Content Outline: Batteries & Work (2.5)

Content Outline: Batteries & Work (2.5)

Unit 2: Electrochemistry

Content Outline: Batteries & Work (2.5)

Associated AP Learning Objectives: 3.12, 3.13

Important Concepts from previous units:

1)Chemical reactions can run in both directions…forward or reverse (at one time or simultaneously…equilibrium).

2)Electricity is associated with metals, ions, and moving electrons.

3)Electron quantity, like chemical quantity, can be measured in moles.

  1. Work
  1. This is a force applied over a distance. (For batteries, the “pushing” force of electrons moving through a wire.)
  2. For batteries, it can be thought of as the electromotive force (emf). “See” a possible definition in the term.
  1. To measure the force (electron flow), we need at least two distinct points on the same wire/circuit.
  2. The two points must exhibit a difference in potential between them. “Like” a concentration gradient for diffusion to occur in cells…remember your biology? If no difference exists, it is a dead battery at equilibrium.
  1. The difference will be measured in volts, just like you did to calculate cell potential using reduction potentials.
  1. Volt is a joule of work per Coulomb of charge transferred between the two points.
  1. The mathematical expression for emf or potential difference is:

Emf = potential difference (V) = work (Joule) See it as: V = J/C

Charge (Coulomb)

  1. The emf/potential coming out of the battery has a positive value. It is positive because we can use the force to power a device, such as a light or motor.
  2. The value of work though is a negative value. Think of it as negative because the work is consuming the force.
  1. Therefore work and emf/potential have opposite values.
  2. This can be mathematically expressed as:

ECELL = -w/q or w = -qECELL

  1. q = the quantity of charge in coulombs transferred between the two points. It can be thought of as “How many electrons were pushed through the wire.” Usually expressed in moles of electrons.
  2. Therefore, the maximum amount of work can be determined by the maximum cell potential.

Remember, the greater the difference in reduction potentials made for stronger batteries…more work can be done.

  1. Not all current (flowing electrons) will be used for work as a portion is always lost as heat due to friction as the electrons move through the wire. Just like your body produces heat as a byproduct of breaking down glucose in cellular respiration by the mitochondria.
  1. This is reflective of the Second Law of Thermodynamics: Energy moves from a state of high potential (can do work) toward low potential (Entropy)spontaneously.
  2. Entropy is referred to as disorder. Work cannot be done if there is no order to a system. Imagine how good a band would be if they never had a band director.
  1. Michael Faraday (1791 – 1867)
  1. He was an English physicist who invented such items as the electric motor, the generator, and electrolysis.
  2. His name is used as to describe the charge on1 mole of electrons, a Faraday (F).

1 Faraday = 96,485 Coulombs of charge transferred for 1 mole of electrons Remember, a mole is 6.022 x 1023 particles. That is a massive amount of electrons!

  1. To Find the amount of work a battery (cell) can produce:
  1. So q = the number of moles of electrons(n) X the charge per mol (F)

For example, a battery releases 1.5 moles of electrons along a wire at 2.0 V. The battery has a maximum potential of 2.2 V

To find q… we know the number of moles (n) = 1.5 moles.

We also know the charge (F) = 96,485 Coulombs/mol

So… q = nF = (1.5 moles) x (96,485 Coulombs/mol) = 1.44 x 105 Coulombs Estimation is important in Chemistry, so can you see that 1.44 is about 1.5 times that of 96 (96 + 48 = 144) 48 is ½ of 96.

Now that we know q, we can solve to find the actual amount of work that this battery(cell) can perform using w = -qECELL w = (-1.4 x 105 Coulombs) x (2.0 V) = -2.8 x 105 Joules of work

To find the maximum amount of work, replace 2.0V with 2.2 V in the above calculation.

  1. To find the efficiency of the battery: How good of a battery is it as it relates to actual work performed?

1. Efficiency = w x 100% Think of it as: the portion relationship.

wMAX the whole

so using the above example… -2.8 x 105 Coulombs x 100% = 90.3% Efficient

- 3.1 x 105 Coulombs

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