10 Minute Chemistry – The Mole and Molar Conversions Section 1: Avogadro’s Number and Molar Conversions Objectives: • Identify the mole as the unit used to count particles • Use Avogadro’s number to convert between amount in moles and number of particles • Solve problems converting between mass, amount in moles, and number of particles using Avogadro’s number and molar mass
Assignments and Instructional Materials
Sample Problems A, B, C, D See the Mole Map on the web under Chemistry Resources
Key Terms: • Mole: • Avogadro’s Number: • Molar Mass: Key Concepts & Outline Topics: 1. Avogadro’s Number and the Mole Avogadro’s number(NA) is the name for the quantity that represents the number of particles found in the mole. The mole is the SI unit for quantity. (Refer to Chemistry Resources (SI Base Units)) for additional SI Units. Current value for Avogadro’s Number is 6.0221415 ±0.0000010 x 1023 *Note the ± symbol which is the current method of reporting error or precision of a value. a. The mole is a counting unit The concept of a counting unit is such that you apply a ‘word’ that represents a specific quantity to aid in expressing larger or smaller values. We see this in our daily life with the use of Unit Value Dozen 12 Score 20 Gross 144 Pair 2 *Ream 144 sheets of paper *roll 50 pennies *These items are listed as a counting unit but in actuality they are poor examples as they either count a specific item (ream=sheets of paper) or they change value (roll of quarters ≠ roll of pennies in either numeric count or monetary value). A counting unit should relate a qty to a number and be nonspecific to what it is counting. We can setup a general equation which will convert the number of our counting units to the quantity of items based on the value of the counting unit by creating a conversion factor. Conversion factors always relate two items and are not changed in values but can be inverted. The conversion factors are setup as fractions and because we are multiplying we can always use multiple conversion factors to get to our answer and the order that we use them will not matter. This work is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. Digital Versions can be found at crhsteacherpages.com under Chemistry A
10 Minute Chemistry – The Mole and Molar Conversions
General Equation for converting units, the setup is called dimensional analysis Example 1: Dozen → 12 (the conversion factor will be
)
1 dozen nails = x nails a. Setup as proportion
, solved via cross multiplication is 12 nails.
b. Setup via dimensional analysis
solved via multiplication is 12 nails
1.5 dozen nails = x nails a. Setup as a proportion
, solved via cross multiplication is 18 nails
b. Setup via dimensional analysis
solved via multiplication is 18 nails Example 2: gross = 144 (the conversion factor will be
)
1.4 gross = x pencils a. Setup as a proportion
, solved via cross multiplication is 201.6 pencils,
we can express this value as the answer as solved or if we are interested in whole pencils would need to express the value as 201 as we are not able to round up in this case. When using the mole we will not run into this case. b. Setup via dimensional analysis
solved via multiplication is 201.6 pencils. b. Amount in moles can be converted to number of particles In the same fashion, we can convert moles to number of particles using dimensional analysis or proportions. Dimensional analysis is the preferred method due to its ability to stack multiple This work is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. Digital Versions can be found at crhsteacherpages.com under Chemistry A
10 Minute Chemistry – The Mole and Molar Conversions conversion factors without having to solve at each step. However proportions are sometimes used for the most simplistic of these molar conversion problems. Steps to solving molar conversion problems • Determine the conversion factors that are needed • Determine the desired unit of answer • Determine the ‘seed’ value or starting number • Setup the problem as a multiplication problem In these type of problems the conversion factor between moles → particles will always take the form of where particles can be atoms(monatomic elements), molecules/compounds(diatomic elements). Example 1: 1 moles → particles (The conversion factors will be ) 1 mole = x particles Solved via dimensional analysis, the answer is 6.022x1023 particles, and we take note of the exponent as a requirement for the answer.
Example 2: moles → particles (for values other than 1 we will set the equation up the same) 1.38 moles = x particles Solved via dimensional analysis, the answer is 8.31 x 1023 particles, and we take note of the exponent as a requirement for the answer.
c. Number of particles can be converted to amount in moles We solve this conversion problem conceptually the same as the previous example however we will invert the conversion factor such that particles are on the bottom. The conversion factor will be Example 1: particles → moles (the conversion factor will be
)
6.022 x 1023= x moles Solved via dimensional analysis, the answer is 1mole *Hopefully one should recognize the value of a mole and be able to provide an answer without any work. However these base conversions are given on assessments in order to provide the opportunity to recognize the correct method of setting up the equation. Care should be taken to show the necessary work for problem sets.
Example 2: particles →moles (values other than 1, conversion factor is the same) 324 x 1023 particles = x moles Solved via dimensional analysis, the answer is 53.8 moles
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10 Minute Chemistry – The Mole and Molar Conversions
When entered into the calculator it is important to ensure that you follow order of operations and include any necessary parentheses. There are two methods of avoiding the exponent error (obtaining large exponents). 1. Utilize the EE button(TI Calculators, TI-89, TI-34MV, TI-34II) EE Button or exponent button
Figure 1 - TI-89
Figure 2 - TI-34 MultiView
Figure 3- TI 34II
Using the exponent button on the TI-34 MultiView Calculator 2. Deal with the non exponent number first and divide, then subtract powers and that is the exponent
Non exponent numbers are 324 and 6.022, so divide those, 53.8. Subtract the powers, 23-23=0 Thus the answer 53.8 x 100 or 53.8 moles *Note about significant figures – Utilizing significant figures we report answers via multiplication that match the least number in our problem set. We will consider that the conversion factor contains an unlimited number of significant figures and thus we will match the significant figures with our ‘seed’ number or starting number.
2. Molar Mass Relates Moles to Grams Molar mass is simply the mass of a 6.022 x1023 things. Normally we apply molar mass to a compound however we as the definition provides for ‘things’ we can apply this to molecules/compounds, atoms/elements knowing that 6.022 x1023 things is really 1 mole. The process allows us to count items by weight rather than by a specific quantity. This work is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. Digital Versions can be found at crhsteacherpages.com under Chemistry A
10 Minute Chemistry – The Mole and Molar Conversions Thus if we know how much one particle weighs which we call the atomic mass we will convert this into the molar mass by simply change the unit. Thus the atomic mass of carbon is 12.011 amu however the molar mass of carbon is also 12.011 but we change the unit to moles from amu. We will utilize molar mass as a conversion factor that relates mass(g) to quantity(moles) and molar mass is specific for the item that we are counting. a. Amount in moles can be converted to mass We utilize the conversion molar mass to covert moles to mass where the conversion factor will be ‘x’ must be calculated or provided for each molecule, atom or thing we are measuring.
and
We solve the problems using dimensional analysis with the first step of the process is to determine the molar mass of the compound or thing we are weighing. Example 1: moles → mass (Conversion factor is ) 1 mole CH4 = x grams Solving the equation via dimensional analysis the answer is 16.043g.
We note that the answer is to the correct significant digits based on the molar mass of carbon however due to the varied periodic table we end up rounding masses off the periodic table to the closest whole number. Remember though that it is up to the researcher to report their numbers in such a way that is most closely represents the true nature of the problem. Example 2: moles → grams (for values other than 1 mole) The conversion factor is the same and setup will remain the same. 1.23 moles CO2 = x grams Solving the equation via dimensional analysis the answer is 54.1 grams with the correct number of significant figures. We did not change any layout of the problem but we note that the molar mass is specific to the compound and is found by determining how much a single part weighs and the quantity of that part. We utilize subscripts to determine the quantity of each element, and like in math we distribute a subscript into a set of parenthesis by multiplication. It is important for us to only apply subscripts to the object that is just before the subscript and nothing else. We also do not include coefficients in our calculations. b. The mole is central in chemical conversions This will be explored in more depth though out chemistry education however the mole map is a great place to see the relationships between the varied quantities and values as we see them in chemical equations and in lab.
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10 Minute Chemistry – The Mole and Molar Conversions
Figure 4- The Mole Map
c. Mass can be converted to amount in moles We are also able to convert a mass to a quantity using the same conversion factor of molar mass but have moles on top such that the fraction will be
.
Example 1: mass → moles the conversion factor is 36.3 grams C2H4 = x moles We set the problem in the same fashion as all other problems via dimensional analysis. Solved via dimensional analysis with the correct number of significant figures we obtain 1.294 moles C2H4 with the complete label including the ‘what’ we are counting or weighing due to molar mass being unique to the compound measured.
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10 Minute Chemistry – The Mole and Molar Conversions Section 2: Relative Atomic Mass and Chemical Formulas Objectives: • Use a periodic table or isotopic composition data to determine the average atomic masses of elements. • Infer information about a compound from it chemical formula. • Determine the molar mass of a compound from its formula. Key Term: • Average Atomic Mass: Key Concepts and Outline Topics 1. Average Atomic Mass and the Periodic Table a. Most Elements are mixtures of isotopes 2. Chemical Formulas and Moles a. Formulas express composition b. Formulas give ratios of polyatomic ions c. Formulas are used to calculate molar masses Section 3: Formulas and Percentage Composition Objectives: • Determine a compound’s empirical formula from its percentage composition • Determine the molecular formula or formula unit of a compound from its empirical formula and its formula mass. • Calculate the percentage composition of a compound from its molecular formula or formula unit. Key Term: • Percentage composition: • Empirical Formula: • Molecular formula: Key Concepts and Outline Topics 1. Using Analytical data a. Determining empirical formula b. Molecular formulas are multiples of empirical formulas
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