# 2 Stoichiometry: Chemical Arithmetic Formula Conventions (1 of 24) 2 Stoichiometry: Chemical Arithmetic Stoichiometry Terms (2 of 24)

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1 Formula Conventions (1 of 24) Superscripts used to show the charges on ions Mg 2+ the 2 means a 2+ charge (lost 2 electrons) Subscripts used to show numbers of atoms in a formula unit H 2 SO 4 two H s, one S, and 4 O s Coefficients used to show the number of formula units 2Br the 2 means two individual bromide ions Hydrates CuSO 4 5 H 2 O some compounds have water molecules included Stoichiometry Terms (2 of 24) stoichiometry atomic mass formula mass molecular mass study of the quantitative relationships in chemical formulas and equations. weighted average mass of an atom, found on the periodic table sum of the atomic masses of the atoms in a formula sum of the atomic masses of the atoms in a molecular formula gram molecular mass molecular mass written in grams empirical formula same as gram molecular mass formula reduced to lowest terms Formula or molecular mass is found by simply summing the atomic masses (on the periodic table) of each atom in a formula. Calculating Formula Mass (3 of 24) H 2 SO = u 2(1.01) (16.0) = u or g/mole Generally, round off your answers to the hundredths or tenths place. Don t round off too much (98.06 g/mol or 98.1 g/mol is OK, but don t round off to 98 g/mol) Units Use u or amu if you are referring to one atom or molecule Mole Facts (4 of 24) A mole (abbreviated mol) is a certain number of things. It is sometimes called the chemist s dozen. A dozen is 12 things, a mole is 6.02 x things. Avogadro s Number of any substance contains 6.02 x molecules Molar Volume (measured at P = 760 mmhg and T = 0 C) of any gas has a volume of 22.4 Liters Molar Mass (see gram formula mass) 6.02 x molecules 22.4 L

2 A Line Equation is the preferred way to show conversions between quantities (amount, mass, volume, and number) by canceling units (moles, grams, liters, and molecules) Line Equations (5 of 24) The line equation consists of the Given Value, the Desired Unit, and the line equation itself. Example: What is the mass of 135 Liters of CH 4 (at STP)? Given: 135 L CH 4 Desired:? g CH L CH 4 x 1 mol CH 4 x 16.0 g CH 4 = g CH 22.4 L CH 4 1 mol CH 4 4 The Mole Map shows the structure of mole problems Mole Relationships (6 of 24) 1) Mass Volume at STP 1 mol number of atoms or molecules ➀ ➁ ➂ 2) 1 mol 22.4 L moles 3) ➂ ➀ ➁ Mass Volume at STP number of atoms or molecules 1 mol 6.02 x molecules Percentage Composition quantifies what portion (by mass) of a substance is made up of each element. Percentage Composition (by mass) (7 of 24) mass of element Set up a fraction: mass of molecule mass of element Change to percentage: 100 x mass of molecule Generally, round off your answers to the tenth s place. The percentage compositions of each element should add up to 100% (or very close, like 99.9% or 100.1%) Formula from % Composition (8 of 24) Given the Percentage Composition of a formula, you can calculate the empirical formula of the substance. Step 1 assume you have 100 g of substance so the percentages become grams Step 2 change grams of each element to moles of atoms of that element Step 3 set up a formula with the moles example: C 2.4 H 4.8 Step 4 simplify the formula by dividing moles by the smallest value C H = CH 2 Step 5 If ratio becomes 1:1.5 multiply by 2 1:1.33 or 1:1.66 multiply by 3

3 Equation Terms (9 of 24) equation reactants products word equation coefficients condensed statement of facts about a chemical reaction. substances that exist before a chemical rxn. Written left of arrow. substances that come into existence as a result of the reaction. Written to the right of the arrow. an equation describing a chemical change using the names of the reactants and products. a number preceding atoms, ions, or molecules in balanced chemical equationns that showing relative # s. Other Mole Problems and Conversions (10 of 24) The gas density is often converted to : Example : The gas density of a gas is g/liter (at STP). What is the of the gas? Knowing that 22.4 L is, you can set up the ratio: g = 1 Liter 22.4 L Other metric conversions you should know: 1000 ml 1 kg 1 Liter 1000 grams Writing Formula Equations Things To Remember (11 of 24) Example: Write the formula equation of... sodium metal + water sodium hydroxide + hydrogen gas Na + H 2 O NaOH + H 2 metals often are written with the symbol to emphasize that the metal is in the neutral elemental state, not an ion. some compounds have common names that you should just know... water, H 2 O; ammonia, NH 3 ; methane, CH 4 remember the seven diatomic elements so they can be written as diatomic molecules when they appear in their elemental form. Other elemental substances are written as single atoms (e.g. sodium metal or helium gas, He) Since every gas takes up the same amount of room (22.4 L for a mole of a gas at STP), the coefficients in an equation tell you about the volumes of gas involved. Coefficients and Relative Volumes of Gases (12 of 24) Example: N 2 (g) + 3 H 2 (g) 2 NH 3 (g) +

4 The heart of the problem conversion factor relates the Given and the Desired compounds using the coefficients from the balanced equation. Heart of the Problem (13 of 24) could be 3 moles H 2 2 moles NH 3 which means that every time 2 moles of NH 3 is formed, 3 moles of H 2 must react. moles of Desired The format is always, moles of Given Mass-Mass Problems Mass-Volume Problems (14 of 24) Mass-Mass problems are probably the most common type of problem. The Given and Desired are both masses (grams or kg). The pattern is: Given x of Given x x of Desired In Mass-Volume problems, one of the es is replaced with 22.4 L depending on whether the Given or the Desired is Liters. Mass-Volume-Particle Problems (15 of 24) If the Given or Desired is molecules, then the Avogadro s Number conversion factor, 6.02 x 1023 molecules is used and the problem is a Mass-Particle or Volume-Particle problem. The units of the Given and Desired will guide you as to which conversion factor to use: Mass Volume Particles grams or kg Liters or ml molecules or atoms In a problem with two Given values, one of the Given s will limit how much product you can make. This is called the limiting reactant. The other reactant is said to be in excess. Limiting Reactant Problems (16 of 24) Solve the problem twice using each Given the reactant that results in the smaller amount of product is the limiting reactant and the smaller answer is the true answer. When 28.0 grams of N 2 reacts with 8.00 grams of H 2, what mass of NH 3 is produced? (in this case, the N 2 is the limiting reactant)

5 How Much Excess Reactant is Left Over (17 of 24) When 28.0 grams of N 2 reacts with 8.00 grams of H 2, what mass of NH 3 is produced? (in this case, the N 2 is the limiting reactant) To find out how much H 2 is left over, do another line equation: Given: 28.0 g N 2 Desired:? g H 2 subtract the answer of this problem from 8.00 g H 2 Limiting Reactants (18 of 24) It is difficult to simply guess which reactant is the limiting reactant because it depends on two things: (1) the of the reactant and (2) the coefficients in the balanced equation The smaller mass is not always the limiting reactant. (28 g N 2 ) will just react with 3 moles (6.06 g H 2 ) so, if we react 28.0 g N 2 with 8.0 g H 2, only 6.06 g H 2 will be used up and 1.94 g of H 2 will be left over. In this case, N 2 is the L.R. and H 2 is in X.S. The answer you calculate from a stoichiometry problem can be called the Theoretical Yield. Theoretically, you should get this amount of product. Theoretical Yield and Percentage Yield (19 of 24) In reality, you often get less than the theoretical amount due to products turning back to reactants or side reactions. The amount you actually get is called the Actual Yield. Actual Yield Percentage Yield = Theoretical Yield x 100 Balancing Chemical Equations (20 of 24) The balanced equation represents what actually occurs during a chemical reaction. Since atoms are not created or destroyed during a normal chemical reaction, the number and kinds of atoms must agree on the left and right sides of the arrows. Na 2 CO 3 + HCl NaCl + H 2 O + CO 2 To balance the equation, you are only allowed to change the coefficients in front of the substances... not change the formulas of the substances themselves. Reduce the coefficients to the lowest terms. Fractions may be used in front of diatomic elements.

6 The burning of fuels made of C, H, and O is called combustion. You need to memorize O 2, CO 2 and H 2 O Combustion Equations (21 of 24) Example: The combustion of propane, C 3 H 8, is written: C 3 H 8 + 5O 2 3CO 2 + 4H 2 O Be careful when writing equations for alcohols, such as butanol, C 4 H 9 OH don t forget to add the H s (a total of 10 of them) don t forget to take account of the O atom in the alcohol C 4 H 9 OH + 6O 2 4CO 2 + 5H 2 O Solutions -- Molar Concentration (22 of 24) Many reactions are carried out in solution. Solutions are convenient and speed up many reactions. Concentration is often expressed as Molarity ( M ) = moles of solute Liters of solution You can calculate the molarity of a solution when given moles (or grams) of a substance and its volume. You can use the molarity of a solution as a conversion factor moles HCl M HCl or 1 Liter HCl to convert moles to Liters and vice versa. Volumetric flasks are used to make solutions. 1 Liter HCl moles HCl Dilution Problems (23 of 24) You can calculate the moles of a solute using the volume and molarity of the substance. Since diluting a solution adds water and no solute, the moles of solute before and after the dilution remains constant. So... V i M i = V f M f where I means initial and f means final The units of volume or concentration do not really matter as long as they match on the two sides of the equation. Acid-Base Titrations (24 of 24) Acids form the H + ion. Bases form the OH ion. Acids + bases mix to form H 2 O (HOH) and a salt. The moles of H + = the moles of OH in a neutralization. An acid-base titration is the technique of carefully neutralizing an acid with a base and measuring the volumes used. An indicator (we used phenolphthalein) allows us to observe when the endpoint is reached. If a monoprotic acid is neutralized with a base that only has one OH ion per formula unit, the simple formula: V a M a = V b M b allows you to determine the molarity of the unknown.

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