Chemistry for Changing Times: Chapter 5 - Chemical Accounting

Learning Objectives

• Identify balanced and unbalanced chemical equations, and balance equations by inspection ($5.1$).

• Determine volumes of gases that react, using a balanced equation for a reaction ($5.2$).

• Calculate the formula mass, molecular mass, or molar mass of a substance ($5.3$).

• Use Avogadro’s number to determine the number of particles of different types in a mass of a substance ($5.3$).

• Convert from mass to moles and from moles to mass of a substance ($5.4$).

• Calculate the mass or number of moles of a reactant or product from the mass or number of moles of another reactant or product ($5.4$).

• Calculate the concentration (molarity, percent by volume, or percent by mass) of a solute in a solution ($5.5$).

• Calculate the amount of solute or solution given the concentration and the other amount ($5.5$).

• Explain how the concept of atom economy can be applied to pollution prevention and environmental protection.

• Calculate the atom economy for chemical reactions.

Chemical Sentences: Equations

• Chemical equations are the sentences in the language of chemistry.

• They communicate a chemical change using symbols and formulas for elements and compounds.

• Reactants: Species present before the reaction.

• Products: Species present after the reaction.

• Arrow notation: Reactants $<br>ightarrow$ Products, where the arrow means "yield(s)" or "react(s) to produce."

• State notations:

  • $(s)$ = solid

  • $(l)$ = liquid

  • $(g)$ = gas

  • $(aq)$ = aqueous solution

• Coefficients are numbers used to balance a chemical equation.

  • Crucial rule: Never change the subscripts in a chemical formula when balancing equations. Changing subscripts changes the identity of the substance.

• Examples of balancing $H<em>2 + O</em>2 ightarrow H_2O$:

  • Not balanced: $H<em>2 + O</em>2 <br>ightarrow H_2O$

  • Incorrectly balanced (Product added): $H<em>2 + O</em>2 <br>ightarrow H<em>2O + O</em>2$ (adding a product is incorrect)

  • Incorrectly balanced (Product formula changed): $H<em>2 + O</em>2 <br>ightarrow H<em>2O</em>2$ (changing $H<em>2O$ to $H</em>2O_2$ alters the substance)

  • Correctly balanced: $2 H<em>2 + O</em>2 <br>ightarrow 2 H_2O$

Volume Relationships in Chemical Equations

• Law of Combining Volumes: When all measurements are at the same temperature and pressure, the volumes of gaseous reactants and products are in small whole-number ratios.

• Avogadro’s Hypothesis: When measured at the same temperature and pressure, equal volumes of all gases contain the same number of molecules.

Avogadro’s Number and The Mole

• Avogadro’s number: Defined as the number of atoms in a $12 ext{-g}$ sample of carbon-12. Its value is $6.02 imes 10^{23}$.

• Mole (mol): The amount of a substance that contains $6.02 imes 10^{23}$ particles.

  • Magnitude of a mole: $6.02 imes 10^{23}$ baseballs roughly equals the mass of the Earth; $6.02 imes 10^{23}$ drops of water roughly equals the mass of the oceans.

• Formula mass: The average mass of a formula unit relative to that of a carbon-12 atom. It is the sum of the atomic masses for all atoms in a formula.

• Molecular mass: A term used interchangeably with formula mass when the formula represents a molecule.

• Molar volume of a gas: One mole of any gas occupies a volume of $22.4 ext{ L}$ at Standard Temperature and Pressure (STP).

  • STP Defined: $1 ext{ atmosphere (atm)}$ of pressure and a temperature of $0 ext{ °C}$.

Mole and Mass Relationships in Chemical Equations (Stoichiometry)

• Stoichiometry: Involves the quantitative relationship between reactants and products in a balanced chemical equation.

• The coefficients of a balanced chemical equation represent the mole ratios of reactants and products.

  • Example: $2 H<em>2 + O</em>2 <br>ightarrow 2 H<em>2O$ can be read as "Two moles of $H</em>2$ react with $1$ mole of $O<em>2$ to yield $2$ moles of $H</em>2O$".

• Steps in a Stoichiometric Calculation:

  1. Write and balance the chemical equation for the reaction.

  2. Determine the molar masses of the substances involved in the calculation.

  3. Use the coefficients of the balanced equation to convert moles of the given substance to moles of the desired substance.

  4. Use the molar mass to convert moles of the desired substance to grams of the desired substance.

• Conversion Pathway:

  • Mass of A (grams) $<br>ightarrow$ Amount of A (moles) (using Molar mass as conversion factor $rac{ ext{mol A}}{ ext{g A}}$)

  • Amount of A (moles) $<br>ightarrow$ Amount of B (moles) (using Coefficients from balanced reaction $rac{ ext{mol B}}{ ext{mol A}}$)

  • Amount of B (moles) $<br>ightarrow$ Mass of B (grams) (using Molar mass as conversion factor $rac{ ext{g B}}{ ext{mol B}}$)

Green Chemistry

• One goal of green chemistry is to reduce waste.

• Atom Economy: A measure of reaction efficiency, focusing on how much of the reactants end up in the desired product.

• Formula for Percent Atom Economy (% A.E.):
  ext{% A.E.} = rac{ ext{molar mass of desired product}}{ ext{molar masses of all reactants}} imes 100 ext{%}

Solutions and Concentration

• Solution Concentration: The amount of solute in a given amount of solvent.

• Dilute solution: Contains relatively small amounts of solute in a given amount of solvent.

• Concentrated solution: Contains relatively large amounts of solute in a given amount of solvent.

• Molarity (M): Defined as moles of solute per liter of solution.
  $M = rac{ ext{mol}}{ ext{liter}}$

• Percent Concentration (by volume):
  $ext{Percent by volume} = rac{ ext{volume of solute}}{ ext{volume of solution}} imes 100$

• Percent Concentration (by mass):
  $ext{Percent by mass} = rac{ ext{mass of solute}}{ ext{mass of solution}} imes 100$

• Example: Reagent grade hydrochloric acid is sold as a 38 ext{%} mass solution of $HCl$ in water.