Expressions Of Pj Problems

Pj Problems - Overview

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Painting

Electrolysis As Oxidation-Reduction Reaction

Figure 14.56 is a simple conceptual illustration of the electrolytic decomposition of molten sodium chloride.

(a) Describe the half-reactions of the chemical reaction then derive arithmetically, the whole oxidation-reduction reaction from the half-reactions.

(b) Using Faraday's Law of electrolysis, calculate the amount of Chlorine (in grams), a chemist could produced from molten sodium chloride (NaCl) if she uses a current of 1 ampere for 5 minutes?

**The strings**:

S_{7}P_{5}A_{52} (Change - Chemical Change)
**The math**:

Pj Problem of Interest is of type *change* (chemical change).

(a) *Electrolysis* is the use of electric current to cause a chemical reaction. The basic set-up (figure 14.56) is called an *electrolytic cell*. It consists of a voltage source connected to two electrodes immersed in a chemical substance. One of the electrodes, called the *cathode*, is negatively charged. The other, called the *anode* is positively charged. The substancce in which the electrodes are immersed is a solution or molten form of an *electrolyte*. An electrolyte is a substance whose aqueous solution conducts electricity. The conduction (called *electrolytic conduction*) that occurs in an electrolytic cell is due to the movement of positive ions (*cations*) and negative ions (*anions*) in the molten electrolyte. The cations are attracted to the cathode while the anions are attracted to the anode. In the electrolytic cell given in figure 14.56, the cations are sodium ions while the anions are chloride ions. So, the electrodes used must not react chemically with sodium or chloride ions.

The half-reactions are the reactions occuring at the electrodes:

Half-reaction at the cathode:

positively charged sodium ions are attracted to highly negatively charge cathode. Cathode electrons are at a higher potential energy than electrons in sodium atom. So electrons move from the cathode (high potential energy) to the sodium ions (lower potential energy). So at the cathode each sodium ion will be converted to a sodium atom by the addition of an electron and the half-reaction is:

Na^{+} + e^{-} --------> Na -------(1)

This reaction at the cathode results in a gain of electron. So it is a reduction reaction.

Half-reaction at the anode:

Negatively charged chloride ions are attracted to highly positively charge anode. Anode electrons are at a lower potential energy than the electrons of the chloride ions. So, electrons move from the chloride ions to the anode. So at the anode, each chloride ion loses an electron and the half-reaction is:

2Cl^{-} -------> Cl_{2} + 2e^{-} -------(2)

This reaction at the anode results in a loss of electron. So, it is an oxidation reaction.

In general, oxidation always occurs at the anode and reduction always occurs at the cathode.

The half-reactions at the cathode and anode do not occur independently. So, they must be combine to get the *whole* oxidation-reduction reaction as follows:

reaction (1) is multiplied by 2 and added to reaction (2)

So, 2Na^{+} + 2e^{-} + 2Cl^{-} --------> 2Na + Cl_{2} + 2e^{-}

So, 2Na^{+}(*l*) + 2Cl^{-}(*l*) --------> 2Na(*l*) + Cl_{2}(*g*)

(b) Michael Faraday's (1791-1867 A.D) law of electrolysis relates the mass of substance produced at either eletrode during electrolysis to the amount of electricity used (expressed in Coulombs). The formula is as follows:

mass of substance = moles of electrons x formula mass of substance/moles of electrons transfered.

1 mole of electron is defined as the *Farad* and equals 96485 Coulombs of electricity.

The half-equation at the anode for the production of Cl_{2} is as follows:

2Cl^{-} -------> Cl_{2} + 2e^{-}

Quantity of electricity used in Coulombs = 1 ampere x 300secs = 300 Coulombs

So, moles of electrons = 300/96485

moles of electrons transferred = 2 (from the half-reaction)

So, mass of chlorine = (300/96485) x (70.9/2) = .00311 x 35.45 = 0.111g

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

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