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VI Calculations with Chemical Formulas and Equations
The Mole Concept: Mole (mol) is S.I. Unit for amount of substance
We buy a quantity of groceries in several ways. If you buy eggs, you buy then by
the dozen-that is by number. Eggs are easy to count out. So are oranges and apples.
Other items, though countable, are more conveniently sold by mass. A dozen of peanuts
is too small a number to buy, and the several hundreds are too difficult to count. We buy
peanuts by the pound or by the gram-that is, by mass. The quantity of an element or a
compound, which like grocery items, can be measured by number or by mass. Molecules
and atoms are extremely small objects - both in size and mass. Consequently, working
with them in the laboratory requires a large collection of them. How large does this
collection need to be? Chemists have adopted the mole concept as a convenient way to
deal with the enormous numbers of atoms, molecules or ions in the sample they work
with.
Definition of mole:
The mole is based upon the carbon-12 isotope. The next question we ask is how many
carbon-12 atoms are needed to have a mass of exactly 12 g.
The term mole, like dozen, thus refers to a particular number of things. 1 dozen = 12
objects. A dozen of eggs equals 12 eggs and a mole eggs equals 6.022 x 1023 of eggs.
Avogadro’s number is an incredibly large number - almost a trillion trillion. For example,
if we stack NA pennies on top of one another how tall would the stack be? The answer is
it would be so tall that the stack of pennies could reach the sun and back almost 500
million times!
Recall that the atomic mass unit (amu) is defined as 1/12 the mass of a carbon-12 atom.
Consequently we have the relation
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Thus, a mole of carbon-12 atoms has a mass of just 12 g. What about other atoms? In the
periodic table the atomic mass of the elements is given. For example the atomic mass of
magnesium is 24.305 amu. This is the average isotopic mass of naturally occurring
magnesium. What is the molar mass of magnesium in grams?
From the equation above we get
This example demonstrates that the atomic mass of magnesium can be interpreted in one
of two ways: (1) the average mass of a single magnesium atom is 24.305 amu or (2) the
average mass of a mole of magnesium atoms is 24.305 g;
A similar conclusion follows for all of the other elements.
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Quick-Think
E. g. Both empirical and molecular formula of halothane is C2HBrClF3; What is its
molecular mass and its molar mass?
E.g. What is the mass in gram of a chlorine atom, Cl?
E.g. What is the mass in grams of a hydrogen chloride molecule?
Avogadro's number, the mole concept, formula units and molar mass allow us to convert
among masses, moles and number of atoms or molecules.
Formula
Units
related by
Avogadro's
number
Mole
relate to
grams by
Molar mass
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Now that we know how to find the mass of one mole of substance, there are two
important questions to ask. First, how much does a given number of moles of a substance
weigh? Second, how many moles of a given formula unit does a given mass of substance
contain? Consider the conversion of grams of sodium chloride to moles of sodium
chloride. The molar mass of sodium chloride is 58.44 g/mole, so we can write
1 mol NaCl = 58.44 g
Thus, the factor converting grams of NaCl to moles of NaCl is 1mol NaCl/ 58.44 g NaCl
Suppose we are going to use 10.0 g of NaCl, how many mole of NaCl is this?
E.g Zinc iodide can be prepared by the direct combination of elements. A chemist
determines from the amounts of elements that 0.0654 mol of zinc iodide can be form.
How many grams of zinc iodide is this?
The preceding examples show how we can relate moles and mass. The next example
shows how to calculate the number of molecules in a given mass.
E.g. How many HCl molecules are there in 3.46 kg of hydrogen chloride?
E.g. How many H atoms are present per mole of water?
Determining Chemical Formulas
When a chemist has discovered a new compound, the first question to answer is, what is
the formula? To determine this, we begin by analyzing the compound into amounts of
elements for a given amount of compound. This is conveniently expressed as percentage
composition-that is, as the mass percentages of each element in the compound. We then
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determine the formula from this percentage composition. We must also know the
molecular mass of the compound in order to determine the molecular formula.
1) Mass Percentages from the Formula
Suppose that A is a part of something. It could be an element in a compound or one
substance in a mixture. We define the mass percentage of A as the part of A per hundred
parts of the total, by mass. That is
We can look at the mass percentage of A as the number of grams of A in 100 grams of
the whole.
E.g. Calculate the percentage composition from formula. What is the mass percent
composition of formaldehyde, CH2O?
E.g Calculating the mass of an element in a given mass of compound. How many grams
of carbon are there in 83.5 g of CH2O?