# Mass Relationships in Chemical Reactions

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1 Mass Relationships in Chemical Reactions Chapter Molar mass and the mole one mole is defined as the number of carbon atoms in exactly grams of pure 1C. From the sugar example, a mole of C 1 H 11 would have a mass of 4.99 grams. This quantity is known as the molar mass, a term that is often used in place of the terms atomic mass or molecular mass. Determine the molar mass of NaH? NaH contains one Na atom + one oxygen atom + one hydrogen atom Molar mass 1 x mass of Na atom + 1 x mass of atom + 1 x mass of H atom The masses of the elements can be obtained from the periodic table. 1 x x x g Molar mass of NaH 9.99 g 1

2 Calculate the molecular weight of the following: a) H S 4 MW of H S 4 x H + 1xS +4x x1 + 1x + 4x16 98 g/mole b) CH H MW of CH H 4x H + 1xC +1x 4x1 + 1x1 + 1x16 g/mole c) Lauric acid C H 4 MW of C H 4 4 x H + xc +x 4x1 + x1 + x16 9 g/mole Number of moles To determine the number of moles use the following formula or triangles: mass ( g) number of moles molar mass ( g / mole) How many moles are there in.99 g of sodium? mass (g).99g number of moles molar mass (g / mole).99g / mole (from the periodic table) number of moles 1 mole. How many moles are there in 1 g of chlorine? mass (g) 1g number of moles molar mass (g / mole) 5.45g / mole (from the periodic table) number of moles 0.08 mole. 4

3 How many grams are there in 0.10 mole of CH 4? First calculate the molar mass of CH 4 Molar mass of CH 4 1 x mass of C atom + 4 x mass of H atoms 1 x x g / mole Then use the formula: mass of CH 4 number of moles molar mass of CH mole x16.0 g/ mole 1.60 g Which one is the lightest in mass: one mole of hydrogen, one mole of sodium, one mole of iron, one mole of sulfur? ne mole for an element contains the atomic mass of the element. Atomic mass of H g / mole, Atomic mass of Na.99 g / mole, Atomic mass of Fe g / mole, Atomic mass of S.07 g / mole. The lightest one is one mole of hydrogen The heaviest one mole is the iron. 5 Avogadro s number and the mole 1 mole of anything contains the Avogadro s Number (N A ) of this thing Avogadro s Number (NA) x 10 1 mole of particles x 10 particles for any substance 1 mole of shoes x 10 shoes 1 mole of cars x 10 car 1 mole of carbon atoms x 10 carbon atoms 1 mole of water molecules x 10 water molecules Number of particles number of moles x Avogadro s number 6

4 To calculate the number of particles (atoms, molecules, shoes.etc) use the following formula: Number of particles number of moles x Avogadro s number Calculate the number of atoms in mole of hydrogen? Number of hydrogen atoms moles of H x x 10 H atom / mole Number of hydrogen atoms 1.0 x 10 4 H atom Calculate the number of atoms in 6.46 grams of helium (He)? mass(g) 6.46g number of moles molar mass(g / mole) 4.00g / mole(from the periodic table) number of moles 1.61 mole. Number of He atoms number of moles Avogadro s number 1.61 moles of He x x 10 He atom / mole 9.66 x 10 He atom 7 Caffeine is a stimulant drug and it is found in coffee, tea and beans. Its molecular formula is C 8 H 10 N 4. Calculate the number of oxygen atoms in grams of caffeine. Molar mass of caffeine 8 x C + 10 x H + 4 x N + x 8 x x x 14 + x g / mole mass (g) g number of moles molar mass (g / mole) 194g / mole (from the periodic table) number of moles 0.10 mole Total number of C 8 H 10 N 4 molecules number of moles x N A 0.10 moles x 6.0 x 10 molecules / mole Total number of C 8 H 10 N 4 molecules 6.0 x 10 molecules number of Number of oxygenatoms Number of oxygen atoms oxygenatoms molecules oxygen atoms molecules x total number of molecules x 6.0 x 10 molecules Number of oxygen atoms 1.0 x 10 oxygen atoms Number of carbon atoms 4.8 x 10 carbon atoms Number of hydrogen atoms 6.0 x 10 hydrogen atoms Number of nitrogen atoms.40 x 10 nitrogen atoms 8 4

5 Mass Percent The Mass Percent of an element is defined as: Mass of the element Mass Percent of an element x100% Total molar mass of the sample What is the mass percent of carbon, hydrogen, and oxygen in pure ethanol C H 6? -First: calculate the molar mass of C H 6 MW of C H 6 x C + 6 x H + 1 x x x x MW C H g/mole -Second: calculate the mass percents Mass % C 100 x ( mass of C ) 100 x ( x 1.01 ) 5.14 % total molar mass Mass % H 100 x ( Mass % 100 x ( mass of H total molar mass mass of total molar mass ) 100 x ( 6 x ) 1.1 % ) 100 x ( 1 x ) 4.7 % Note that the mass percentages should add up to 100%. Mass % Mass % C + Mass % H + Mass % 5.14 % % % % 9 Chemical and structural Formulas The chemical formula tells you how many of each type of atom are in a molecule. The structural formula tells you how many of each type of atoms are in a molecule and also how they are connected. For example, the chemical formula for ethanol is C H 6 and The structural formula of ethanol is Be carful, the chemical formula could be the same for different molecules, but the structural formula is unique. The chemical formula for dimethyl ether is C H 6 and The structural formula of dimethyl ether is: 10 5

6 Empirical Formulas (simplest formula) It shows the simplest whole number ratio of atoms in a molecule. For example, hydrogen peroxide's chemical formula is H, but its empirical formula is H Molecular weight of unknown (g/mole) Molecular Formula ( )xemperical formula mass of Emperical formula Write the different formulas for the glucose molecule The chemical formula for glucose is C 6 H 1, but its empirical formula is CH, and its structural formula is 11 Combustion Analysis It is used to determine the mass % for different elements in the compound. The sample is burned in the presence of excess oxygen which converts all the carbon to carbon dioxide and all the hydrogen to water. The C and H produced are absorbed in two different stages and their masses determined by measuring the increase in weight of the absorbers. 1 6

7 Ascorbic acid (vitamin C) contains only C, H, and. Combustion of g of Ascorbic acid produced 40.9% C and 4.5% H. What is the empirical formula for Ascorbic Acid? First: calculate the mass percent of xygen. Since the sample contains C, H, and, then the remaining 100% % - 4.5% 54.6% is xygen Second: Suppose 100 g of this substance Steps C H 1 Mass /g No. of moles mass molar mass smallest number (.4) x by a number to make step integer numbers (x ) 1 x 1. x 4 1 x 5 Empirical formula C H 4 C 4 H 1 What is the molecular formula if the molecular mass of Ascorbic Acid was founded to be 176 g/mole? Molecular Formula ( Molecular weight of unknown (g/mole) ) x empirical Formula mass of emperical formula Molecular Formula ( 176 (g/mole) x1 + 4x1 + x16 ) x C H 4 x C H 4 C 6 H

8 Chemical Reactions It is process in which one or more pure substances are converted into one or more different pure substance. All chemical reactions involve a change in substances and a change in energy. Neither matter nor energy is created or destroyed in a chemical reaction, only changed. Chemical equation When a chemical reaction occurs, it can be described by an equation. This shows the chemicals that react (reactants) on the left-hand side, and the chemicals that they produce (products) on the righthand side. Reactants Reaction conditions Products Reaction between hydrogen gas and oxygen gas to produce liquid water hydrogen gas + oxygen gas liquid water H (g) + (g) H (l) 15 Balancing chemical equations first write the correct formula for both reactants and products and then balance all of the atoms on the left side of the reaction with the atoms on the right side. Write the chemical equation which represents the burning of glucose in presence of oxygen gas which produces carbon dioxide and water. To answer this question, follow the following steps: 1. Identify the reactants and the products and put an arrow in between. glucose + oxygen gas carbon dioxide + water. Try to figure out the correct formula for the reactants and products, Glucose is C 6 H 1, oxygen gas is, carbon dioxide is C, and water is H. C 6 H 1 + C + H.Count the number of each atom at both sides of the equation: C 6 H 1 + C + H (6 C + 1 H + 6 ) + ( ) (1C + ) + (H + 1 ) Total: (6 C + 1 H + 8 ) (1C + H + ) 16 8

9 Balance C first, then H, and finally : At the left side there are 6 C atoms and at the right side there are 1 C atom, so multiply C by 6 (x 6) C 6 H C + H At the left side there are 1 H atoms and at the right side there are H atom, so multiply H by 6 (x 6) C 6 H C + 6H At the left side there are 8 atoms and at the right side there are 18 atom, so multiply by 6 (x 6) C 6 H C + 6H Recount all atoms again, C 6 H C + 6H (6 C + 1 H + 6 ) + (1 ) (6C + 1 ) + (1H + 6 ) Total: (6 C + 1 H + 18 ) (6 C + 1 H + 18 ) 17 Amount of reactants and products problems aa bb In this type of problems, you are given the mass (#moles) of the reactant and you calculate the mass (#moles) of the product. You can use the following formula to calculate the #moles of B: b number of moles of(b) number of moles of(a)x a You can use the following formula to calculate the mass of B: mass of(b) mass of (A) b x x Molar mass of(b) Molar mass of(a) a How many grams of water are produced when 7.00 grams of oxygen react with an excess of hydrogen according to the reaction shown below? H (g) + (g) ----> H (g) The "excess" reactant has nothing to do with the problem. Identify which is the "given" and which is the unknown. H (g) + (g) ----> H (g) 7 g? 18 9

10 Use the formula: Mass of H 7.89 g massof (H ) massof(h) x x Molar massof(h ) Molar mass of 1( ) 7.0g (H ) massof(h ) x x18g / mole g / mole 1( ) Calculate the number of moles of C resulted from the reaction of.5 moles of C H 6 with excess oxygen according to the equation C H C + 6 H Use the formula: 4(C H6 ) number of molesof(c ) number of molesof(c H )x 6 (C ) 4(C H6 ) number of molesof(c ).5moles of(c H )x 6 (C ) Number of moles of C 7.0 moles 19 Calculate the mass of chlorine that reacts with g of hydrogen to form hydrogen chloride according the following equation: H + Cl HCl Use the formula: mass of H 1(H ) massof(cl ) x x Molar massof(cl ) Molar mass of H 1(Cl ) 4.770g of H 1(H ) massof(cl ) x x71.0g / mole.0g / mole 1(Cl ) Mass of Cl 169. g 0 10

11 Limiting Reagents aa+ bb dd When two substances A and B are present in random quantities and react with each other to produce D, the first consumed one is the limiting reagent and the second one is remained in excess. To determine the limiting reagent from given moles of substance, do the followings: 1- Calculate the ratio for each reagent, by dividing the given moles of a reagent to its factor in the chemical equation. - Compare the ratios for the reagents and the limiting reagent is the smallest one. 1 If 5 moles of N were mixed with 5 moles of to react as: N (g) + (g) N (g) Determine the limiting reagent. The ratio of The ratio of 5mol (given) N.5 mol (factor) 5mol 5 1mol The limiting reactant is N because it is the smallest If 400g Fe were mixed with 00g to react as: 4 Fe (s) + (g) Fe (s) Determine the limiting reagent. Step 1: Change the mass in grams into moles for the given substances 1mol Fe 1mole 400 g Fe 7.17 mol Fe 00 g 9.8mol 55.8g / mole Fe g / mole Step: Calculate the ratio and compare 7.17mol 9.8mol Fe mol mol Fe is the limiting reactant 11

12 Chemical Reaction Yield For any chemical reaction there are theoretical and actual (practical) yield. Theoretical yield (T.Y.) is the amount of product that would result if all the limiting reactant reacted. Actual yield (A.Y.) is the amount of product actually obtained from a reaction. Due to many factors can affected on the reaction, A.Y. is always less than T.Y. Percent yield is the efficient for a given reaction: A.Y. % yield 100 T.Y. Many tons of urea (C(NH ) ) are produced every year in fertilizer industries. When 119 g ammonia react with 80 g C as the equation: NH (g) + C (g) C(NH ) (s) + H and produce 100 g urea, calculate % yield? - Step 1: Determine the limiting reagent - Change the mass in grams into moles for the given substances 1mole NH 1moleC 119 g NH 7mol NH 80 g C 1.8mol C 17 g NH 44g C - Calculate the ratio and compare 7mol NH mol C 1. 8 mol C 1mol is the limiting reagent Now, ignore NH and compare between C and C(NH ) only. - Step : Calculate the Theoretical Yield [#moles of C(NH ) ] b number of molesof(b) number of moles of(a)x a 1 # moles C(NH ) #molesofcx 1.8molesCx1 1 Number of moles of C(NH ) 1.8 moles 4 1

13 Step : Calculate the Theoretical Yield [mass of C(NH ) ] produces: 60g urea The T.Y. 1.8 mole urea 109g urea 1mole urea Step 4: Calculate the %Yield of C(NH ) : A.Y. % yield 100 T.Y. 100 % yield %

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