Chemical Reactions and Equations

Chemical Reactions

• Chemical reactions can be expressed through a chemical equation, where reactants are on the left and products on the right side.
• The equation $2H_2 + O_2 \rightarrow 2H_2O$ is an example of a chemical reaction.

Balancing Chemical Equations

• In chemical reactions, mass is conserved.
• To balance a chemical equation, begin with the unbalanced equation
• Count the number of atoms of each element on both sides
• Balance the number of atoms by adding coefficients.
• As a final step, double-check the balance.
• The balanced form of $CH_4 + O_2 \rightarrow CO_2 + H_2O$ is $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$

Reaction Types

• Reactions can be categorized into synthesis, decomposition, single replacement, double replacement, and combustion.

• Synthesis (Combination)

• Two or more reactants combine into a single product following the form $A + B \rightarrow AB$.

• An example synthesis reaction is $2Na(s) + Cl_2(g) \rightarrow 2NaCl(s)$

• Decomposition

• A single compound breaks down into two or more products following the form $AB \rightarrow A + B$

• $CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$ exemplifies decomposition.

• Single Replacement (Displacement)

• One element replaces another in a compound following the model $A + BC \rightarrow AC + B$.

• $Zn(s) + CuSO_4(aq) \rightarrow ZnSO_4(aq) + Cu(s)$ demonstrates a single replacement reaction.

• Double Replacement (Metathesis)

• Ions in two compounds exchange, represented as $AB + CD \rightarrow AD + CB$.

• $AgNO_3(aq) + NaCl(aq) \rightarrow AgCl(s) + NaNO_3(aq)$ illustrates a double replacement reaction.

• Combustion

• Combustion is when a substance reacts with oxygen, producing heat and light according to the form $Fuel + O_2 \rightarrow CO_2 + H_2O$

• With $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$ being a combustion reaction.

Stoichiometry

• The mole ratio is the ratio of moles of reactants and products in a balanced equation.
• For the reaction $N_2 + 3H_2 \rightarrow 2NH_3$, the mole ratio of $N_2$ to $H_2$ is 1:3.
• Molar mass is the mass of one mole of a substance and is measured in grams per mole (g/mol).
• The molar mass of $H_2O = 2(1.008) + 16.00 = 18.02 , g/mol$

Limiting Reactant

• The limiting reactant determines the product amount.
• The excess reactant remain after the reaction.
• The theoretical yield is the maximum product amount from the reactants.
• The actual yield is the obtained product amount.
• The percent yield is calculated as $(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}) \times 100%$.

Tensiones

• Tensiones are efforts that act on a specific area, defined as $\sigma = \dfrac{F}{A}$.

• $\sigma$: Strés

• F: Fuerza [N]

• A: Área $[m^2]$

• The area must be perpendicular to the force.

• Tensiones' types are traction, compression, and shear.

• Tracción

• Ocurre cuando las fuerzas tiran del objeto.

$\epsilon = \dfrac{\Delta L}{L_0}$

• $\epsilon$: Deformación
• $\Delta L$: Cambio de longitud [m]
• $L_0$: Longitud original [m]

The Young's module is $E = \dfrac{\sigma}{\epsilon}$

• E: Módulo de Young [Pa]

• Compresión

• Occurs when the forces push the object.

• Cizalladura

• Occurs when the forces are parallel to the area.

$G = \dfrac{\tau}{\gamma}$

• G: Módulo de cizalladura [Pa]
• $\tau$: Esfuerzo de cizalladura [Pa]
• $\gamma$: Deformación de cizalladura (sin unidades)

Poisson's relationship

• This relations describe the material's tendency to thin in other directions when streched.

$v = -\dfrac{\epsilon_{trans}}{\epsilon_{axial}}$

• $\epsilon_{trans}$: Deformación transversal

• $\epsilon_{axial}$: Deformación axial

• The elastic limit is the point where the material no longer deforms elastically and plastic deformation starts.

• Tensile strenght is the maximum about of stress that a material can withstand before fracturing.

• Ductility is a measure of much a material can plasitcally deform before fracturing.

• Tenacity is a measure of power that a material can absorb before fracturing.

Lecture 19: Hypothesis Testing I

• Statistical hypothesis involve an assertion or conjecture about one or more populations.

• $H_1$: The average blood pressure of smokers is normally higher than that of non-smokers.

• $H_2$: A new drug has more effective than the existing drug in reducing blood sugar levels.

• $H_3$: The average height of male students in University A is the same as that in University B.

• The statistical significance of a statement is initially considered thrue.

• Alternative hypothesis contradicts the null hypothesis, never containing an equal.

• $H_0: \mu = \mu_0$ versus $H_1: \mu \neq \mu_0$

• $H_0: \mu \geq \mu_0$ versus $H_1: \mu < \mu_0$

• $H_0: \mu \leq \mu_0$ versus $H_1: \mu > \mu_0$

• In this case $\mu$ is population mean and $\mu_0$ is a specific value.

• Hypothesis test results from the sample to reject the null hypothesis.

• Hypothesis test statistic example: $Z = \frac{\bar{X} - \mu_0}{\sigma / \sqrt{n}}$

• $\bar{X}$ is the sample mean.

• $\mu_0$ is the value of $\mu$ under the null hypothesis.

• $\sigma$ is the population standard deviation.

• $n$ is the sample size.

• The critical region is where the null hypothesis is rejected.

Errors

• A Type I error occurs when the null hypothesis is rejected, but is thrue

• $\alpha = P(\text{Reject } H_0 \mid H_0 \text{ is true})$

• Type II - failing to reject the null even if it is false

• $\beta = P(\text{Fail to reject } H_0 \mid H_0 \text{ is false})$

• the level of significance shows the probability for a Type I error. Common significance are 0.01, 0.05, and 0.10.
• The p-value is as extreme as in the sample, for the null is thrue.
• Rule for desicion with p:
  • reject for p-value $\leq \alpha$.
  • fail to reject the null for p-value $>\alpha$

Guía de inicio rápido de PostgreSQL

• PostgreSQL is a open-source relational database management system (RDBMS). It is known for his reliability, data integrity and complience to the SQL standards. The PostgreSQL is often used to applications of single users or for empresarial aplications.
• The supported data types in PostgreSQL includes data types like primitivos, structured or user-defined.
• ACID transactions are supported
• PostgreSQL has support for views, triggers and alcamenados procedures.
• High availability and replication are also compatible.

PostgreSQL instalation

• PostgreSQL site is downloaded or package administrator is used to install

• Installing in Windows

• First you need to download the installer from their web-site.

• Run the installer and go as instructions indicate

• Insert a password for the user "postgres" upon request

• The PostgreSQL is initied automaticaly after the installation

• Installing in macOS

  • In macOS Homebrew is used:

brew install postgresql

brew services start postgresql

• Installing in Linux
  • With package installer based in the distro that you using, for example:

sudo apt update
sudo apt install postgresql postgresql-contrib

• The PostgreSQL starts automaticaly after the installation

Connect to PostgreSQL

• After PostgreSQL is installed it needs to be conected. For the connection you can use variety of clients, like "psql" or GUI-based tools like pgAdmin

  • Using psql
  • Open a terminal and insert:

psql -U postgres

Insert the password to the user "postgres" when the psql ask.

• Using pgAdmin
• Open pgAdmin
• Click on "Agregar nuevo servidor" button
• Put the connection info to the PostgreSQL server
• click "Save" button
• Creating databases
• to create database you can use the command:

CREATE DATABASE mydatabase;

• Creating databases
  • to create table you can use:

CREATE TABLE customers (
    id SERIAL PRIMARY KEY,
    name VARCHAR(255) NOT NULL,
    email VARCHAR(255)
);

• Inserting data
  • For inserting data you can use:

INSERT INTO customers (name, email) VALUES ('John Doe', '[email protected]');

• Consulting data
  • For consulting data you can use:

SELECT * FROM customers;

• Updating data*
  • For updating data you can use:

UPDATE customers SET email = '[email protected]' WHERE id = 1;

• Deleting data
  • For deleting you can use:

DELETE FROM customers WHERE id = 1;

quickstart of Linux's guide

• LInux is a open-source OS
• It's known for it's stabilyty, security and flexibility
• Linux Distributions: like OS based on Linux
• The Linux distro includes components like desktop environments, system apps and management tools
• Many people use Ubuntu, Fedora, Debian, Linux Mint or elementary OS
• Desktop environments give interface for interact with SO

Linux installation

• The system requirements' must be verified before installing

Processor: 1 GHz +
RAM: 1 GB +
Space on Hard disc: 20 GB +

• Installing steps

1. the ISO image must be downloaded
2. The installation media is made with the downloaded with USB or DVD
3. Init SO in the installation media that was made
4. Follow the instructions' assistant to finish Linux's instalation

• Usage basics of Linux:

• For interact with SO the command line interface called "terminal" is need

• Basics commands

• "ls": list items

• "cd": change directory

• "mkdir": for make directory

• "rm": for deleting files or folders

• "cp": copy files

• "mv": for move or rename files

• For management ofpackages

• For each package manager the order is different

Personalization

• For personalization "themes" can added.
• For extending functionalities extensions' are used.
• For seting config, the system preferences are used.

Algorithmic Trading

• Algorithmic Trading uses programs for automate desitions, known as automated trading, black-box trading, or algo-trading.

Types:

1. Trend Following
2. Arbitrage
3. Index Fund Rebalancing
4. Mathematical Model-Based
5. Execution Algorithms

• Trend Following: Capitalizes on identified trends.
• Arbitrage: Exploits price differences.
• Index Fund Rebalancing: Adjusts portfolio holdings to match index weights.
• Mathematical Model-Based: Uses complex models.
• Execution Algorithms: Aims to execute large orders at the best possible prices.

Algorithmic Trading Strategies

• Mean Reversion:
• Capitalize when there is defition from average rate.
• Example: Pairs trading
• Momentum:
• Capitalize assets with upward prices treads.
• Trading highs
• High-Frequency Trading (HFT):
• Uses computers for a high number of orders
• Sentiment Analysis:
• Uses language processing for know how market felt.
• Time Series Analysis:
• Uses movements on historic

Advantages:

• Faster execution
• Reduced emotional bias
• Backtesting -24/7 trading
• Diversification ###Disadvantages:
• Technical glitches
• Over-optimization
• Market shocks

Key Considerations

• Backtesting
• Risk Management
• Execution Platform
• Monitoring
• Adaptability

Bernoulli's principle

• Bernoulli`s principle happens with an increase in the speed or a pressure decrease associated.
• Explanation
  • Bernoulli`s principle related with low conservation of energy. Also, a fluids kinetic increases as well with a decrease in its potential.
• Applications Airplanes,Carburetors,Spray bottles´s mathematical expression of conservation of energy states that pressure + kinetic energy + potential energy remains constant. The limitations of the same involves that fluidss are incompressible.

Learn about chemical reactions, including balancing equations to conserve mass. Explore different types of reactions such as synthesis, decomposition, single and double replacement, and combustion. Examples are included.