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Chemistry Calculations This is where you apply the Math that you have been learning. Density The amount of matter present in a given volume of a substance. Formula: Density = mass/volume or D=m/v Unit: g/mL or g/cm3 1 mL = 1 cm3 Density Problems A student finds that 23.5 mL of a liquid weighs 35.062 g. What is the density of this liquid? A solid substance has a weight of 65.89 g and a volume of 31.4 mL, what is the density? Density Problems on WB 1. If a substance has a volume of 24.67 mL and a mass of 98.6 g, what is the density? 2. Using the following pieces of information, determine the density: 14.8 mL and 84.78 g. 3. If a solid object has a mass of 75.9 g and a volume of 23.9 cm3, what is the density? How to Find Volume When the volume of a sample is unknown, it can be determined by placing the solid in a graduated cylinder and seeing how much the water is displaced by the object. Final volume – initial volume = volume of object Using the Density Chart A student finds a medallion at a pawn shop. The store owner tells the student that the medallion is platinum, but the student believes that it is silver. If the medallion weighs 55.64g, has an initial volume = 75.2 mL and a final volume = 77.8 mL, what is the density of the medallion and what is it made from? Using the Density Chart A piece of wood was found to have a mass of 7.182 g, an initial volume of 24.6 mL and a final volume of 37.9 mL. What is the density of the wood and what is it made from? Using the Density Chart on WB 1. Mr. Jacobs has found a substance and needs to know what it is and it’s density. Use the following to determine both: mass = 96.408 g, initial volume = 65.28 mL and final volume = 77.64 mL. 2. Mrs. Maki has found a sticky substance on one of her desks and she wants to determine what it is. If the substance weighs 8.1834 g has a final volume of 82.46 mL and an initial volume of 76.53 mL, what is the substance? Density Calculations Using the D=m/v formula you can also determine mass and volume. m = D x v where the units are grams (g) v = m/D where the units are mL or cm3 Density Calculations Examples Corn syrup has a density of 1.38 g/cm3. What volume would need to be measured for a mass of corn syrup weighing 24.5 g? Silver has a density of 10.5 g/cm3. What would the mass be of a silver sample with a volume of 36.5 cm3? Density Calculations Examples What would the volume be for a copper sample weighing 94.8 g? What would the mass be for a chromium sample with a volume of 23.1 mL? Density Calculations on WB 1. What would the mass be for a bakelite sample with a volume of 14.6 mL? 2. What would the volume be for an oak sample weighing 21.1 g? 3. A mahogany desk weighs 1653.7 grams. What is the volume of the desk? 4. What is the mass of a lead pipe that has a volume of 258.9 cm3? Moles The amount of a substance that contains 6.02 x 1023 representative particles of that substance Abbreviated mol 6.02 x 1023 is know as Avogadro’s Number 1 dozen eggs = ? 1 mole of eggs = 6.02 x 1023 Moles 1 mole of hydrogen = 1.008 g 1 mole of calcium = 40.078 g 1 mole of sodium = 1 mole of potassium = 1 mole of iron = Mole Example Problems Calculate the number of moles in a 25.0 g sample of calcium. Calculate the number of moles in a 52.3 g sample of phosphorus. Calculate the number of moles in a 78.9 g sample of helium. Mole Problems on WB 1. Calculate the number of moles in a 75.6 g sample of chlorine. 2. Calculate the number of moles in a 89.8 g sample of scandium. 3. Calculate the number of moles in a 13.7 g sample of manganese. 4. Calculate the number of moles in a 20.4 g sample of silver. Mole Problems on WB 5. Calculate the number of moles in a 444 g sample of radon. 6. Calculate the number of moles in a 151 g sample of mercury. 7. Calculate the number of moles in a 95.6 g sample of osmium. 8. Calculate the number of moles in a 302 g sample of tungsten. Molar Mass/Formula Mass The mass of a mole of any substance. To find the molar mass of a compound, you simply add up the total atomic masses of all the elements in the compound. For example: CH4 C = 1 x 12.0 = 12.0 H = 4 x 1.0 = 4.0 MM of CH4 = 16.0 g/mol Molar Mass/Formula Mass KNO3 NH4 Zn3(PO3)2 Molar Mass/Formula Mass Examples on WB 1. C6H12O6 2. Na2SO4 3. KMnO4 4. Pb(CO3)2 5. (NH4)2SO3 Calculating Mass from Moles To determine mass from moles, simply find the molar mass of the compound and multiply that by moles given in the problem. Determine the mass of a 4.86 mol of CaCO3. Ca = 1 x 40.08 = 40.08 MM = 100.08 C = 1 x 12.0 = 12.0 4.86 x 100.08 = O = 3 x 16.0 = 48.0 486.39 g Calculating Mass from Moles Examples Calculate the mass of 1.48 mol of K2O Calculate the mass of 2.68 mol of Ag2SO4 Calculate the mass of 5.89 mol of Fe(NO3)3 Calculating Mass from Moles on WB 1. Calculate the mass of 4.13 mol of Na2S2O3 2. Calculate the mass of 1.68 mol of CsClO4 3. Calculate the mass of 2.46 mol of Zn3(PO4)2 4. Calculate the mass of 6.41 mol of LiSCN Percent Composition % = Mass of element in Cmd x 100 Composition MM of compound C2H5OH Na2SO3 Percent Composition Examples C10H14O C3H7OH CsClO4 Be3(AsO3)2 Percent Composition on WB 1. Fe(NO3)3 2. NaHCO3 3. Cd3(C6H5O7)2 4. Na2S2O3 Empirical Formulas The simplest whole-number ratio of atoms in a compound. Rules for Determining Empirical Formulas: 1. Obtain the mass of each element present from the problem. 2. Determine the number of moles of each type of element. Empirical Formulas 3. Divide the number of moles of each element by the smallest number of moles out of all the elements. This number will be a whole or a half number – nothing else!! If all the number are whole numbers after this division, these numbers are the subscripts in the empirical formula. If there is even one half number, go to step 4. Empirical Formulas 4. Multiply the numbers you got in step 3 by 2 to make them all whole numbers. YOU MUST MULTIPLY ALL THE NUMBERS BY 2, NOT JUST THE HALF NUMBER. This set of numbers will be your subscripts in the empirical formula. Empirical Formula Examples: An oxide of aluminum is formed by the reaction of 4.151 g of Al with 3.692 g of O. Calculate the empirical formula for this compound. A sample of lead arsenate contains 1.3813 g of lead, 0.00672 g of hydrogen, 0.4995 g of arsenic and 0.4267 g of oxygen. Determine the empirical formula. Empirical Formulas on WB 1. A sample of phosphoric acid contains 0.3086 g of hydrogen, 3.161 g of phosphorus and 6.531 g of oxygen. Determine the empirical formula of phosphoric acid. 2. A sample of para-dichlorobenzene contains 5.657 g of carbon, 0.3165 g of hydrogen and 5.566 g of chlorine. Determine the empirical formula for this compound. Empirical Formulas on WB 3. A 4.550 g sample of cobalt reacts with 5.475 g of chlorine to form a compound. Determine the empirical formula for this compound. 4. When a 0.3546 g sample of vanadium metal is heated in air, it reacts with oxygen to achieve a final mass of 0.6330 g. Calculate the empirical formula of this vanadium oxide. (HINT: Subtract the mass of the vanadium sample from the final mass to get the mass of oxygen in the compound.) Empirical Formula Examples 5. Sevin, the commercial name for an insecticide used to protect crops such as cotton, vegetables and fruit is made from carbamic acid. A chemist analyzing a sample of carbamic acid finds 0.8007 g of carbon, 0.9333 g of nitrogen, 0.2016 g of hydrogen and 2.133 g of oxygen. Determine the empirical formula for carbamic acid. Empirical Formulas from % Composition A compound has been analyzed and found to have the following percent composition: 66.75% copper, 10.84% phosphorus and 22.41% oxygen. Determine the empirical formula for this compound. Empirical Formulas from % Composition on WB 1. What is the empirical formula of a sample whose mass percent composition is: 21.9% Mg; 27.8% P; 50.3% O? 2. Determine the empirical formula of a compound that is 29.0% sodium, 40.5% sulfur, and 30.4 % oxygen by weight. Molecular Formulas The exact formula of a molecule, giving the types of atoms and the number of each type. Molecular Formula = (Empirical Formula)n n = molar mass/empirical formula mass n = will be a whole number Molar mass will be given in the problem Molecular Formula Examples A white powder is analyzed and found to have an empirical formula of P2O5. The compound has a molar mass of 283.88 g. What is the molecular formula? The empirical formula of a compound is NO2. It has a molar mass of 92 g. What is its molecular formula? Molecular Formula Examples A compound used as an additive for gasoline to help prevent engine knock shows the following percent composition: 71.65% chlorine, 24.27% carbon and 4.07% hydrogen. The molar mass is 98.96 g. Determine the empirical and molecular formulas for this compound. Molecular Formula Problems on WB 1. The empirical formula of a compound is CH2. Its molecular mass is 70.0 g/mol. What is its molecular formula? 2. Caffeine is a compound containing 49.47 % carbon, 5.191% hydrogen, 28.86% nitrogen and 16.48% oxygen. The molar mass of caffeine is 194 g/mol. Determine the molecular formula for caffeine. Molecular Formula Problems on WB 3. The empirical formula of a compound is CH2O and its molar mass is 150 g/mol. What is its molecular formula? 4. A compound contains 12.8% carbon, 2.1% hydrogen, and 85.1% bromine by mass. Calculate the empirical formula and the molecular formula of this compound given that the molecular mass is 188.0 g/mol. Molecular Formula Problems on WB 5. A compound is 64.9% C, 13.5% H, and 21.6% O. Its molecular mass is 88.0 g/mol. What is its molecular formula?
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