Atoms are so small, however, that even atoms are too small to see or measure by most common techniques. Any readily measurable mass of an element or compound contains an extraordinarily large number of atoms, molecules, or ions, so an extremely large numerical unit is needed to count them.
There is a difference in degree, however, because the mole of anything 6. A stack of paper containing a mole of sheets would extend more than a million times the distance from the earth to the sun, and 6. Obviously there are a great many particles in a mole of anything. A mole is formally defined as the amount of substance containing the same number of discrete entities such as atoms, molecules, and ions as the number of atoms in a sample of pure 12 C weighing exactly 12 g.
Consistent with this definition, 1 mole of any element contains the same number of atoms as 1 mole of any other element. The masses of 1 mole of different elements, however, are different, since the masses of the individual atoms are drastically different.
Because the definitions of both the mole and the atomic mass unit are based on the same reference substance, 12 C, the molar mass of any substance is numerically equivalent to its atomic mass in amu. Per the amu definition, a single 12 C atom weighs 12 amu its atomic mass is 12 amu. The word "mole" suggests a small, furry burrowing animal to many.
But in this lesson, we look at the concept of the mole in chemistry. Learn the incredible magnitude of the mole--and how something so big can help us calculate the tiniest particles in the world. Although chemists usually work with moles as units, occasionally it is helpful to refer to the actual number of atoms or molecules involved.
For example, in referring to 1 mol of helium atoms, we could write. This which is defined by the equation. Since for any substance there are 6. The molar mass of a substance is defined as the mass in grams of 1 mole of that substance. One mole of isotopically pure carbon has a mass of 12 g. For an element, the molar mass is the mass of 1 mol of atoms of that element.
That is, the molar mass of a substance is the mass in grams per mole of 6. In each case, the number of grams in 1 mol is the same as the number of atomic mass units that describe the atomic mass. The periodic table lists the atomic mass of carbon as As discussed in Section 1. Step 1: Calculate the number of Cl - ions in the solution Assume the water used to make the solution does NOT contain any chloride ions, Cl -. Is your solution to the question reasonable?
Let's work backwards to see if the number of sodium ions we have calculated will give us the correct moles of chloride ions in solution. Do you know this? Do you understand this? Can you apply this?
Take the exam now! What chemical principle will you need to apply? Step 3: Solve the equation to determine the number of sodium ions GO! Go with the Plan. Ponder Plausability. Have you answered the question that was asked? Yes, we have determined the number of sodium ions in the solution. State the solution.
What is the number of sodium ions in the solution? Footnotes: 1 The Avogadro number is sometimes referred to as Loschmidt's number and is given the symbol L. N carbon dioxide molecules N A. Just like the dozen and the gross, it is a name that stands for a number. There are therefore 6.
There also would be 6. Italian scientist Amedeo Avogadro, whose work led to the concept of the mole as a counting unit in chemistry.
The number 6. It is an experimentally determined number. A representative particle is the smallest unit in which a substance naturally exists. For the majority of elements, the representative particle is the atom. Iron, carbon, and helium consist of iron atoms, carbon atoms, and helium atoms, respectively.
The representative particle for these elements is the molecule. Likewise, all molecular compounds such as H 2 O and CO 2 exist as molecules and so the molecule is their representative particle. The animal mole is very different than the counting unit of the mole. Chemists nonetheless have adopted the mole as their unofficial mascot. Use the link below to answer the following questions:. Big numbers or little numbers?
Do you hate to type subscripts and superscripts? Even with a good word-processing program, having to click on an icon to get a superscript and then remembering to click off after you type the number can be a real hassle. If we did not know about moles and just knew about numbers of atoms or molecules those big numbers that require lots of superscripts , life would be much more complicated and we would make many more typing errors. Using our unit conversion techniques, we can use the mole label to convert back and forth between the number of particles and moles.
The element carbon exists in two primary forms: graphite and diamond. How many moles of carbon atoms is 4. Step 1: List the known quantities and plan the problem. One conversion factor will allow us to convert from the number of C atoms to moles of C atoms. Step 3: Think about your result. Suppose that you wanted to know how many hydrogen atoms were in a mole of water molecules. First, you would need to know the chemical formula for water, which is H 2 O. There are two atoms of hydrogen in each molecule of water.
How many atoms of hydrogen would there be in two water molecules? How about in a dozen? To get the answers, 4 and 24 you had to multiply the given number of molecules by two atoms of hydrogen per molecule. So to find the number of hydrogen atoms in a mole of water molecules, the problem could be solved using conversion factors. The first conversion factor converts from moles of particles to the number of particles.
The second conversion factor reflects the number of atoms contained within each molecule. Two water molecules contain 4 hydrogen atoms and 2 oxygen atoms. A mole of water molecules contains 2 moles of hydrogen atoms and 1 mole of oxygen atoms. Sulfuric acid has the chemical formula H 2 SO 4. A certain quantity of sulfuric acid contains 4.
How many moles of sulfuric acid is the sample? Two conversion factors will be used. First, convert atoms of oxygen to molecules of sulfuric acid. Then, convert molecules of sulfuric acid to moles of sulfuric acid. Since each sulfuric acid molecule contains 4 oxygen atoms, there are about 20 moles of sulfuric acid molecules.
Read the relevant portions of the following article and do problems 3, 5, 9, 13, and Do not worry about the calculations involving conversions dealing with molar mass that will come next.
When creating a solution, how do I know how much of each substance to put in? I want to make a solution that contains 1. If I know the relationship between moles and the number of grams in a mole, I can use my balance to measure out the needed amount of material. Molar mass is defined as the mass of one mole of representative particles of a substance.
By looking at a periodic table, we can conclude that the molar mass of lithium is 6. Each of these quantities contains 6.
A molecular formula of the compound carbon dioxide is CO 2. One molecule of carbon dioxide consists of 1 atom of carbon and 2 atoms of oxygen. We can calculate the mass of one molecule of carbon dioxide by adding together the masses of 1 atom of carbon and 2 atoms of oxygen.
The molecular mass of a compound is the mass of one molecule of that compound. The molecular mass of carbon dioxide is The molar mass of any compound is the mass in grams of one mole of that compound. One mole of carbon dioxide molecules has a mass of The molar masses are In both cases, that is the mass of 6. The representative particle of CO 2 is the molecule, while for Na 2 S, it is the formula unit.
Calcium nitrate, Ca NO 3 2 , is used as a component in fertilizer Determine the molar mass of calcium nitrate. Step 1: List the known and unknown quantities and plan the problem. First we need to analyze the formula. Since the Ca lacks a subscript, there is one Ca atom per formula unit. The 2 outside the parentheses means that there are two nitrate ions per formula unit and each nitrate ion consists of one nitrogen atom and three oxygen atoms.
Thus, 1 mol of calcium nitrate contains 1 mol of Ca atoms, 2 mol of N atoms, and 6 mol of O atoms. Use the molar masses of each atom together with the number of atoms in the formula and add together. Read the material at the link below and work the problems at the end:.
How can we get more product? Chemical manufacturing plants are always seeking to improve their processes. One of the ways this improvement comes about is through measuring the amount of material produced in a reaction. By knowing how much is made, the scientists and engineers can try different ways of getting more product at less cost.
The molar mass of any substance is the mass in grams of one mole of representative particles of that substance. The representative particles can be atoms, molecules, or formula units of ionic compounds.
This relationship is frequently used in the laboratory. Suppose that for a certain experiment you need 3. Since calcium chloride is a solid, it would be convenient to use a balance to measure the mass that is needed. The molar mass of CaCl 2 is Dimensional analysis will allow you to calculate the mass of CaCl 2 that you should measure.
When you measure the mass of g of CaCl 2 , you are measuring 3. Calcium chloride is used as a drying agent and as a road deicer. Chromium metal is used for decorative electroplating of car bumpers and other surfaces. Find the mass of 0. One conversion factor will allow us to convert from the moles of Cr to mass. Since the desired amount was slightly more than one half of a mole, the mass should be slightly more than one half of the molar mass.
The answer has three significant figures because of the 0. A similar conversion factor utilizing molar mass can be used to convert from the mass of an substance to moles. In a laboratory situation, you may perform a reaction and produce a certain amount of a product which can be massed.
It will often then be necessary to determine the number of moles of the product that was formed. The next problem illustrates this situation. A certain reaction produces 2. Determine the number of moles produced in the reaction. One conversion factor will allow us to convert from mass to moles. The molar mass is The relatively small mass of product formed results in a small number of moles. Read the material in the link below and work the problems at the end.
How much gas is there? Avogadro was interested in studying gases. He theorized that equal volumes of gases under the same conditions contained the same number of particles. Other researchers studied how many gas particles were in a specific volume of gas. Eventually, scientists were able to develop the relationship between number of particles and mass using the idea of moles.
Now you have seen how to convert back and forth between moles and mass of a substance in grams. We can combine the two types of problems into one. Mass and number of particles are both related to grams.
In order to convert from mass to number of particles or vice-versa, it will first require a conversion to moles. Conversion from number of particles to mass or from mass to number of particles requires two steps. How many molecules is Use two conversion factors. The first converts grams of Cl 2 to moles. The second converts moles of Cl 2 to the number of molecules. The problem is done using two consecutive conversion factors.
There is no need to explicitly calculate the moles of Cl 2. How do scuba divers know if they will run out of gas? Knowing how much gas is available for a dive is crucial to the survival of the diver. A basic knowledge of gas behavior allows the diver to assess how long to stay under water without developing problems. Volume is a third way to measure the amount of matter, after item count and mass.
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