Latex for Atomic Structure Electrochemistry Thermochemistry Chemical Equations and Formulas

rockingdingo 2023-05-28 #Chemistry #Atomic Structure #Electrochemistry

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In this blog, we will summarize the latex code of most popular equations and formulas for Atomic Structure, Electrochemistry, Thermochemistry, Chemistry. The topics include Bohr Radius, De Broglie Wavelength, Linear Momentum, Planck Quantized Energy Equation, Radii of stable orbits in Bohr model, Energy and Principal Quantum Number, Rydberg Equation, Speed of Light, Cell Voltage, Electric Current, Reaction Quotient, Equilibrium Constant and Cell Voltage, Enthalpy Change,Entropy Change, Gibb Free Energy Change, Specific Heat Capacity to Heat Equation, etc.

1. Chemical Equations

Bohr Radius

De Broglie Wavelength

Linear Momentum

Planck Quantized Energy Equation

Radii of stable orbits in Bohr model

Energy and Principal Quantum Number

Rydberg Equation

Speed of Light

Cell Voltage

Electric Current

Reaction Quotient

Equilibrium Constant and Cell Voltage

Enthalpy Change

Entropy Change

Gibb Free Energy Change

Specific Heat Capacity to Heat Equation

1. Chemical Equations

Bohr Radius
Chemistry,Atomic Structure
Equation

$a_0 = \frac{{\hbar ^2 }}{{m_e ke^2 }}$

Latex Code
```
            a_0 = \frac{{\hbar ^2 }}{{m_e ke^2 }}
        
```
Explanation

Latex code for the Bohr Radius. A Bohr radius is the distance between the nucleus and the outermost shell of an atom, specifically the distance between the nucleus and electron in the ground state of the hydrogen atom.
- $a_0$ : Bohr Radius, the electron is moving with velocity v around the nucleus in an orbit of radius
- $m$ : Electron of mass m
- $h$ : the number of orbits. The Bohr radius is proportional to the square of the number of orbits as h^2.
Related Documents
- Bohr radius - definition and derivation
Related Videos
De Broglie Wavelength
Chemistry,Atomic Structure
Equation

$\lambda = \frac{h}{{m\upsilon }}$

Latex Code
```
            \lambda = \frac{h}{{m\upsilon }}
        
```
Explanation

Latex code for the De Broglie Wavelength.
- $m$ : Electron of mass m
- $v$ : Velocity v
- $h$ : The number of orbits h
Related Documents
- Bohr radius - definition and derivation
Related Videos
Linear Momentum
Chemistry,Atomic Structure
Equation

$p = m\upsilon$

Latex Code
```
            p = m\upsilon
        
```
Explanation

Latex code for Linear Momentum.
- $p$ : Linear Momentum
- $v$ : Velocity v
- $m$ : Mass m
Related Documents
- Bohr radius - definition and derivation
Related Videos
Planck Quantized Energy Equation
Chemistry,Atomic Structure
Equation

$\Delta E = h\nu$

Latex Code
```
            \Delta E = h\nu
        
```
Explanation

Latex code for Planck Quantized Energy Equation.
- $\Delta E$ : Quantized Energy
- $h$ : h
- $\nu$ : \nu
Related Documents
- Bohr radius - definition and derivation
Related Videos
Radii of stable orbits in Bohr model
Chemistry,Atomic Structure
Equation

$r = n^2 \frac{{\hbar ^2 }}{{m_e kZe^2 }} = n^2 \frac{{a_0 }}{Z}$

Latex Code
```
            r = n^2 \frac{{\hbar ^2 }}{{m_e kZe^2 }} = n^2 \frac{{a_0 }}{Z}
        
```
Explanation

Latex code for Radii of stable orbits in Bohr model.
- $r$ : Radii of stable orbits r
- $a_0$ : Bohr Radius, the electron is moving with velocity v around the nucleus in an orbit of radius
- $m$ : Electron of mass m
- $h$ : the number of orbits. The Bohr radius is proportional to the square of the number of orbits as h^2.
Related Documents
- Bohr model radii
Related Videos
Energy and Principal Quantum Number
Chemistry,Atomic Structure
Equation

$E_n = - R_H \left( {\frac{1}{{n^2 }}} \right) = \frac{{ - 2.178 \times 10^{ - 18} }}{{n^2 }}$

Latex Code
```
            E_n = - R_H \left( {\frac{1}{{n^2 }}} \right) = \frac{{ - 2.178 \times 10^{ - 18} }}{{n^2 }}
        
```
Explanation

Latex code for Energy and Principal Quantum Number.
- $E_n$ : Energy E_n
- $R_h$ : R_h
Related Documents
- Bohr model radii
Related Videos
Rydberg Equation
Chemistry,Atomic Structure
Equation

$\Delta E = R_H \left( {\frac{1}{{n_i ^2 }} - \frac{1}{{n_f ^2 }}} \right)$

Latex Code
```
            \Delta E = R_H \left( {\frac{1}{{n_i ^2 }} - \frac{1}{{n_f ^2 }}} \right)
        
```
Explanation

Latex code for Rydberg Equation. Rydberg suggested that all atomic spectra formed families with this pattern (he was unaware of Balmer's work). It turns out that there are families of spectra following Rydberg pattern, notably in the alkali metals, sodium, potassium, etc., but not with the precision the hydrogen atom lines fit the Balmer formula, and low values of n2 predicted wavelengths that deviate considerably. The results given by Balmer and Rydberg for the spectrum in the visible region of the electromagnetic radiation start with n2=3, and n1=2.
- $E_n$ : Energy E_n
- $R_H$ : RH is the Rydberg constant and is equal to 109,737 cm -1 (2.18 Ã? 10 â?? 18J)
- $n_1,n_2$ : n1 and n2 are integers (whole numbers) with n2>n1
Related Documents
- Bohr model radii
- The Rydberg Formula and the Hydrogen Atomic Spectrum
Related Videos
Speed of Light
Chemistry,Atomic Structure
Equation

$c = \lambda \nu$

Latex Code
```
            c = \lambda \nu
        
```
Explanation

Latex code for Speed of Light to Wavelength and Frequency Relationship.
- $c$ : Speed of Light
- $\lambda$ : Wavelength
- $\nu$ : Frequency
Related Documents
- Bohr model radii
- The Rydberg Formula and the Hydrogen Atomic Spectrum
Related Videos
Cell Voltage
Chemistry,Electrochemistry
Equation

$E_{cell} = E^\circ _{cell} - \frac{{RT}}{{n\Im }}\ln Q = E^\circ _{cell} - \frac{{0.0592}}{n}\log Q$

Latex Code
```
            E_{cell} = E^\circ _{cell} - \frac{{RT}}{{n\Im }}\ln Q = E^\circ _{cell} - \frac{{0.0592}}{n}\log Q
        
```
Explanation

Latex code for Cell Voltage.
- $E_{cell}$ : Energy of Cell
- $\lambda$ : Wavelength
- $\nu$ : Frequency
Related Documents
- The Reaction Quotient
Related Videos
Electric Current
Chemistry,Electrochemistry
Equation

$I = \frac{q}{t}$

Latex Code
```
            I = \frac{q}{t}
        
```
Explanation

Latex code for Electric Current.
- $I$ : Electric Current
- $\lambda$ : Wavelength
Related Documents
- The Reaction Quotient
Related Videos
Reaction Quotient
Chemistry,Electrochemistry
Equation

$\begin{array}{*{20}c} {Q = \frac{{\left[ C \right]^c \left[ D \right]^d }}{{\left[ A \right]^a \left[ B \right]^b }}} \\ {\begin{array}{*{20}c} {aA + bB \rightleftharpoons cC + dD} \\ \end{array}} \\ \end{array}$

Latex Code
```
            \begin{array}{*{20}c} {Q = \frac{{\left[ C \right]^c \left[ D \right]^d }}{{\left[ A \right]^a \left[ B \right]^b }}} \\ {\begin{array}{*{20}c} {aA + bB \rightleftharpoons cC + dD} \\ \end{array}} \\ \end{array}
        
```
Explanation

Latex code for Reaction Quotient. The reaction quotient (Q) measures the relative amounts of products and reactants present during a reaction at a particular point in time. The reaction quotient aids in figuring out which direction a reaction is likely to proceed, given either the pressures or the concentrations of the reactants and the products. The Q value can be compared to the Equilibrium Constant, K , to determine the direction of the reaction that is taking place. Q equation is written by multiplying the activities (which are approximated by concentrations) for the species of the products and dividing by the activities of the reactants. If any component in the reaction has a coefficient, indicated above with lower case letters, the concentration is raised to the power of the coefficient. Q for the above equation is therefore as above.
- $Q$ : Reaction Quotient
Related Documents
- The Reaction Quotient
Related Videos
Equilibrium Constant and Cell Voltage
Chemistry,Electrochemistry
Equation

$\log K = \frac{{nE^\circ }}{{0.0592}}$

Latex Code
```
            \log K = \frac{{nE^\circ }}{{0.0592}}
        
```
Explanation

Latex code for Equilibrium Constant and Cell Voltage.
- $K$ : Equilibrium Constant
- $E^\circ$ : Cell Voltage
Related Documents
- The Reaction Quotient
Related Videos
Enthalpy Change
Chemistry,Thermochemistry
Equation

$\Delta H^\circ = \sum {H^\circ _f {\rm{products}}} - \sum {H^\circ _f {\rm{reactants}}}$

Latex Code
```
            \Delta H^\circ = \sum {H^\circ _f {\rm{products}}} - \sum {H^\circ _f {\rm{reactants}}}
        
```
Explanation

Latex code for Enthalpy Change.
- $\Delta H^\circ$ : Enthalpy Change
Related Documents
- The Reaction Quotient
Related Videos
Entropy Change
Chemistry,Thermochemistry
Equation

$\Delta S^\circ = \sum {S^\circ {\rm{products}}} - \sum {S^\circ {\rm{reactants}}}$

Latex Code
```
            \Delta S^\circ = \sum {S^\circ {\rm{products}}} - \sum {S^\circ {\rm{reactants}}}
        
```
Explanation

Latex code for Entropy Change.
- $\Delta S^\circ$ : Entropy Change
Related Documents
- The Reaction Quotient
Related Videos
Gibb Free Energy Change
Chemistry,Thermochemistry
Equation

$\Delta G^\circ = \sum {G^\circ _f {\rm{products}}} - \sum {G^\circ _f {\rm{reactants}}} \\ \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \\ \Delta G^\circ = - n\Im E^\circ$

Latex Code
```
            \Delta G^\circ = \sum {G^\circ _f {\rm{products}}} - \sum {G^\circ _f {\rm{reactants}}} \\
            \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \\
            \Delta G^\circ = - n\Im E^\circ
        
```
Explanation

Latex code for Gibb Free Energy Change. Gibb's Free Energy Change in Terms of Enthalpy, Absolute Temperature, and Entropy. Also, Gibb's Free Energy Change can be expressed in Terms of Gas Constant, Absolute Temperature, and Equilibrium Constant. Additionally, Gibb's Free Energy Change can be expressed in Terms of Number of Moles, Faraday, and Standard Reduction Potential.
- $\Delta G^\circ$ : Gibb Free Energy Change
- $\Delta H^\circ$ : Enthalpy chage
- $T$ : Absolute Temperature
- $\Delta S^\circ$ : Entropy Change
- $R$ : Gas Constant
- $R$ : Gas Constant
- $K$ : Equilibrium Constant
- $n$ : Number of Moles
- $\Im$ : Faraday
- $E^\circ$ : Standard Reduction Potential
Related Documents
- The Reaction Quotient
Related Videos
Specific Heat Capacity to Heat Equation
Chemistry,Thermochemistry
Equation

$q = mc\Delta T$

Latex Code
```
            q = mc\Delta T
        
```
Explanation

Latex code for Specific Heat Capacity to Heat Equation.
- $q$ : Heat Capacity
- $m$ : Mass
- $T$ : Absolute Temperature
Related Documents
- The Reaction Quotient
Related Videos