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Albia Dugger • Miami Dade College
Eldra SolomonLinda BergDiana W. Martin
Chapter 2
Atoms and Molecules: The Chemical Basis of Life
Chemistry and Life
• All organisms share fundamental similarities in their chemical composition and basic metabolic processes
• The structure of atoms determines the way they form chemical bonds to produce complex compounds
• molecular biology• Chemistry and physics of the molecules that constitute
living things
Inorganic and Organic Compounds
• inorganic compounds • Small, simple substances • Biologically important groups include water, simple acids
and bases, and simple salts
• organic compounds• Generally large, complex carbon-containing compounds• Typically, two or more carbon atoms are bonded to each
other to form the backbone, or skeleton, of the molecule
2.1 ELEMENTS AND ATOMS
LEARNING OBJECTIVES:
• Name the principal chemical elements in living things and provide an important function of each
• Compare the physical properties (mass and charge) and locations of electrons, protons, and neutrons. Distinguish between the atomic number and the mass number of an
atom
• Define the terms orbital and electron shell; relate electron shells to principal energy levels
Elements
• elements • Substances that can’t be broken down into simpler
substances by ordinary chemical reactions• Each element has a chemical symbol (Example: C for
carbon)
• Four elements (oxygen, carbon, hydrogen, and nitrogen) make up more than 96% of the mass of most organisms• Calcium, phosphorus, potassium, and magnesium, are
present in smaller quantities• Iodine and copper are trace elements
Functions of Elements in Organisms
Table 2-1, p. 27
Atoms and Matter
• atom• Smallest unit of an element that retains that element’s
chemical properties• Made up of tiny subatomic particles of matter
• matter• Anything that has mass and takes up space
Subatomic Particles
• There are three basic types of subatomic particles:• An electron carries a unit of negative electric charge• A proton carries a unit of positive charge• A neutron is an uncharged particle
• Protons and neutrons compose the atomic nucleus
• Electrons move rapidly around the atomic nucleus
• In an electrically neutral atom, the number of electrons equals the number of protons
Atomic Number and the Periodic Table
• Every element has a fixed number of protons in the atomic nucleus (atomic number) which determines an atom’s identity and defines the element
• The periodic table is a chart of the elements arranged in order by atomic number and chemical behavior
• Bohr models represent the electron configurations of elements as a series of concentric rings
The Periodic Table
Fig. 2-1, p. 28
Chemical symbol
Atomic number
Chemical name
Number of e– in each energy level
Atomic Mass
• The mass of a subatomic particle is expressed in terms of the atomic mass unit (amu) or dalton
• One amu equals the approximate mass of a single proton or a single neutron; an electron is about 1/1800 amu
• The atomic mass of an atom equals the total number of protons and neutrons, expressed in amus or daltons
Characteristics of Subatomic Particles
Particle Charge ~Mass Location
Proton Positive 1 amu Nucleus
Neutron Neutral 1 amu Nucleus
Electron Negative ~1/1800 amu Outside nucleus
Isotopes
• Most elements consist of a mixture of atoms with different numbers of neutrons and different masses
• isotopes• Atoms of the same element (having the same number of
protons and electrons) with varying numbers of neutrons
• The mass of an element is expressed as an average of the masses of its isotopes
Isotopes of Carbon
Radioisotopes
• Some isotopes are unstable and tend to break down (decay) to a more stable isotope (usually a different element)
• radioisotope• Unstable isotope that emits radiation as it decays• Example: 14C decays to 14N when a neutron decomposes
to form a proton and a fast-moving electron
• Radioactive decay can be detected by autoradiography, on photographic film
Radioisotopes in Biology
• Radioisotopes such as 3H (tritium), 14C, and 32P can replace normal molecules and are used as tracers in research
• In medicine, radioisotopes are used for both diagnosis (such as thyroid function or blood flow) and treatment (such as cancer)
Autoradiography
• Tritium (3H) incorporated into the DNA of a fruit fly
Atomic Orbitals and Energy
• Electrons move through characteristic regions of 3-D space (orbitals), each containing a maximum of 2 electrons
• The energy of an electron depends on the orbital it occupies
• Electrons in orbitals with similar energies (the same principal energy level) make up an electron shell
• Electrons farther from the nucleus generally have greater energy than those closer to the nucleus
Valence Electrons
• The most energetic electrons (valence electrons) occupy the valence shell, represented as the outermost concentric ring in a Bohr model
• Valence electrons participate in chemical reactions
• An electron can move to a higher orbital by receiving more energy, or give up energy and sink to a lower orbital
• Changes in electron energy levels are important in energy conversions in organisms
Atomic Orbitals
Fig. 2-4a, p. 30
Nucleus
(a) The first principal energy level contains a maximum of 2 electrons, occupying a single spherical orbital (designated 1s). The electrons depicted in the diagram could be present anywhere in the blue area.
1s
Fig. 2-4b, p. 30
(b) The second principal energy level includes four orbitals, each with a maximum of 2 electrons: one spherical (2s) and three dumbbell-shaped (2p) orbitals at right angles to one another.
2s 2py 2px 2pz
Fig. 2-4c, p. 30
(c) Orbitals of the first and second principal energy levels of a neon atom are shown superimposed. Note that the single 2s orbital plus three 2p orbitals make up neon's full valence shell of 8 electrons. Compare this more realistic view of the atomic orbitals with the Bohr model of a neon atom at right.
1s2s
2py
2px
2pz
x
z
y
Fig. 2-4d, p. 30
(d) Neon atom (Bohr model)
ANIMATION: The shell model of electron distribution
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Key Concepts 2.1
• Carbon, hydrogen, oxygen, and nitrogen are the most abundant elements in living things
ANIMATION: Atomic number, mass number
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ANIMATION: Electron arrangement in atoms
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Animation: Electron distribution
ANIMATION: Subatomic particles
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2.2 CHEMICAL REACTIONS
LEARNING OBJECTIVES:
• Explain how the number of valence electrons of an atom is related to its chemical properties
• Distinguish among simplest, molecular, and structural chemical formulas
• Explain why the mole concept is so useful to chemists
Valence Electrons
• Chemical behavior of an atom is determined by the number and arrangement of its valence electrons
• Atoms with full valence shells are unreactive
• When the valence shell is not full, an atom tends to lose, gain, or share electrons to achieve a full outer shell
• Elements in the same vertical column (group) of the periodic table have similar chemical properties
Compounds and Molecules
• Two or more atoms may combine chemically
• A chemical compound consists of atoms of two or more different elements combined in a fixed ratio
• Two or more atoms joined very strongly form a stable molecule
• Example: H20 (water) is a molecular compound
Chemical Formulas
• A chemical formula is a shorthand expression that describes the chemical composition of a substance
• In a simplest formula (empirical formula), subscripts give the smallest ratios for atoms in a compound (e.g. NH2)
• A molecular formula gives the actual numbers of each type of atom per molecule (e.g. N2H4)
• A structural formula shows the arrangement of atoms in a molecule (e.g. water, H—O—H)
The Mole
• The molecular mass of a compound equals the sum of the atomic masses of the component atoms of a single molecule
• The amount of a compound whose mass in grams is equivalent to its molecular mass is 1 mole (mol)
• Example:
• Molecular mass of water (H2O) is (hydrogen: 2 × 1 amu) + (oxygen: 1 × 16 amu) = 18 amu
• 1 mol of water is 18 grams (g)
The Mole (cont.)
• 1 mol of any substance has exactly the same number of atoms or molecules: 6.02 × 1023 (Avogadro’s number)
• Avogadro’s number allows scientists to calculate the number of atoms or molecules in sample simply by weighing it
• A 1 molar solution (1 M) contains 1 mol of a substance dissolved in a total volume of 1 liter (L)
Chemical Reactions
• Chemical reactions, such as the reaction between glucose and oxygen, are described by chemical equations:
C6H12O6 + 6 O2 → 6 CO2 + 6 H2O + energy
• Substances that participate in the reaction (reactants) are written on the left side of the arrow
• Substances formed by the reaction (products) are written on the right side
Chemical Reactions (cont.)
• Many reactions proceed forward and reverse simultaneously
• At dynamic equilibrium, the rates of forward and reverse reactions are equal
CO2 + H2O ↔ H2CO3
• When this reaction reaches equilibrium, there will be more reactants (CO2 and H2O) than product (H2CO3)
Key Concepts 2.2
• The chemical properties of an atom are determined by its highest-energy electrons, known as valence electrons
ANIMATION: Chemical bookkeeping
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Animation: Covalent bonds
2.3 CHEMICAL BONDS
LEARNING OBJECTIVE:
• Distinguish among covalent bonds, ionic bonds, hydrogen bonds, and van der Waals interactions
• Compare them in terms of the mechanisms by which they form and their relative strengths
Chemical Bonds
• Atoms can be held together by chemical bonds
• Valence electrons dictate how many bonds an atom can form
• bond energy• Energy necessary to break a chemical bond
• Two types of strong chemical bonds: covalent and ionic
Covalent Bonds
• Covalent bonds involve sharing electrons between atoms in a way that fills each atom’s valence shell
• A molecule consists of atoms joined by covalent bonds
• Example: hydrogen gas (H2)
• Unlike atoms linked by covalent bonds form a covalent compound
Lewis Structure
• A simple way of representing valence electrons is to use dots placed around the chemical symbol of the element:
• Oxygen (6 valence electrons) shares electrons with two hydrogen atoms to complete its valence shell of 8 – each hydrogen atom completes a valence shell of 2
Carbon Bonds
• Carbon has 4 electrons in its valence shell, all of which are available for covalent bonding (e.g. methane, CH4)
• Each orbital holds a maximum of 2 electrons
Single, Double, and Triple Covalent Bonds
• When one pair of electrons is shared between two atoms, the covalent bond is called a single covalent bond
• A double covalent bond is formed when two pairs of electrons are shared (represented by two parallel solid lines)
• A triple covalent bond is formed when three pairs of electrons are shared (represented by three parallel solid lines)
Electron Sharing in Covalent Compounds
Fig. 2-5a, p. 33
Hydrogen (H) Hydrogen (H) Molecular hydrogen (H2) or H H
(a) Single covalent bond formation. Two hydrogen atoms achieve stability by sharing a pair of electrons, thereby forming a molecule of hydrogen. In the structural formula on the right, the straight line between the hydrogen atoms represents a single covalent bond.
Fig. 2-5b, p. 33
Oxygen (O) Oxygen (O) Molecular oxygen (O2) (double bond is formed)
or O O
(b) Double covalent bond formation. In molecular oxygen, two oxygen atoms share two pairs of electrons, forming a double covalent bond. The parallel straight lines in the structural formula represent a double covalent bond.
Bonds Found in Biologically Important Molecules
Atom Symbol Covalent Bonds• Hydrogen H 1• Oxygen O 2• Carbon C 4• Nitrogen N 3• Phosphorus P 5• Sulfur S 2
Molecular Shape and Function
• The functions of molecules in living cells are determined largely by their geometric shapes
• When atoms form covalent bonds, orbitals in valence shells may become rearranged (orbital hybridization), affecting the shape of the resulting molecule
• Example: In methane (CH4), the hybridized valence shell orbitals of the carbon form a tetrahedron
Tetrahedron: Methane (CH4)
• Geometric shape of a molecule provides the optimal distance between atoms to counteract repulsion of electron pairs
Fig. 2-6, p. 34
Methane (CH4)
Polar and Nonpolar Covalent Bonds
• electronegativity • A measure of an atom’s attraction for shared electrons in
chemical bonds (e.g. oxygen has high electronegativity)
• nonpolar covalent bond• When covalently bonded atoms have similar
electronegativities, electrons are shared equally
• polar covalent bond • Covalent bond between atoms that differ in
electronegativity; electrons are pulled closer to the nucleus of the atom with greater electron affinity
Polar Molecules
• A polar covalent bond has two dissimilar ends (poles), one with a partial positive charge and the other partially negative
• A polar molecule has one end with a partial positive charge and another end with a partial negative charge
• Example: Water has a partial positive charge at the hydrogen end and a partial negative charge at the oxygen end, where “shared” electrons are more likely to be
Water: A Polar Molecule
Fig. 2-7, p. 34
Hydrogen (H) Oxygen (O) Hydrogen (H)
Fig. 2-7b, p. 34
Oxygen part
Partial negative
charge at oxygen end of molecule
Hydrogen parts
Partial positive charge at hydrogen end of molecule
Water molecule (H2O)
Ions
• An atoms or group of atoms with 1 or more units of electric charge is called an ion
• Atoms with 1, 2, or 3 valence electrons tend to lose electrons to other atoms and become positively charged cations
• Atoms with 5, 6, or 7 valence electrons tend to gain electrons from other atoms and become negatively charged anions
Functions of Ions
• The properties of ions are different from those of the electrically neutral atoms from which they were derived
• Electric charges of cations and anions provide a basis for energy transformations within the cell, transmission of nerve impulses, muscle contraction, and other biological processes
Ions and Biological Processes
• Sodium, potassium, and chloride ions are essential for a nerve cell to stimulate muscle fibers, initiating a muscle contraction
• Calcium ions in the muscle cell are required for muscle contraction
Fig. 2-8, p. 35
Muscle fiber
Nerve
Ionic Bonds
• An ionic bond is formed by attraction between the positive charge of a cation and the negative charge of an anion
• An ionic compound is a substance consisting of anions and cations bonded by their opposite charges
• Example: Sodium chloride (NaCl), an ionic compound• When sodium reacts with chlorine, sodium’s single
valence electron is transferred completely to chlorine• Sodium becomes a cation (Na+); chlorine becomes an
anion (Cl−)
Fig. 2-9, p. 35
11 protons 17 protons
and
11 electrons Sodium (Na)
17 electrons Chlorine (Cl)
10 electrons Sodium ion (Na+)
18 electrons Chloride ion (Cl–)
Sodium chloride (NaCl)
Arrangement of atoms in a crystal of salt
Ionic Bonding
ANIMATION: Ionic bonding
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Ionic Compounds in Solution
• In the absence of water, ionic bonds are very strong
• Example: Electrical attraction in ionic bonds holds Na+ and Cl− together to form NaCl (sodium chloride, table salt)
• When placed in water, ionic compounds (such as sodium chloride) tend to dissociate into individual ions :
NaCl (in H2O) → Na+ + Cl–
Water as a Solvent
• Water is an excellent solvent, capable of dissolving many substances (solutes)
• Because of their polarity, water molecules easily dissolve polar or ionic substances
• In solution, each cation or anion is surrounded by oppositely charged ends of the water molecules (hydration)
Hydration of an Ionic Compound
Fig. 2-10, p. 36
Salt
ANIMATION: Spheres of hydration
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Hydrogen Bonds
• Hydrogen bonds are relatively weak bonds (easily formed and broken) that are very important in living organisms
• When hydrogen combines with a relatively electronegative atom, it acquires a partial positive charge
• Hydrogen bonds form between an atom with a partial negative charge and a hydrogen atom that is covalently bonded to oxygen or nitrogen
• Water molecules interact with one another extensively through hydrogen bond formation
Hydrogen Bonding
ANIMATION: Examples of hydrogen bonds
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van der Waals Interactions
• Adjacent molecules may interact in transient regions of weak positive and negative charge
• The resulting attractive forces (van der Waals interactions) operate over very short distances and are weaker and less specific than other types of interactions
• They are important when they occur in large numbers and when molecular shapes permit close contact between atoms
Key Concepts 2.3
• A molecule consists of atoms joined by covalent bonds
• Other important chemical bonds include ionic bonds
• Hydrogen bonds and van der Waals interactions are weak attractions
ANIMATION: How atoms bond
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2.4 REDOX REACTIONS
LEARNING OBJECTIVE:
• Distinguish between the terms oxidation and reduction, and relate these processes to the transfer of energy
Redox Reactions
• Many energy conversions involve oxidation–reduction (redox) reactions in which an electron (and its energy) is transferred from one substance to another
• oxidation • Chemical process in which an atom, ion, or molecule loses
one or more electrons
• reduction• Chemical process in which an atom, ion, or molecule gains
one or more electrons
Redox Reactions (cont.)
• Redox reactions occur simultaneously; one substance accepts electrons that are removed from the other• The oxidizing agent accepts electrons and is reduced • The reducing agent gives up electrons and is oxidized
• In cells, oxidation often involves removal of a hydrogen atom (an electron plus a proton) from a covalent compound• Reduction often involves the addition of a hydrogen atom
Key Concepts 2.4
• The energy of an electron is transferred in a redox reaction
2.5 WATER
LEARNING OBJECTIVE:
• Explain how hydrogen bonds between adjacent water molecules govern many of the properties of water
Importance of Water
• About 70% of our total body weight is water• Water (via photosynthesis) is the source of oxygen in air,
and hydrogen atoms used in many organic compounds• Water is a solvent for biological reactions, and a reactant
or product in many chemical reactions• Water is a principal environmental factor for organisms• Water’s unique properties are essential to life
Fig. 2-12a, p. 37
(a) Commonly known as "water bears," tardigrades, such as these members of the genus Echiniscus, are small animals (less than 1.2 mm long) that normally live in moist habitats, such as thin films of water on mosses.
Effects of Water on an Organism
Fig. 2-12b, p. 37
(b) When subjected to desiccation (dried out), tardigrades assume a barrel-shaped form known as a tun, remaining in this state, motionless but alive, for as long as 100 years. When rehydrated, they assume their normal appearance and activities.
10 μm
Hydrogen Bonds Between Water Molecules
• Water molecules are polar
• Hydrogen bonds form between the partial positive charge (hydrogen) of one water molecule and the partial negative charge (oxygen) of a neighboring water molecule
• Each water molecule can form hydrogen bonds with up to four neighboring water molecules
Hydrogen Bonding of Water Molecules
Fig. 2-13, p. 38
Cohesion and Adhesion
• cohesion • Tendency of water molecules to stick to one another, due
to hydrogen bonds among molecules• Any force exerted on part of a column of water is
transmitted to the column as a whole• Major mechanism of water movement in plants
• adhesion• The ability of water to stick to other substances,
particularly those with charges on their surfaces• Explains how water makes things wet
Capillary Action and Surface Tension
• capillary action• The tendency of water to move in narrow tubes, even
against the force of gravity• A combination of adhesive and cohesive forces
• surface tension • Molecules at water’s surface crowd together, producing a
strong layer as they are pulled downward by the attraction (cohesion) of water molecules beneath them
Capillary Action
• Adhesion between water and glass in a narrow tube pulls other water up by cohesion
• In the wider tube, adhesion is not strong enough to overcome the cohesion below
Fig. 2-14, p. 38
Surface Tension
• Water striders (Gerris) supported by surface tension of water
Fig. 2-15, p. 38
Interactions with Water
• Because water molecules are polar, water dissolves many kinds of substances, and excludes others
• Hydrophilic (“water-loving”) substances interact easily with water (polar and ionic compounds)
• Hydrophobic (“water-fearing”) substances are not soluble in water (nonpolar molecules)
• Hydrophobic interactions occur between groups of nonpolar molecules, which cluster together in water
Water and Temperature
• Water exists in three states, which differ in degree of hydrogen bonding: gas (vapor), liquid, and ice (crystalline)
• Adding heat energy makes molecules move faster (increases kinetic energy) and breaks hydrogen bonds
• heat• The total kinetic energy in a sample of a substance
• temperature• The average kinetic energy of the particles
Water and Temperature (cont.)
• Much of the heat energy added is used to break hydrogen bonds – less energy is available to speed the movement of water molecules (increasing temperature)
• heat of vaporization• Amount of heat energy required to change 1 g of a
substance from liquid phase to vapor phase
• calorie (cal)• Amount of heat energy – equivalent to 4.184 joules (J) –
required to raise 1 g of water 1 degree Celsius (C)
Water and Temperature (cont.)
• evaporative cooling• As water is heated, some molecules move faster than
others and are more likely to evaporate, taking heat with them and lowering the temperature of the water
• Humans dissipate excess heat as sweat evaporates
• specific heat• A large amount of energy is required to raise the
temperature of water (1 cal/g of water per degree Celsius)• Maintains constant environmental temperatures
Water and Temperature (cont.)
• Hydrogen bonding causes ice to have unique properties with important environmental consequences
• Liquid water expands as it freezes, making ice about 10% less dense than liquid water – ice floats on denser cold water
• Ice insulates liquid water below it, retarding freezing and permitting organisms to survive without freezing
Three Forms of Water
Fig. 2-16, p. 39
212°F 100°C
(a) Steam becoming water vapor (gas)
50°C
(b) Water (liquid)
32°F 0°C
(c) Ice (solid)
ANIMATION: Structure of water
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Key Concepts 2.5
• Water molecules are polar, having regions of partial positive and partial negative charge that permit them to form hydrogen bonds with one another and with other charged substances
ANIMATION: Dehydration synthesis and hydrolysis
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3D Animation: Dissolution
2.6 ACIDS, BASES, AND SALTS
LEARNING OBJECTIVES:
• Contrast acids and bases, and discuss their properties
• Convert the hydrogen ion concentration (moles per liter) of a solution to a pH value and describe how buffers help
minimize changes in pH
• Describe the composition of a salt and explain why salts are important in organisms
Ionization of Water
• In pure water, a small number of water molecules dissociate into hydrogen ions (H+) and hydroxide ions (OH−)
HOH ↔ H+ + OH−
• The concentrations of hydrogen ions and hydroxide ions in pure water are exactly equal
• Such a solution is said to be neutral – neither acidic nor basic
Acids and Bases
• acid • Substance that dissociates in solution to yield hydrogen
ions (H+) and anion; a proton donor• Acid → H+ + anion
• base • Substance that dissociates in solution to yield a hydroxide
ion (OH−) and a cation; a proton acceptor• NaOH → Na+ + OH-
• OH- + H+ → H2O
Acids and Bases (cont.)
• Some bases do not dissociate to yield hydroxide ions directly
• Example: Ammonia (NH3) acts as a base by accepting a proton from water, producing an ammonium ion (NH4
+) and releasing a hydroxide ion:
• NH3 + H2O → NH4+ + OH−
pH
• A solution’s acidity is expressed in terms of pH
• pH• The negative logarithm (base 10) of the hydrogen ion
concentration [H+] (expressed in moles per liter):
• pH = −log10[H+]
• The negative logarithm corresponds to a positive pH value• Pure water has a hydrogen ion concentration of 0.0000001
(10—7 mol/L) • Logarithm = −7; pH is 7
pH of Solutions
• neutral solution (pH 7)• Equal concentrations of hydrogen ions and hydroxide ions
(concentration of each is 10−7 mol/L)
• acidic solution (pH <7)• Hydrogen ion concentration is higher than hydroxide ion
concentration
• basic solution (pH >7)• Hydrogen ion concentration is lower than hydroxide ion
concentration
Calculating pH Values and Hydroxide Ion Concentrations
Table 2-2, p. 41
pH Values
• pH of most plant and animal cells (and their environment) ranges from around 7.2 to 7.4
Fig. 2-17, p. 41
0 Battery acid 0.0
pH scale
1Hydrochloric acid 0.8 Stomach acid 1.0
2 Stomach gastric juice 2.0
Increasing acidity
3 Vinegar 3.0
4Beer 4.5
5 Black coffee 5.0
Rainwater 6.256
Neutrality 7 Distilled water 7.0
Blood 7.4
8 Seawater 8.0
9 Bleach 9.0
10 Mono Lake, California 9.9
Increasing alkalinity
Household ammonia 11.5
11
12
13 Oven cleaner 13.0
14 Lye 14.0
Cow milk 6.5
Animation: The pH scale
Buffers Minimize pH Change
• Homeostatic mechanisms maintain appropriate pH values
• Example: pH of human blood is about 7.4 and must be maintained within very narrow limits
• buffer• Substance that resists changes in pH when an acid or
base is added• A buffering system includes a weak acid or a weak base
A Buffering System
• In blood, carbon dioxide reacts with water to form carbonic acid, a weak acid that dissociates to yield H+ and bicarbonate:
CO2 + H2O ↔ H2CO3 ↔ H+ + HCO3–
• Addition of excess hydrogen ions shifts the system to the left, as H+ combine with bicarbonate ions to form carbonic acid
• Addition of hydroxide ions shifts the system to the right
Formation of Salts
• When an acid and a base are mixed in water, anions from the acid and cations from the base combine to form a salt
• salt • Compound in which the hydrogen ion of an acid is
replaced by some other cation• Example: Sodium chloride (NaCl) is a salt in which the
H+ of HCl has been replaced by the cation Na+
• HCl + NaOH → H2O + NaCl
Salts (cont.)
• When a salt, acid, or base is dissolved in water, its dissociated ions (electrolytes) can conduct an electric current
• Animals and plants contain a variety of dissolved salts (important mineral ions) essential for fluid balance and acid–base balance
• Homeostatic mechanisms maintain concentrations and relative amounts of various cations and anions
Key Concepts 2.6
• Acids are hydrogen ion donors; bases are hydrogen ion acceptors
• The pH scale is a convenient measure of the hydrogen ion concentration of a solution