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Calculations with Elements and Compounds The Mole Concept Rev Pisgah High School M. Jones

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Moles?

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No. Not real moles, or Whack-a-moles, or even the moles on your back. Chemistry moles

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What is a mole? Its a way of measuring atoms and molecules. The mole concept is a lot like the dozen concept.

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A dozen is 12. It doesnt make any difference what you are counting. A dozen is always 12.

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A dozen is 12. It doesnt make any difference what you are counting. A dozen is always 12. A dozen donuts.

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A dozen is 12. It doesnt make any difference what you are counting. A dozen is always 12. A dozen donuts. A dozen pencils.

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A dozen is 12. It doesnt make any difference what you are counting. A dozen is always 12. A dozen donuts. A dozen pencils. A dozen Volkswagons.

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A dozen is always 12.

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Like we can count by dozens, or multiples of 12, we can also count by multiples of a much larger number, which we call Avogadros number.

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Avogadros number is much larger… Avogadros number is x So how did chemists come up with such a huge number?

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It began with Amedeo Avogadro about a 150 years ago. He said that for equal volumes of gases at constant temperature and pressure, the masses of the gases are proportional to their atomic weights.

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10.0 liters of CO 2 weighs 19.6 grams 10.0 liters of N 2 weighs 12.5 grams 10.0 liters of Xe weighs 58.6 grams 44.0 g 28.0 g = 1.57 Avogadros law g 12.5 g = Ratio of the masses of equal volumes of CO 2 and N 2 Ratio of the molar masses of CO 2 and N 2

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10.0 liters of CO 2 weighs 19.6 grams 10.0 liters of N 2 weighs 12.5 grams 10.0 liters of Xe weighs 58.6 grams Avogadros law 19.6 g 58.6 g = g g =0.335 Ratio of the masses of equal volumes of CO 2 and Xe Ratio of the molar masses of CO 2 and Xe

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He said that for equal volumes of gases at constant temperature and pressure, the masses of the gases are proportional to their atomic weights. See! I told you so.

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But Avogadro never determined the value we know as Avogadros number. I wish I knew what my number was. It was called Avogadros number as a tribute to his pioneering work.

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After Avogadros death, Stanislao Cannizzaro published an explanation of Avogadros law. Equal volumes of gases at the same temperature and pressure have equal numbers of particles.

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Cannizzaro was able to convince chemists of the value of standardized atomic weights. Loschmidt (1865) was the first to determine the number of atoms or molecules in a fixed volume of gas.

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Jean Perrin was the first to use the term Avogadros number in 1909 to describe the number of atoms in the atomic weight of an element. He was the first to determine a value of Avogadros number which is close to the present-day value of x

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We can relate Avogadros number to the amount of an element equal to its atomic mass measured in grams. Atomic Mass

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This used to be called the gram atomic weight. Atomic weights are now called atomic masses. Atomic masses are given in units of atomic mass units, or amu. The amu is also called the dalton.

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The atomic mass unit (amu) is based on the mass of the carbon-12 isotope. It was decided that an atom of C- 12 be assigned a mass of exactly amu Atomic Mass

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This way, hydrogen,the lightest element (H) would have a mass very close to 1. The average atomic mass of hydrogen is amu. Atomic Mass

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Instead of amu of carbon-12, which is too small to even see, we consider grams of C-12. How many atoms are in g of C-12? Atomic Mass

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A C-12 atom has a mass of x g How many atoms are in g of carbon-12? g C x 1 C atom x g C = x C atoms C atom Atomic Mass

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A mole is the quantity of an element which has a mass equal to the atomic mass expressed in grams. Atomic Mass The mole is the official metric unit for the quantity of matter.

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The word mole can be abbreviated as mol.

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So, what is a mole? It is a word that describes a very large number of atoms x is also called Avogadros Number. It comes from the Latin word moles which means quantity x atoms

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A mole is … – any particle. Since they are so small, we must count atoms indirectly. Can you count to a mole? x atoms, molecules, electrons or ions …

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Suppose you wanted to know the number of marbles in a large jar. use a conversion factor. weigh all the marbles, Weigh a few marbles,

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Like this: 10 marbles = grams Avg. marble = grams All the marbles = g 1 marble g 286 marbles This is a conversion factor Suppose … Suppose … g x =

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We can count a large number of particles by weighing them.

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We can count atoms if we know the mass of an Avogadro's number of atoms.

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An Avogadro's number of atoms has a mass equal to the molar mass x atoms of sodium have a mass of 23.0 g x atoms of iron have a mass of 55.8 g x atoms of aluminum have a mass of 27.0 g

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Q. How many atoms are in 50.0 grams of potassium? We know that 1 mole of K has a mass of 39.1 grams; and 1 mole is 6.02 x atoms g K 39.1 g K 6.02 x atoms K 7.70 x atoms K x =

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The molar mass of an element is the mass of x atoms or 1 mole of that element.

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FYI: We now use molar mass instead of.. gram formula weight. gram molecular weight, gram atomic weight,

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The molar mass of an element is usually rounded to one decimal place: sodium (Na) sodium (Na) 23.0 g/mol iron (Fe) iron (Fe) 55.8 g/mol chlorine (Cl) chlorine (Cl) 35.5 g/mol phosphorous (P) phosphorous (P) 31.0 g/mol

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What do the subscripts in a formula tell us? 1 mole of Fe 2 O 3 contains … 2 moles of iron (Fe), and … 2 moles of iron (Fe), and … 3 moles of oxygen (O) 3 moles of oxygen (O) The subscripts give the number of moles of each element in one mole of the compound.

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How many moles of each kind of element are in one mole of … 3 moles Fe, 2 moles P, 8 moles O 12 moles C, 22 moles H, 11 moles O 1 mole Ca and 2 moles Cl CaCl 2 C 12 H 22 O 11 Fe 3 (PO 4 ) 2

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Calculating molar masses of compounds … Calculating molar masses of compounds … Molar mass of the compound Sum of the molar masses of the elements = The molar mass of an element its atomic mass

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Calculate the molar mass of water: (2 x 1.0) + (1 x 16.0) = 18.0 g/mol 2 hydrogen atoms 1 oxygen atom Molar mass of H 2 O =

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General Equation for Molar Mass Molar mass = (atomic masses) (atomic masses) For each element, multiply its atomic mass by its subscript, then add them all together.

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What is the molar mass of calcium chlorate? Start with the formula: Ca(ClO 3 ) 2 1 mol Ca, 2 mol Cl, 6 mol O (1 x 40.1) + (2 x 35.5) + (6 x 16.0) = g/mol = g/mol

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What are the molar masses of each of the following? 1. HCl 2. Fe 2 O 3 3. H 2 SO 4 4. Ca 3 (PO 4 ) 2 5. (NH 4 ) 2 CO g/mol g/mol 98.1 g/mol g/mol 96.0 g/mol

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Molar Conversions Use conversion factors to convert between moles, grams, molecules and the volumes of gases at STP. 1 mol = 1 molar mass 1 mol = x particles 1 mol = 22.4 L of any gas at STP

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Convert the following: moles Fe x molecules of SO 3 to moles moles of CaCl 2 to grams grams of iron metal to moles g CaCl moles SO 3

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Detailed solutions:

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Why 22.4 L? Why 22.4 L? What is STP? What is STP? What has this all got to do with a mole? 1 mole equals 22.4 L of any gas at STP

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STP stands for Standard temperature and pressure

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STP … STP … Standard temperature …the freezing point of water …the freezing point of water 0 C or 273 K Standard pressure … atmospheric pressure at sea level 1.00 atmosphere, kPa, 760. mm Hg, 760. Torr or 14.7 lbs/in 2

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1 mole of any gas at STP has a volume of 22.4 L Consider a box with a volume of 22.4L O2O2 1 atm 0 C 1.00 mol 22.4 L If the box contains 1.00 mole of oxygen gas, at a temperature of 0 C, the pressure will be 1.00 atm.

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More molar conversions … 3. How many molecules are in mL of NH 3 at STP? 2. Convert moles of HCl(g) to liters at STP. 1. Convert 3.00 liters of N 2 gas at STP to moles mol N L HCl 6.72 x molecules NH 3 Click for solutions

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Detailed solutions: Click to return

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Calculations with density… We can find the density of a gas at STP if we know the molar mass. Recall that density is the mass per unit volume … D = mV

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Sample density calculation: Sample density calculation: Q. What is the density of carbon dioxide at STP? We know that the molar mass of CO 2 is 44.0 g/mol and the volume of 1 mole of gas is 22.4L at STP

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Mass of 1 mole of CO 2 Volume of 1 mole of CO 2 Sample density calculation: Sample density calculation: Q. What is the density of carbon dioxide at STP?

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1. Find the density of nitrogen gas (N 2 ) at STP. Additional problems:

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2. Find the mass of mL of propane (C 3 H 8 ) at STP. This is the density of propane Hint: What is the density of propane? m = V D m = V D

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This is the density of propane D = mass of one mole mass of one mole volume of one mole volume of one mole m = V D m = V D

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This concludes the presentation on moles and molar mass.

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