12.1 The Arithmetic of Equations Read the lesson title aloud to students.

What Is a Chemical Equation? A chemical equation shows what substances are involved in a chemical reaction. Explain to students that a chemical equation is a shorthand way of summarizing the substances that are involved in a chemical equation. Ask: What are the parts that you need to make this tricycle? Answer: frame, seat, three wheels, handlebars, two pedals Click to reveal the parts of the tricycle. Guide students to identifying the use of initials or letters to represent each part and ask them how they would write the different components as “chemical formulas.” Click to reveal the “equation” of the tricycle. F S 3W H 2P FSW3HP2

What If You Need More Than One? 5 15 10 To make five tricycles, you need ________ frames, _______seats, ________ wheels, _________ handlebars, and __________ pedals. Explain that chemical equations do more than just show the substances involved. They also show the amounts of substances involved. Therefore, they can be used to perform calculations involving the reaction. Ask: How many of each part would you need to make five tricycles? Answer: 5 frames, 5 seats, 15 wheels, 5 handlebars, 10 pedals Click to reveal the correct answer. __F + __S + __W + __H + __P  5FSW3HP2

Stoichiometry Stoichiometry uses conversion factors to calculate quantities. How many wheels are needed to make 640 tricycles? Explain that stoichiometry includes all of the calculations chemists do to figure out the quantities of substances involved in a chemical reaction. Click to reveal the question on the slide. Read the problem aloud. Click to reveal the knowns and unknowns for the problem.

Conversion Factors Conversion factor: Focus students’ attention on the idea of a conversion factor. Remind students that a conversion factor is a ratio and that ratios can be written as fractions. Ask: What is the conversion factor for the number of wheels for each tricycle? Answer: three wheels for one tricycle or one tricycle for every three wheels Click to reveal the conversion factors written in fraction form. Conversion factor:

Solving Stoichiometry Problems Walk students through the calculation. Encourage them to solve the problem in their notebooks along with you. Remind students to use dimensional analysis to be sure they write the equation correctly. Guide them to write the conversion so that the given quantity (the number of tricycles) cancels with the denominator of the conversion factor, leaving the units in the numerator (number of wheels). Click to reveal how the similar units cancel. Ask a student to write the number of wheels needed. Click to reveal the correct answer. 1920W

Interpreting Chemical Equations You can interpret a chemical equation in terms of number of atoms number of molecules number of moles mass volume Explain that there are a variety of ways to interpret a chemical equation.

Number of Atoms The number of each type of atom should be the same in the reactants and the products. 2 6 _____ atoms N _____ atoms H Remind students that a chemical formula shows the number and type of atoms in a substance. Ask students to identify the number of atoms of nitrogen and hydrogen in the reactants and products of the equation shown. If necessary, remind them how to handle subscripts and coefficients. Click to reveal the correct answer. Point out that the number of each type of atom is the same on both sides of the equation. ____ atoms N ____ atoms H

Number of Molecules Coefficients show the number of each type of molecule in the reaction. 1 3 2 ___ N2 molecule ___ H2 molecules Remind students that coefficients in a chemical reaction show the number of molecules involved. Ask a student to write the number of each type of molecule present in the reaction as written. Click to reveal the correct answer. Ask: Do most chemical reactions involve only one or a few molecules? Answer: No, most involve huge numbers of molecules. Click to reveal the lower equation. Ask students to predict how many hydrogen and ammonia molecules would be involved if there are 100 nitrogen molecules. Have a volunteer write the number of molecules. ____ NH3 molecules 100 N2 molecules ____ H2 molecules 300 ____ NH3 molecules 200

Number of Moles 1.00 mol 3.00 mol 2.00 mol Coefficients also show the number of moles of a substance involved in a reaction. If necessary, remind students of the definition of a mole. Ask: How many atoms or molecules are present in one mole of a substance? Answer: 6.02 × 1023 atoms or molecules Remind students what they just reviewed on the previous slide: The coefficients in a chemical equation can be multiplied by the same number if there is more than one molecule involved. Click to reveal the equation written in terms of one mole of molecules. Ask for a volunteer to write the number of moles of each substance represented by the equation. Click to reveal the correct answer. 1.00 mol 3.00 mol 2.00 mol

Mass The total mass of the reactants is equal to the total mass of the products. 28.0 g N2 3 × 2.0 g H2  2 × 17.0 g NH3 Explain that you can use a chemical equation to determine the masses of substances involved. Ask: What is the law of conservation of mass? Answer: Mass cannot be created or destroyed in a chemical reaction. Ask: How can molar mass be used to convert moles to mass? Answer: Multiply the number of moles of a substance by its molar mass to obtain the mass in grams. Ask one or two students to calculate the total mass of the reactants and the total mass of the products and to fill in the answers. Click to reveal the correct answer. Point out that both masses are the same. Tell students that all chemical reactions obey the law of conservation of mass. Click to reveal the relationship between the total mass of reactants and the total mass of products. 34 Total mass of reactants: ________ g Total mass of products: ________ g

Volume For gases, coefficients indicate the volumes involved as long as temperature and pressure are constant. 22.4 L N2 67.2 L H2  44.8 L NH3 Remind students that if we assume gases are behaving ideally, then one mole of any gas has the same volume as one mole of any other gas at the same temperature and pressure conditions. Explain that it is possible to perform gas volume calculations based on a chemical equation. In these calculations, chemists typically assume STP. Remind students that the term STP represents “standard temperature and pressure.” Ask: What are the values of STP? Answer: 0ºC and 101.3 kPa Ask: Why is the volume of a gas usually measured at STP? Answer: Its volume varies with temperature and pressure; the molar volume at STP always has one mole of particles. Ask: What is the molar volume of any gas at STP? Answer: 22.4L/mol of any ideal gas at STP Ask: How many particles does it contain? Answer: 22.4 L of any gas contains 6.02 × 1023 particles. Click to reveal the volumes of gases shown in the equation.