Electrochemistry and Electrical Circuits

Electrochemistry and electrical circuits and their elements Electrostatics (PHY) • Charge, conductors, charge conservation o Charges are either positive or negative. Zero is neutral ▪ Like charges repel, unlike charges attract ▪ Charge is quantized, and the unit of charge is the Coloumb o Conductors are materials in which charges can move freely. Metals are good conductors o Law of conservation of charge ▪ Charge can never be created nor destroyed. Isolating a negative charge also isolates a positive charge and vice versa • Insulators o Insulators are materials in which charges cannot move freely. Nonmetals are good insulators • Coloumb’s Law o F = kq1q2/r2 o k = 9E9 Nm2/C2 o If the charges have the same sign, the force is repulsive o If the charges have opposite signs, the force is attractive • Electric field E: electrostatic force per unit charge o Field strength ▪ Field strength decreases as distance between charges increases ▪ For an infinitely large, flat electric plate, field strength is constant • Lines have nowhere to spread. Without spreading, field strength can’t diffuse o Field lines ▪ Representations of fields, point in the direction of the field (positive to negative) ▪ Lines that are closer together denote stronger fields than lines that are farther apart ▪ Drawn from positive to negative o Field due to charge distribution ▪ Inside of a hollow sphere would have no electric field • This is because a field line has to start on a positive charge and end on a negative charge. No positive charge to start on in a hollow sphere • No gravitational field in a hollow sphere, so probably no electric field either ▪ ▪ ▪ ▪ • Electric fields come out of positive charges, and goes into negative charges The unit for electric field is N/C, or Newtons per Coloumb Field comes out of the positive end and goes into the negative end of a dipole Field lines for two negative charges are the same as those for two positive charges except the direction of the field lines would be reversed • The direction and magnitude of the field at any point in space can be calculated as the vector sum of all the field components there ▪ Electric field in between a capacitor is uniform until it reaches the end of the capacitor ▪ Electric field for wires runs radially perpendicular to the wire ▪ Electric field for a cylinder runs perpendicular to the cylinder, and is zero inside the cylinder Electrostatic energy, electric potential at a point in space o Electric potential ▪ As potential increases, a charge’s ability to do work increases • Voltage = work that can be done in an electric field per unit charge (Coulomb) ▪ Formulas for potential • U = qEd o E = electric field strength, q = charge, d = displacement in direction opposite of field • U = kq1q2/r o k = constant, r = distance between two charge centers o Voltage ▪ Work that can be done in an electric field per unit charge (Coulomb) • Measure of the strength of an electric field. Higher voltage = a charge can have more electric potential in there ▪ Different from electric potential in that… • Electric potential: refers to the potential electric field energy of a charge “q” and is dependent on the value of the charge • Voltage: depends on the strength of the electric field itself rather than a specific charge within that field Circuit Elements • Current I = ∆Q/∆t, sign conventions, units o Current is the rate of charge flow through the cross-section of a conductor (wire) o Traditionally, the direction of current is taken as the flow of positive charges o The unit for current is Coulombs per second, C/s • Electromotive force, voltage o Electromotive force (emf) is really not a force, but a potential difference, with the unit voltage • • o A battery is a source of emf o If the battery has no internal resistance, then potential difference across the battery = EMF o If the batter has internal resistance, then potential difference across battery = EMF - voltage drop due to internal resistance Resistance o Ohm’s Law: I = V/R ▪ Electric current (I) equals potential difference (V) divided by resistance ® o Resistors in series ▪ Rtot = R1 + R2 + … o Resistors in parallel ▪ 1/Rtot = 1/R1 + 1/R2 + … ▪ Voltage • Resistors in parallel experience the same voltage drop • Current flowing through each resistor in parallel is different (can be calculated using voltages and resistances of each resistor) o If parallel resistors have same individual resistances, then total current through each parallel resistor is I/n ▪ I = current of circuit, n = number of parallel wires o Resistivity R = ρ*L/A ▪ Resistivity vs. resistance • Resistivity: an intrinsic property of a substance to resist charge flow • Resistance: the quantitative measurement of an object’s ability to resist charge flow (taking into account shape and size of the object) ▪ Resistivity formula • Finds the resistance of a wire of length L and with a cross sectional area A • Shows resistance is directly proportional to the length of a wire and inversely proportional to the cross-sectional area of a wire o Resistance and temperature ▪ R = R0[1+α(T-T0)] ▪ Resistance is directly related to temperature o Resistance and Power ▪ Power: joules per second ▪ P = I2R = V2/R = IV • Shows that greater resistance for a resistor = less power drained • The greater the current, voltage through a resistor = more power drained Capacitance o Parallel plate capacitor ▪ Function: place to temporarily store energy in a circuit ▪ Composition: two plates made from conductive material separated by small distance • Separation of charges creates an E-field • Larger surface area of plates = smaller E-field • Larger charge on plates = larger E-field ▪ C = Q/V = κε0A/d ▪ Greater capacitance is created by a greater charge on plates (Q) for a given voltage (V), greater plate area (A), or smaller distance between plates (d) ▪ V = Ed, where V is voltage across capacitor, E is electric field between capacitor, and d is the distance between capacitor plates o Energy of a charged capacitor ▪ U = Q2/2C = ½ Q∆V = ½ C(∆V)2 ▪ U is the potential energy of the charged capacitor, Q is charge stored (magnitude of either +Q or -Q on one of the plates), C is capacitance • • o Capacitors in series ▪ 1/Ctot = 1/C1 + 1/C2 + … o Capacitors in parallel ▪ Ctot = C1 + C2 + … o Dielectrics ▪ Dielectric = nonconducting material ▪ Inserting a dielectric between the plates of a capacitor increases the capacitance by either increasing Q (if V is constant) or decreasing V (if Q is constant) ▪ V = V0/κ ▪ C = κC0 Conductivity o Conduction: when charge moves along an object ▪ An object conducting charge also resists the movement of charge (resistivity) o What makes a good conductor? ▪ Allows electrons to move freely (metals), doesn’t hold them in place (diamond, glass) o Metallic: conduct charge through transfer of electrons with no chemical change occurring as a result ▪ Ex. metals. It’s electrons from a “sea of electrons” conducive to electron flow o Electrolytic: conduct charge through a flow of ions through a membrane. Ion flow entails a transfer of matter ▪ Ex. salt bridge. Ions flow across the membrane to maintain neutral charge in half cells Meters o Ammeter ▪ Measures current in a circuit ▪ Connected in series (allows all current flowing through circuit to flow through the meter as well) ▪ Resistance is near zero (so that current can flow through it unobstructed) o Voltmeter ▪ Measures potential difference between two points on a circuit ▪ Connected in parallel to the circuit ▪ Resistance is basically infinite (to avoid drawing a current and thereby changing the potential difference) o Multimeter ▪ Functions both as an ammeter and voltmeter (have to switch between the two functions) Magnetism (PHY) • Definition of magnetic field B o Magnetic field B exists in a region of space if a moving charge experiences a force due to its motion in that region o The unit for magnetic field is the Tesla (T) or N•s/m•C • Motion of charged particles in magnetic fields, Lorentz force o F = qvB sinθ o θ is the angle between the charge velocity and magnetic field. Sometimes the sinθ is omitted as θ is assumed to be 90˚ o The force is always perpendicular to both the magnetic field and to the velocity of the charge o You can use the right-hand rule to predict the direction of the force. The thumb is the direction of a positive charge, the middle finger is the direction of the magnetic field, and the palm faces the direction of the force o Special scenarios / cases ▪ Charge moving in a circle • F = qvB = mv2/r • ▪ You are setting the electromagnetic force equal to the centripetal force, which maintains the orbit. Using this equation, you can solve for whatever the question asks you Current carrying wires • F = qvB sinθ = (I•t)vB sinθ = (I•t)(L/t)B sinθ = ILB sinθ • I is current, L is length of wire • Consider the current in the wire as moving positive charges (by tradition, the direction of the current is defined as the direction of moving positive charges) • You can calculate direction of the force on the wire in the same way using the right-hand rule. Just treat the direction of current the same as direction of velocity of a positive charge • Two wires will attract each other if the current is in the same direction • Two wires will repel each other if the current is in opposite directions Electrochemistry (GC) • Electrolytic cell o Electrolysis ▪ Hooking up a power source to a galvanic cell and forcing reactions to run in reverse ▪ Allows metal that’s normally reduced to be oxidized and vice versa ▪ Nonspontaneous o Anode, cathode ▪ Anode: Positively charged, oxidation takes place here ▪ Cathode: Negatively charged, reduction takes place here • Cathode is negative b/c additional power enables the more species to be reduced o Electrolyte: compound that forms ions in aqueous solution ▪ Ionized or ionizable components of an electrochemical cell o Faraday’s Law relating number of elements deposited (or gas liberated) at an electrode to current o Electron flow; oxidation, and reduction at the electrodes ▪ Electrons flow from cathode to anode • Galvanic or Voltaic cells o Half-reactions ▪ Each half-cell has its own half-reaction ▪ Subtracting anode half-rxn reduction potential from cathode half-rxn reduction potential = EMF of cell ▪ Nernst equation ▪ At 298 K and in base 10 log form, the equation is • E = E˚ + .06/n log(Q) ▪ Used to find potential difference in a cell in nonstandard conditions o Reduction potentials; cell potential ▪ Reduction potentials: components of a cell potential • Cannot occur by itself, every reduction half rxn needs an accompanying oxidation half rxn • More positive potential = rxn more likely to proceed ▪ Cell potential: sum of standard state potentials for each half reaction SHE: standard hydrogen electrode, oxidizes H 2 to H+ to get e-’s. Reduction potential (anodal) of this half reaction is zero • Cell potential with SHE at anode is reduction potential of electrodes used in conjunction with SHE o Direction of electron flow ▪ Electrons flow from anode to cathode (- to +) ▪ Salt Bridge • At least one phase in a voltaic cell must be impermeable to electrons • Purpose: Salt bridge connects two liquid phases of galvanic cell, allowing for free movement of ions, this prevents charge differences between solutions (half-cells) o Salt bridge carries current through movement of ions, not electrons • Electrons can only flow across electrodes if there isn’t a charge difference between solutions (uneven charge of electrodes and equal charges of solutions create the potential difference necessary for charge movement) Concentration cell o Like galvanic cell, except potential difference is 0 and ion concentrations differ. Ion concentrations drive electron movement ▪ In galvanic, potential difference drives electron movement o Two half-cells contain the same half-reaction, keeping potential difference 0 ▪ Only the ion concentration between half cells differ o Salt bridge still present to prevent ion concentration from equilibrating o Electron flow ▪ Electrons flow from half-cell with more negative ions to that with more positive ions Batteries o Electromotive force, Voltage o Lead-storage batteries ▪ Anode and cathode • Anode made of lead, cathode made of lead oxide • Discharges in presence of sulfuric acid ▪ Behave as both galvanic and electrolytic cell • Galvanic: happens when it’s in use. Lead is anode and lead oxide is cathode. Forms lead sulfate (hazardous compound) and water • Electrolytic: happens when battery needs to recharge. Voltage must be applied for rxn to proceed ▪ Can provide large currents necessary for car starts, backup generators. However, produce hazardous lead sulfate which complicates disposal o Nickel-cadmium batteries ▪ Unlike lead storage batteries, its electrolytes aren’t consumed during discharge ▪ Arranged in cylindrical configuration to reduce resistance ▪ • • Specialized Cell - Nerve Cell (BIO) • Myelin sheath, Schwann cells, insulation of axon o Myelin sheath = covers the axon intermittently, with gaps called nodes of Ranvier o The purpose of myelin sheath is to speed up conduction by insulating the nerve in intervals. This intermittent insulation causes action potential to jump from one node of Ranvier to the next o Schwann cells = makes myelin sheath in the peripheral nervous system by wrapping around the axon o Oligodendrocytes = the central nervous system analogue of Schwann cells, makes myelin sheath around CNS axons o Insulation of axon = achieved by the myelin sheath. Insulation occurs in intervals, which causes action potential to jump from one node of Ranvier to the next • o Myelin sheath is a good insulator because it is fatty and does not contain any channels Nodes of Ranvier: propagation of nerve impulse along axon o Action potential jumps from one node of Ranvier to the next o This jumping of action potential speeds up conduction in the axon