Chemical Kinetics: Reaction Rates and Rate Law

Chemical Kinetics: Reaction Rate

• Rate of reaction is the rate of decrease in reactant concentration or the rate of increase in product concentration
• For a reaction $A + B \rightarrow C + D$, the rate r is given by $r = -\frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{d[C]}{dt} = \frac{d[D]}{dt}$.

Chemical Kinetics: Average Rate

• Average rate $r_{av}$ is expressed as $r_{av} = -\frac{\Delta[R]}{\Delta t} = \frac{\Delta[P]}{\Delta t}$

Chemical Kinetics: Instantaneous Rate

• Instantaneous rate $r_{inst}$ is expressed as $r_{inst} = \lim_{\Delta t \to 0} -\frac{\Delta[R]}{\Delta t} = \lim_{\Delta t \to 0} \frac{\Delta[P]}{\Delta t}$.
• $r_{inst}$ can also be written as $r_{inst} = -\frac{d[R]}{dt} = \frac{d[P]}{dt}$

Chemical Kinetics: Rate Law Expression

• For a reaction $aA + bB \rightarrow cC + dD$, the rate r is proportional to $[A]^x [B]^y$.
• The rate law is given by $r = k[A]^x [B]^y$, where k is the rate constant, [A] and [B] are reactant concentrations, x and y are orders with respect to A and B, respectively, and (x + y) is the overall order of reaction.
• x and y must be determined experimentally and may not be equal to the stoichiometric coefficients a and b.

Chemical Kinetics: Units of Rate Constant

• The rate constant k can be expressed as $k = \frac{r}{[A]^x [B]^y}$.
• $k = \frac{mol : L^{-1} s^{-1}}{(mol : L^{-1})^n}$ leading to $k = mol^{1-n} L^{n-1} s^{-1}$, where n is the order of reaction.
• For a zeroth-order reaction, the units of k are $mol : L^{-1} s^{-1}$.
• For a first-order reaction, the units of k are $s^{-1}$.
• For a second-order reaction, the units of k are $mol^{-1} L s^{-1}$.
• For a third-order reaction, the units of k are $mol^{-2} L^2 s^{-1}$.
• For an nth-order reaction, the units of k are $mol^{1-n} L^{n-1} s^{-1}$.

Chemical Kinetics: Factors Affecting Reaction Rate

• Concentration, temperature, and catalysts affect reaction rate.

Chemical Kinetics: Zero Order Reaction

• The rate law is $r = k[A]^0 = k$.
• The differential rate equation is $-\frac{d[R]}{dt} = k$.
• The integrated rate law is $[R]_t = -kt + [R]_0$, where $[R]_0$ is the initial concentration.
• Half life is $t_{1/2} = \frac{[R]_0}{2k}$.

Chemical Kinetics: First Order Reaction

• The rate law is $r = k[A]^1 = k[A]$.
• The differential rate equation is $-\frac{d[R]}{dt} = k[R]$.
• The integrated rate law is $k = \frac{2.303}{t} log \frac{[R]_0}{[R]_t}$.
• Half life is $t_{1/2} = \frac{0.693}{k}$.

Chemical Kinetics: Pseudo First Order Reaction

• For the reaction $CH_3COOC_2H_5 + H_2O \xrightarrow{H^+} CH_3COOH + C_2H_5OH$, the rate is $r = k[CH_3COOC_2H_5][H_2O]$.
• Since $[H_2O]$ is constant, $r = k'[CH_3COOC_2H_5]$, where $k' = k[H_2O]$.

Chemical Kinetics: Arrhenius Equation

• The Arrhenius equation is $k = Ae^{-E_a/RT}$, where $E_a$ is activation energy, R is the gas constant ($8.314 : J K^{-1} mol^{-1}$), A is the Arrhenius factor, and T is temperature.
• Determining the relationship between two temperatures and rate constants is done with $\log \frac{k_2}{k_1} = \frac{E_a}{2.303R} [\frac{1}{T_1} - \frac{1}{T_2}]$.

Chemical Kinetics: Effect of Catalyst

• A catalyst increases the rate of a reaction without getting consumed
• Catalysts work by providing an alternative pathway or reaction mechanism to lowering the activation energy between reactants and products

Plan d'action ministériel en développement durable 2024-2027: Message de la ministre

• Sustainable development forms the core concern and guides actions for a future where the environment is protected, the economy is prosperous, and society is equitable.
• The Plan d'action ministériel en développement durable 2024-2027 demonstrates on commitment to include principles of sustainable development in all activities.
• The plan was built around specific, clear, actions to progress for a more green and prosperous quebec.
• Dedicated to meet environmental, economic, and social challenges.

Plan d'action ministériel en développement durable 2024-2027: Table des matières

• The table of contents includes a presentation, issues and orientations, objectives and measures, and governance, monitoring and accountability

Plan d'action ministériel en développement durable 2024-2027: Présentation

• Outil de planification stratégique qui vise à intégrer les principes du développement durable dans l'ensemble des activités du ministère
• It is within the context of law on sustainable development and governmental strategy of sustainable development 2023-2028

Plan d'action ministériel en développement durable 2024-2027: Enjeux

• The analysis includes climate change, biodiversity, management of natural resources, and social equity

Plan d'action ministériel en développement durable 2024-2027: Orientations stratégiques

• Intended objectives were reduce our environmental footprint, grow a circular green economy, increase social equality and quality of life, and promoting responsible governance

Plan d'action ministériel en développement durable 2024-2027: Axe 1 Environnement

• The first goal was to diminish greenhouse gas emission via reduction of energy used
• Another goal was to preserve biodiversity via protection habits

Plan d'action ministériel en développement durable 2024-2027: Axe 2 Économie

• The first objective was to support the green innovation via new project creation
• The second goal was to promote responsible consumption

Plan d'action ministériel en développement durable 2024-2027: Axe 3 Social

• The first goal was to improve quality of life with affordable housing
• The second goal was to encourage social equality via support for local communities

Plan d'action ministériel en développement durable 2024-2027: Gouvernance

• The structure includes the sustainable development commitee for integrated and responsible developement

Plan d'action ministériel en développement durable 2024-2027: Conclusion

• This sustainability plan means committed to a strong and responsible future via accountability to our partners.

Algorithmic Trading: quantitative Strategy Development

• The strategy development process includes idea, collection, backtesting, paper, live, and monitoring trades

Algorithmic Trading: Where to look for trading ideas

• Idea generation include academic, broker, news, filings, data, experience, and common sense research
• To consider: universe, market microstructures, cost, risk, capacity, and scalability

Algorithmic Trading: Data Collection

• Common data sources include broker, vendor, scraping, fillings, and government files and releases
• To consider: cost, coverage, update frequency, and adjust delivery frequency

Algorithmic Trading: Backtesting Implementation

• Backtesting platforms can be proprietary, commercial or open source
• Consider realism, speed, flexibility and cost

Algorithmic Trading: Vectorized vs Event Driven Backtesting

• Vectorized are faster, but less flexible, and harder to debug.
• Event driven are slower, but more flexible, and easier to debug.

Algorithmic Trading: Potential Pitfalls

• Potential pitfalls include look-ahead bias, data mining bias, overfitting and survivorship

Algorithmic Trading: Paper Trade

• Considerations for paper trading include realism, execution, monitoring, and record keeping

Algorithmic Trading: Risk management

• Managing risk comes from position sizing, diversification, hedging, and stress testing

Algorithmic Trading: Strategy Monitoring

• How well is the startegy performing, handling risk, and able to avoid adverse events

Algorithmic Trading: Mean Reversion Models

• Common models include pairs trading, statistical arbitrage, index arbitrage, and reverting volecity

Algorithmic Trading: Trend Following and Machine Learning

• Trend following comes from moving averages crossover and breakout
• Machine learning is from supervised (regression) and unsupervised (clustering) learning

Physics - Vectors: Core concept

• Vectors have magnitude, direction, and sense, used for vector physical quantities.

Physics - Vectors: Vector components

• A vector $\vec{A}$ is bidimensional. the components $A_x$ and $A_y$ form the equation $\qquad \vec{A} = (A_x, A_y)$
• The magnitude is written with $|\vec{A}| = \sqrt{A_x^2 + A_y^2}$
• The angled direction in relation to the axis $x$ is $\qquad \theta = \arctan\left(\frac{A_y}{A_x}\right)$

Physics - Vectors: Sums, products, and direction of vectors

• Given vectors $\vec{A} = (A_x, A_y)$ and $\vec{B} = (B_x, B_y)$, this forms the $\qquad \vec{A} + \vec{B} = (A_x + B_x, A_y + B_y)$
• Scalar products can be defined as $\qquad \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos(\theta)$
• Vectors can also be calculated as $\qquad \vec{A} \cdot \vec{B} = A_x B_x + A_y B_y$
• Results in the vector product in $\qquad |\vec{A} \times \vec{B}| = |\vec{A}| |\vec{B}| \sin(\theta)$

Cardiovascular System - Heart Sounds

• S1 (lub) is the sound of closing atrioventricular valve which marks start of systole
• S2 (dub) is the sound of closing semilunar valves which marks start of diastole

Cardiovascular System - Abnormal Heart Sounds

• Abnormal: S3 sounds like ventricular gallop which occur after S2 and indicates increased pressure
• S4 (atrial gallop) occurs before S1 and indicates s stiff ventricle
• Murmurs sounds are from tubulent blood, graded on a scale of I-VI

Cardiovascular System - Electrocardiogram (ECG/EKG)

• P wave is the atrial depolarization and QRS complex is the ventricular
• T wave is the ventricular repolarization

Cardiovascular System - Intervals

• PR interval is how long it take to travel to ventricles where QT interval is the time to depolarize

Cardiovascular System - Heart issues

• Fast hearts are Tachycardia (> 100 bpm) or Bradycardia (< 60 bpm)
• Atrial fibrillation is when rapid irregular activity where ventricular is life threatening

Cardiovascular System - Blood Pressure

• The pressure of flood against artery. measure the systolic & diastolic

Cardiovascular System - Blood Pressure Categories

Cardiovascular System - Cardiac Output

• How much blood does the heart pump at each min, the calculation is CO = SV x HR
• Normally valued at is 4 to 8 L

Cardiovascular System - Law

• Starling's is the more during the more forceful you can contract during
• Ensures that pump has the same result to make sure is recieves

Cardiovascular System - Circulation

• Blood flow is between heart and veins

Linear Algebra and Matrix Analysis - Vectors, Matrices, and Operations

• A vector is an ordered list of numbers while a matrix is a rectangular array
• Operations include addition, scalar multiplication, and matrix multiplication.

Linear Algebra and Matrix Analysis - Transposition and Inversion

• The transpose is obtained by swapping rows and columns.
• The inverse satisfies, where is the identity matrix.

Linear Algebra and Matrix Analysis - Linear Equations

• A system of linear equations is a set of linear equations where methods of solution include substitution, elimination, and matrix
• Linear equations can be subsituted into different equations to have more variable

Linear Algebra and Matrix Analysis - Vector Spaces: Essential definitions and examples

• A vector space (called vectors) consist of adittion and multiplied by scalars.
• Examples include $\mathbb{R}^n$ (n-dimensional vectors with real numbers), $\mathbb{C}^n$ (n-dimensional vectors with complex numbers), and polynomials of degree <= n.

Linear Algebra and Matrix Analysis - Eigenvalues and Eigenvectors

• An eigenvector of the matrix $A$ is non zero satisfies $Ax = \lambda x$ Where $\lambda x$ is the value.
• Characterized by polynomial equation: $\det(A - \lambda I) = 0$.
• Matrices can also use diagnolization to simplify complex linear combination

Linear Algebra and Matrix Analysis - Matrix Decompositions

• LU Decomposition: Factorizing it into a lower triangular matrix $L$
• QR Decomposition: Factorizing $A$ into an orthogonal matrix $Q$ and an upper triangular matrix $R$, s.t. $A = QR$.
• Singular Value Decomposition (SVD): $A = U\Sigma V^T$, where U and V are orthogonal matrices, and $\Sigma$ is a diagonal matrix.
• All matrix have strong used to perform simple operations

Chemical Equilibrium - definition & Factors

• For the reaction $aA + bB \rightarrow cC + dD$, the rate $= -\frac{1}{a}\frac{d[A]}{dt}$

Chemical Equilibrium - factors of reaction rate

• Concentrion, Temp, Catalyst, Solid Reactant, Pressue Gas.

Integrated Rate Laws

• In different order the result change
• Rate = $k[A]^1 = k[A]$
• Rate $= k[A]^2$

Chemical Equilibrium - Molecular step

• The series of steps with the reaction mechanism

Chemical Equilibrium - Activation Energy and Catalysis

• Use $ln(\frac{k_2}{k_1}) = \frac{E_a}{R}(\frac{1}{T_1} - \frac{1}{T_2})$ to determine activation
• Homogeneous Catalysis in the catalyst phase

Static Equilibrium - Tension Examples: Basic explanation

• Calculating the tension in every object for a 50kg sign and with a force $22^\circ$

Static Equilibrium - How to solve tension

• Add all the tension in the object and the solution show below the equation