A mole is a unit used to measure the amount of a substance. It allows us to count particles on a macroscopic scale rather than trying to count individual atoms or molecules. The mole relates the mass of a substance to the number of constituent particles in that substance.
To calculate the amount in moles of a substance, we need to know its molar mass. The molar mass of an element tells us the mass of one mole of that element in grams. For magnesium (Mg), the molar mass is 24.305 grams per mole.
So to calculate the mass of one mole of magnesium, we would multiply the molar mass (24.305 g/mol) by the number of moles we want, in this case 1 mole:
Mass of 1 mole of Mg = 24.305 g/mol x 1 mole = 24.305 g
Therefore, the mass of 1 mole of magnesium is 24.305 grams.
Where Does the Molar Mass Come From?
The molar mass of an element comes from the atomic mass of that element on the periodic table. Specifically, it is the atomic mass in atomic mass units (amu) multiplied by the molar mass constant.
The molar mass constant converts atomic mass units into grams per mole. It has a value of 1 g/mol.
So the molar mass is calculated as:
Molar mass (g/mol) = Atomic mass (amu) x Molar mass constant (1 g/mol)
On the periodic table, magnesium has an atomic mass of 24.305 amu. Therefore:
Molar mass of Mg = 24.305 amu x 1 g/mol = 24.305 g/mol
So the molar mass of 24.305 g/mol for magnesium comes directly from magnesium’s atomic mass in amu, converted to grams per mole using the molar mass constant.
Converting Grams to Moles
We can also calculate the number of moles represented by a certain mass of a substance using its molar mass.
For example, say we have 55 grams of magnesium. We can convert this to moles using the molar mass as a conversion factor:
55 g Mg x (1 mol Mg/24.305 g Mg) = 2.26 moles Mg
So 55 grams of magnesium equals 2.26 moles of magnesium.
In general:
Moles = Mass (g) / Molar mass (g/mol)
This allows us to interconvert between mass in grams and amount in moles for any substance just using its molar mass.
Molar Mass of Compounds
For compounds and molecules made up of multiple elements, the molar mass is calculated by summing the atomic masses of each element multiplied by the number of atoms of that element.
For example, for magnesium chloride (MgCl2):
– 1 Mg atom (molar mass 24.305 g/mol)
– 2 Cl atoms (molar mass 35.453 g/mol)
So the molar mass of MgCl2 is:
Molar mass MgCl2 = (24.305 g/mol x 1) + (35.453 g/mol x 2) = 95.211 g/mol
In general, the molar mass of a compound is calculated using:
Molar mass = (molar mass of element 1) x (number of atoms of element 1) +
(molar mass of element 2) x (number of atoms of element 2) +
…and so on for each element in the compound
This allows us to find the molar mass of ionic compounds like magnesium chloride as well as covalent molecular compounds.
Molarity
Another common unit related to moles is molarity. Molarity (M) represents the moles of solute dissolved per liter of solution.
It is calculated using:
Molarity (M) = Moles solute / Liters solution
For example, to make a 2 M solution of magnesium chloride, you would need:
2 moles MgCl2 / 1 L solution
So you would dissolve 2 moles (190.422 g) of MgCl2 into enough water to make 1 liter of final solution.
The molarity gives the concentration of a solution on a per liter basis. It is useful for many chemistry calculations involving reactions and stoichiometry.
Stoichiometry Using Moles
Moles are useful for stoichiometry problems where you need to relate quantities of reactants and products in a chemical reaction.
For example, consider the reaction between magnesium and hydrochloric acid:
Mg (s) + 2 HCl (aq) → MgCl2 (aq) + H2 (g)
If we start with 1.00 mole of Mg, we can convert between moles of the other substances using mole ratios from the balanced reaction:
1.00 mol Mg x (2 mol HCl / 1 mol Mg) = 2.00 mol HCl
1.00 mol Mg x (1 mol MgCl2 / 1 mol Mg) = 1.00 mol MgCl2
1.00 mol Mg x (1 mol H2 / 1 mol Mg) = 1.00 mol H2
So using mole ratios derived from the coefficients in the balanced equation allows us to quantitatively relate the reactants and products.
Limiting Reactants
When amounts of reactants are given, the reactant present in the lesser amount is the limiting reactant – it limits how much product can be formed.
For example, if we start with 2 moles of Mg and 1 mole of HCl in the reaction above, HCl is limiting because the Mg:HCl ratio in the balanced equation is 1:2.
We can only make as much product as the HCl allows:
1 mol HCl x (1 mol MgCl2 / 2 mol HCl) = 0.5 mol MgCl2
Even though Mg is in excess, the maximum MgCl2 that can be formed is limited by the HCl.
Identifying the limiting reactant is key for determining the theoretical yield in a chemical reaction.
Percent Yield
The theoretical yield is the maximum mass of product that can be formed based on the amount of limiting reactant.
The actual yield is the amount you truly produce in a reaction.
Percent yield relates the actual yield to the theoretical yield:
Percent Yield = (Actual yield/Theoretical yield) x 100%
For example, if the theoretical yield of MgCl2 was 50.0 g but your actual yield was only 40.0 g:
Percent Yield = (40.0 g / 50.0 g) x 100% = 80%
So you achieved 80% efficiency in this reaction. Knowing the percent yield helps you identify how much product was lost during the reaction.
Empirical Formulas
Moles can also be used to calculate empirical formulas. An empirical formula shows the simplest whole number ratio of elements in a compound.
For example, benzene has an empirical formula of CH because it contains a 1:1 ratio of carbon to hydrogen.
To determine an empirical formula based on mass data:
1. Convert masses of each element to moles
2. Divide moles of each element by the smallest number of moles
3. Whole number subscripts in the formula are the resulting ratios
This converts mass data to the simplest mole ratio which reveals the empirical formula.
Molarity and Solution Stoichiometry
Molarity can be used for solution stoichiometry calculations.
For example, if you react 50.0 mL of 2.00 M HCl with 25.0 mL of 1.50 M Mg(OH)2:
1) Convert volumes to moles using molarity:
50.0 mL HCl x (2.00 mol HCl / 1 L) = 0.100 mol HCl
25.0 mL Mg(OH)2 x (1.50 mol Mg(OH)2 / 1 L) = 0.0375 mol Mg(OH)2
2) Use mole ratio from balanced reaction:
2 mol HCl: 1 mol Mg(OH)2
0.100 mol HCl x (1 mol Mg(OH)2 / 2 mol HCl) = 0.0500 mol Mg(OH)2
So 0.0500 moles of Mg(OH)2 will react with the provided HCl.
Molarity allows you to move between solution volume, concentration, and moles.
Conclusion
In summary, here are some key points for calculating moles:
– The mole is a unit for amount of substance based on Avogadro’s number (6.022 x 1023 particles/mole).
– Molar mass (g/mol) allows conversion between mass and moles. It is equal to the atomic mass for elements and the sum of atomic masses for compounds.
– Moles = Mass (g) / Molar mass (g/mol) for any substance.
– Molarity (M) gives moles solute per liter of solution.
– Moles can be used to relate reactants and products in chemical reactions through mole ratios derived from the balanced equation.
– Limiting reactants limit yield; percent yield relates actual yield to theoretical yield.
– Empirical formulas show the simplest whole number mole ratios.
– Molarity allows easy conversion between volume, concentration and moles for solutions.
Understanding moles and molar conversions is fundamental to quantitative chemistry calculations involving mass, volume and stoichiometry.