Name ______Date ______Period ______

Chemical Quantities

Tutorial

The Mole

The mole is the SI unit for the quantity of a substance. The mole is a counting unit, very much like a dozen is a counting unit. One dozen means 12 items. The mole is no different, except that the number is very large. Since atoms and molecules are very small, their counting unit is a very large number.

One mole of a substance contains 6.022 x 1023representative particles of the substance. This number is called Avogadro’s number. Representative particles could be atoms, molecules, electrons, or any other similar particle.

Converting between moles and particles

Avogadro’s number is the conversion factor used to convert between moles and particles. You will use dimensional analysis to make these conversions.

Example: Determine the number of moles of carbon in 2.25 x 10 25 atoms of carbon.

Example: Determine the number of atoms of iron (Fe) in 2.8 moles of iron.

1001A Moles-Particles Conversions

Calculate the following. Show your work. Answer in scientific notation. Ask for help if you cannot get the right answer.

  1. If you have 1.204 x 104 molecules of H2, how many moles of H2 do you have? (2.000 x 10-20 mol)
  2. How many molecules of N2 are there in 0.035 moles of N2? (2.1 x 1022 molecules)
  3. You have 5.80 x 1012 atoms of sulfur, how many moles of sulfur do you have? (9.63 x 10-12 mol)
  4. How many atoms of Cu are there in 12.9 moles of Cu? (7.77 x 1024 atoms)
  5. If you have 5.00 millimoles of iron, how many atoms of iron are present? (3.01 x 1021atoms)
  6. 8.70 x 1025 atoms of Al are equivalent to how many moles of Al? (144 mol Al)
  7. How many moles of Br2 are present if you have 1.85 x 1020 molecules of Br2? (3.07 x 10-4 mol)
  8. If you have 4.66 x 1030 molecules of Cl2, how many moles of Cl2 are present? (7.74 x 106 mol)
  9. How many molecules of O2 are there in 27 moles of O2? (1.6 x 1025 molecules)
  10. What number of millimoles of I2 are present in 3.05 x 105 molecules of I2? (5.06 x 10-16 mmol)
  1. How many atoms are present in 4.2 μmol of Sn(tin)?

Molar Mass

The molar mass of a substance is the mass (in grams) of one mole of the substance. So, it is the mass of Avogadro’s number (6.02 x 1023) of particles of substance. Molar mass is related to atomic mass. Atomic mass is the average mass of an atom of an element in amu’s (atomic mass units). The molar mass of the element is the same number as the atomic mass, except the units are in g/mol. Study the table below to see the relationship between atomic mass and molar mass of selected elements.

Element / Atomic mass (amu) / Molar mass (g/mol)
Ne / 20.18 / 20.18
K / 39.10 / 39.1
Zn / 65.39 / 65.39
Pb / 207.2 / 207.2

Molar Mass of Molecules

The molar mass of molecules is simply the sum of the molar masses of the elements that make up the compound. In the event that there is more than one atom of a particular element, simply multiply the molar mass by the subscript. The molar mass of carbon dioxide, CO2, would be calculated as follows.

ElementMol Mass x Subscript

C 12.01 x 1 = 12.01

O 16.00 x 2 = + 32.00

Mol Mass 44.01 g/mol

The molar mass of calcium hydroxide, Ca(OH)2 would be ….

ElementMol Mass x Subscript

Ca 40.08 x 1=40.08

O 16.00 x 2=32.00

H 1.01 x 2= + 2.02

Mol Mass74.10 g/mol

Practice

Calculate the molar mass of the following substances. Round your numbers to two decimal places. If you are not getting the correct answer, figure out why. If your answer is off by a few decimals, don’t worry about it. Some periodic tables have slightly different atomic masses. If you cannot find your mistake, ask for help.

Formula / Molar Mass
(g/mol) / Name
Br2 / 159.80 / bromine
N2O4 / 92.02 / dinitrogentetroxide
H3PO4 / 98.00 / phosphoric acid
C6H12O6 / 180.18 / glucose
CH3COONa / 82.04 / sodium acetate

1001B Molar Mass Calculations

Calculate the molar mass of the following substances. Remember that subscripts indicate how many of the atoms (or groups inside parentheses) are present in the molecule.

David Scott, Chemistry, Rev. 20131

Name ______Date ______Period ______

  1. KOH______
  2. H2O______
  3. NH3______
  4. Mg(OH)2______
  5. NH4OH______
  6. C6H6______
  7. C6H12O6______
  8. Fe(NO3)2______
  9. HCl______
  10. (NH4)3PO4______
  11. H2SO4______
  12. Na2SO4______
  13. Al(PO4)3______
  14. KH2PO4______
  15. NaCl______
  16. HNO3______
  17. CuSO4______
  18. MnO2______
  19. KMnO4______
  20. KBr______

David Scott, Chemistry, Rev. 20131

Name ______Date ______Period ______

Converting between moles and mass

Molar mass is the conversion factor to convert mass to moles and moles to mass. Again, how you use your conversion factor depends upon what is being converted to what. Your units will guide you as to whether you multiply or divide by molar mass.

1002C Practice mass-moles conversions

Calculate the number of moles in the following. Show your work.

  1. 110 grams of NaHCO3______
  2. 1.1 grams of FeCl3______
  3. 987 grams of Ra(OH)2______
  4. 564 grams of zinc______
  5. 12.3 grams of CO2______
  6. 89 grams of Pb(C2H3O2)4______
  7. 30 grams of H3PO4______
  8. 25 grams of HF______
  9. 1.5 kg of AlBr3______
  10. 38.0 mg Pb(NO3)2______

1002D Calculate the mass of each of the following. Show your work.

  1. 4 moles of Cu(CN)2______
  2. 9.6 moles of C6H6______
  3. 25.3 moles of BaCO3______
  4. 1.7 moles of (NH4)3PO3______
  5. 9.30 mmoles of TiO2______
  6. 5.6 moles of ZnSO4______
  7. 5.4 moles of K2SO4______
  8. 88.4 moles of NBr3______
  9. 2.65 moles CuSO4______
  10. 6.25 μmol C6H12O6______

Moles and Volumes of Gas

Tutorial

In addition to determining Avogadro’s number, Avogadro also is famous for his study of gases. Avogadro determined that the volume of a gas was directly proportional to the moles of gas. This is known, as you might expect, Avogadro’s Law. We will learn more about this when we study gases.

The volume of a gas is greatly affected by pressure and temperature, in addition to the number of moles of gas. Because of this a set of standard conditions is used to describe gases, known as standard temperature and pressure, or STP. Know the following conditions which defineSTP.

Standard Temperature / 0°C / 273°K
Standard Pressure / 1 atm
(atmosphere) / 101.3 kPa
(kilopascals)

At STP, one mole of any gas, regardless of its composition or molar mass, occupies 22.4 liters volume. This gives us another conversion factor when dealing with gases at STP. Study the examples below. All examples are at STP.

  1. Find the volume of 0.50 mol of N2 gas at STP.
  1. How many moles of He are there in a balloon with a volume of 15.0 L at STP?
  1. Find the volume of 45.0 grams of Ne gas at STP.
  1. What mass of argon is contained in a light bulb that has a volume of 0.05L?

Practice by solving the problems on the next page. Show your work. Answers are provided. If you are not getting the correct answers, determine where you are making mistakes. If you cannot find your mistakes, ask for help.

1002E Calculating Moles and Volumes of Gas. Show your work!

  1. Determine the volume of 0.60 moles of NH3 gas at STP. (13 L)
  1. Find the volume of 3.20 x 10-3 mol of CH4 at STP. (7.17 x 10-2 L)
  1. What is the volume of 3.90 mol of N2 gas at STP? (87.4 L)
  1. Calculate the volume, at STP, of 1.67 mol of SO2. (37.4L)
  1. Determine the volume of 0.375 mol of C2H6 (ethane) gas at STP. (8.40 L)
  1. An empty 1 gallon container is filled with CO2 at STP. How many moles of CO2 are in the container? (1 gal = 3.785 L) (0.169 mol)
  1. How many moles of air (a mixture of gases) is contained in an empty 500 mL water bottle? (0.022 mol)
  1. What mass of CO2 is contained in a 2.5 L container at STP? (4.91 g CO2)
  1. Determine the mass of propane (C3H8) that fills a 5.0 gallon container at STP (1 gal = 3.785 L). (37 g)
  1. Calculate the number of molecules of methane (CH4) in a 2.00 L container at STP. (5.38 x 1022 molecules CH4)

Challenge:

  1. Determine the mass and volume of 1.59 x 1025 molecules of propane (C3H8) at STP. (591 L; 1160 g)

Calculating Molar Mass from Density

Recall from an earlier chapter that density is the ratio of mass to volume.

Objects that have a mass greater than their surrounding medium will sink. For example, a stone sinks in water because it has a greater density than the water. The same is true of gases. If a gas has greater density than air, it will sink in air. If a gas has less density than the surrounding air, it will rise in the air.

Different gases have different densities. Because the densities of gases are much lower than the density of liquids or solids, they are usually reported in units of g/L. The density of a gas depends upon pressure and temperature, so the conditions in which density is measured must be known. For now, we will use STP conditions.

The molar mass of a gas can be calculated, if its density is known, using the molar volume of gas.

Molar mass = density x molar volume of gas. Dimensional analysis will show that this is true

For example, determine the molar mass of a gas having a density of 3.58 g/L at STP.

1002F Practice: density, volume, and molar mass of gases

Solve the following conversion problems. Show your work. Ask for help if you are unable to get the correct answer.

  1. What is the molar mass of a gas having a density of 0.715 g/L? (16 g/mol)
  1. A gas is known to have a density of 1.342 g/L. What is its molar mass? If the gas is composed only of carbon and hydrogen, what is the molecular formula for the gas?
  1. Calculate the density of propane (C3H8) at STP. (1.96 g/L)
  1. What is the density of the noble gas neon (Ne) at STP? (0.902 g/L)
  1. Which gas has the greater density at STP, CO2 or N2?
  1. Find the volume, at STP, for 835 g of SO3. (234 L SO3)
  1. What mass of helium is needed to inflate a balloon to 5.50 L at STP? (0.982 g He)
  1. What is the density of nitrogen dioxide (NO2) at STP? (2.05 g/L)
  1. What is the mass of 50.0 L of CO2 STP? (98.2 g CO2)
  1. How many kilograms of methane (CH4) are needed to fill a 2.00 x 103L canister at STP? (1.43 kg CH4)

1003G Percent Composition and Chemical Formulas

In chemistry, when we speak of percent composition, we usually mean percent mass. So, the percent composition of a substance is mass of each part of the substance relative to the entire mass.

The percent by mass of an element in a compound is the mass of the element divided by the mass of the compound, multiplied by 100.

For example, find the percent mass of each element in the ammonia, NH3.

Practice: Percent Composition by Mass

Determine the percent composition by mass of each element in the compound….

  1. A sample of a compound contains 13.4 grams of chromium, 16.45 grams oxygen, and 20.15 g potassium. Determine the percent composition of each element in the compound.
  1. Magnesium 9.03 g combines with nitrogen 3.48 g. What is the percent composition of the compound?

David Scott, Chemistry, Rev. 20131

Name ______Date ______Period ______

  1. BeCl2
  1. FeCl3
  1. BF3
  1. CCl2F2
  1. Mg(OH)2
  1. H3PO4
  1. CH3COOH
  1. (NH4)2SO4
  1. Ga2(SO3)3
  1. KOH

David Scott, Chemistry, Rev. 20131

Name ______Date ______Period ______

Empirical Formula and Molecular Formula

The empirical formula of a substance is represents the smallest whole number ratio of atoms or moles of the elements in the compound. It can be determined using percent mass composition information.

In a sample of a compound, if the mass of each element is known, the moles of each element can be determined. Once the moles of each element are known, then the whole number ratio of each element can be determined.

For example, a compound is known to contain 11.1% hydrogen and 88.9% oxygen. Determine the empirical formula.

  1. Since you know the percent composition data, assume that you have 100 g of substance. Then you can convert your percents to grams.

11.1% H → 11.1g H

88.9 g O → 88.9g O

  1. Convert the mass of each element to moles.

11.1 g H x 1 molH/1 g H = 11.11 mol H

88.9 g O x 1 mol O/ 16 g = 5.56 mol O

  1. Convert the mole ratio to whole numbers by dividing each by the smallest number.

11.11 mol H / 5.56 = 2.00 mol H

5.56 mol O / 5.56 = 1 mol O

  1. Write the empirical formula using the smallest whole number ratio.

H2O

It can be helpful to organize your work in the form of a table. Consider the following problem. A compound is known to be composed of 40% sulfur and 60% oxygen by mass. What is the empirical formula?

Element / % / grams / ÷ MM / moles / ÷ smallest
S / 40 / 40 / 32 / 1.25 / 1
O / 60 / 60 / 16 / 3.75 / 3

The mole ratio of sulfur to oxygen is 1:3, making the empirical formula SO3.

Molecular Formulas

For molecular compounds, sometimes the mole ratios of elements are not the simplest whole number ratios. Observe the following table.

Empirical
Formula / Molecular
Formula
CH / C6H6
CH2O / C6H12O6
HO / H2O2
SO3 / SO3

Some times the molecular and empirical formulas are the same. Sulfur trioxide (SO3) is an example of this.

Question: How is the molecular formula related to the empirical formula?

Determining Molecular Formula

If the empirical formula is known, and the molar mass is known, then the molecular formula can be determined. It turns out that a molecular formula is always a whole-number multiple of the empirical formula. See the table above.

molecular formula = nxempirical formula

Take glucose (C6H12O6) as an example.

C6H12O6 = n(CH2O)n = 6

C6H12O6 = 6(CH2O)meaning glucose contains 6 (CH2O) units per molecule

How would you determine n if you didn’t know the molecular formula? Often you will know the molar mass of the compound. If you know the empirical formula, you can calculate the empirical formula mass in the same way you do molar mass. The value of n will be the molar mass of the compound divided by the empirical formula mass. The empirical formula is then n times the empirical formula.

Example: Suppose you have previously determined that a compound composed of 92.3% C and 7.7% H has an empirical formula of CH. If the molar mass of the compound is 78 g/mol, what is the molecular formula? The empirical formula mass for CH is 13, so ….

and the molecular formula contains six CH units.

6 (CH) = C6H6.

In the event that n =1, the molecular formula is the same as the empirical formula.

1003H Practice: Empirical and Molecular Formulas

Determine the empirical formulas from the percent composition data below.

  1. A compound is known to be 40.05% sulfur and 59.95% oxygen by mass. Determine its empirical formula.
  1. A substance was found to contain 15.9% boron and 84.1% fluorine. Find its empirical formula.
  1. Determine the empirical formula of a compound known to contain 23.79% carbon, 5.99% hydrogen, and 70.22% chlorine.
  1. A compound is 5.93% hydrogen and 94.07% oxygen. Its molar mass is known to be 34.016 g/mol. Determine its empirical formula and its molecular formula.
  1. A chemical is composed of 40.00% carbon, 6.7% hydrogen, and 53.3% oxygen. What is its empirical formula? What is its empirical formula mass? If the compound is known to have a molar mass of 60.05, what is its molecular formula? If the compound had an approximate molar mass of 180 g/mol, what is the molecular formula?
  1. If the percent composition data for a compound was 56.83% oxygen, 41.97% chlorine, and 1.19% hydrogen, what is the empirical formula? If the compound was found to have an approximate molar mass of 84, what is its molecular formula?
  1. A compound has a molar mass of 92.02 and is composed of 30.45% nitrogen and 69.55 % oxygen. Determine its empirical formula , empirical formula mass, and molecular formula.

David Scott, Chemistry, Rev. 20131