume fraction also helps in finding volume percentages.Let's see another example. In a mixture of Water and Hydrochloric acid, water has a volume of 0.001m³ and Hydrochloric acid has a volume of 0.14143m³. Volume fraction of water in this mixture is 0.007 In the same way, we can find the volume fraction of Hydrochloric acid.

Mole Fraction.Mole Fraction is described as the moles of one component in the mixture divided by the number of moles of the total composition of the mixture. It is dimensionless. It is denoted by the symbol x. Can you think of any example describing mole fraction?.

From mole fraction, mole percentage can also be found as shown here.We can do this because it is a unit of amount of constituents divided by the total amount of all constituents in a mixture.Let's see a mixture with the following number of moles in it. It has 1.71 moles of N2, 0.454 moles of CO₂, 0.556 moles of H₂O and 0.969 moles of O₂. We can find the mole fraction of N2 in this mixture as shown here.Similarly, the mole fraction of CO₂, H₂O and O₂ can be found.

Mass to volume ratio.Mass to volume ratio describes density. Density is expressed in grams per cubic unit. Through this formula, any two of the values can be used to calculate the third. An easy way to remember their relationship is shown here.Density is also defined as mass per unit volume. Mass is the amount of stuff inside an object. The more the stuff there is, the more the mass.

Let's see an example. We have to find a mass for material with a density of 6.5 g/cm3 and volume of 3.5cm3. To obtain the mass we multiply the density by volume. Therefore the mass will be 22.75 gram. Let’s consider another example. The mass and volume of osmium metal are 50g and 2.22 cm3 respectively. Therefore to calculate the density we divide the mass by the volume. We obtain density will 22.5 g/cm³.

Mole to volume ratio.The most common application of this mole to volume ratio is the molar volume of gas at standard temperature and pressure. The STP is the temperature 273.15k and pressure is 1atm. One mole of an ideal gas is equal to 22.4 litre.It is also expressed in Molarity. Molarity is the number of moles of solute dissolved in one decimeter cube of solution. In other words, the number of moles of solute divided by volume of solution gives molarity.

To find molar concentration, moles have to be divided by the number of liters used in the solution. It is the amount of substance per unit volume of solution. It is expressed as mol/L. Let's see an example of 10g of acetic acid which is dissolved in 1.25L of water. Its molar concentration is taken as follows. Acetic acid has molecular formula of CH₃COOH.In order to obtain moles, we will divide the mass in grams, which is 10, by molar mass of acetic acid. So, using the molarity formula, we divide the moles by volume. By doing so, we get the molar concentration of Acetic acid as 0.1332 M.

Parts per million(ppm).Parts per million indicates about how many parts of solute are in one million parts of the solution. We can prepare 1ppm solution by dissolving 1mg of solution into 1000ml of the solvent. It is calculated as dividing the mass of solute by the mass of solution and then multiplying it by one million. Therefore, we can say 1ppm is 0.0001 percent of the solution. We can also find percentage from ppm as shown here.

It can also be expressed in different ways as milligrams per kilogram, or micro-gram per liter. For calculating ppm we have to be sure of the following. We ensure we measure it as, either mass of solute and solution, or volume of solute and solution. Both sides should be of the same unit, either mass, or volume.Let's see an example of calculating ppm of salt in water. The solution has 0.007g of salt and a solution of 1 kilogram. First, we will convert the mass of salt grams to kilograms. Then we can calculate ppm by multiplying a decimal by 1 million.

Parts per billion(ppb).It is a smaller concentration than ppm. Substances concentrations are converted to ppb when these are extremely volatile to human life and biological systems. These types of concentrations mandates careful monitoring. It is a thousand times a million, greater in magnitude than a million.ppb can be calculated as shown here.

It is the number of units of mass of a substance per 1000 million units of total mass solution. These are used to measure the concentration of a contaminant in soils and sediments.For example soil having 6 ppm will have ppb as shown here.

Empirical Formula.It is the simplest whole number ratio of atoms in a compound. It gives the proportions of the elements in the compound but not the actual numbers or arrangement of atoms. This is the lowest whole number ratio of elements in the compound.How would you find the empirical formula of a compound? An example of an empirical formula is shown here.

To calculate the empirical formula first have to find the mass percentage of elements in the compound. Then we have to change percentage to grams. Then will have to decide all the masses by their respective molar masses. Pick out the smallest answer of moles and divide all by that. This resulted coefficient will be the subscripts in the chemical formula.Let's see an example of an compound containing 32.65% sulfur 65.3% oxygen and 2.04% hydrogen. Its emperical formula is calculated in given illustration.

Molecular formula.Molecular formula presents the ratio of atoms that constitute the compound. It is a representation of a molecule that uses chemical symbols to indicate the types of atoms followed by subscript. It shows the number of atoms of each type in the molecule. It is a chemical formula that gives the total number of atoms of each element in each molecule of a substance. A subscript when written after the symbol indicates the number of atoms of each element in the molecule.

To calculate the molecular formula these steps have to be followed. Let's see this as an example where a white powder is analyzed and found to have an empirical formula of P₂O₅. The compound has a molar mass of 283.88g. Molecular formula of compound is calculated in illustration.

The Relationship between the empirical and molecular formula.In general empirical formula is multiplied by a whole number n, which gives the molecular formula. Molecular formula is equal to the empirical formula multiplied by n as shown. Here n is an integer, and its value can be calculated as shown here.Similarities between empirical and molecular formula.They both indicate all the elements of a compound. Both indicate the ratio of atoms to each element in the compound.

Differences between empirical and molecular formula.The empirical formula expresses the smallest whole number ratio of atoms in the compound. Ionic compounds are always written in the empirical formula, such as in NaCl and HCl.The molecular formula is the actual formula of a compound that gives the number and type of each atom. Covalent compounds are always written in the molecular formula, such as in as CO₂.

Deriving molecular formulas by measuring physical quantities.Physical quantities are the physical property of a material that can be quantified by measurement. It can be expressed as a numerical value with the unit. Some examples of physical quantities are mass, length, time, temperature, force, velocity and density. We can derive molecular formula from mass and molar mass which are physical quantities.

Let's see an example where the molecular formula has to be determined. If there is a compound with an empirical formula of CF₂ and a molar mass of 200.04 g/mol, how do we calculate the molecular formula? The molecular mass is 200.04g/mol. But we do not know the empirical formula mass. To calculate that we determine atomic masses of atoms from the periodic table and add those masses are added according to the empirical formula as given in the illustration.

Some nontrivial examples.As molecules mass is also equal to vapor density multiplied by 2. We can derive molecular formulas by density physical quantity. Example. Compound 'A' is found to contain 36.5% of Na, 25.4% S and 38.1% of O. Its vapor density is 63. Its molecular formula is determined in illustration.

Determine the molecular formula of a compound containing 6.67% of Hydrogen, 40% of Carbon and 0.6g of compound contained in 224cc at NTP. Carbon and Hydrogen contain 40% and 6.67% of 100% respectively. Therefore, the remaining is taken up by oxygen. Now, we calculate the empirical formula of compounds as shown in the table. As we know weight divided by molar weight is equal to volume divided by molar volume so we can calculate molar weight of oxygen as given in illustration. Molecular formula is calculated in illustration as C₂H₄O₂.