Equations - distribute and combine

Multi step equations (w/combine like terms and distributive property)

A solution is a mixture in which one or more substances are uniformly distributed in another substance. Solutions can be mixtures of liquids, solids, or gases. For example, plasma, the liquid part of blood, is a very complex solution. It is composed of many types of ions and large molecules, as well as gases, that are dissolved in water. A solute (SAHL-YOOT) is a substance dissolved in the solvent. The particles that compose a solute may be ions, atoms, or molecules. The solvent is the substance in which the solute is dissolved. For example, when sugar, a solute, and water, a solvent, are mixed, a solution of sugar water results. Though the sugar dissolves in the water, neither the sugar molecules nor the water molecules are altered chemically. If the water is boiled away, the sugar molecules remain and are unchanged. Solutions can be composed of various proportions of a given solute in a given solvent. Thus, solutions can vary in concentra- tion. The concentration of a solution is the amount of solute dis- solved in a fixed amount of the solution. For example, a 2 percent saltwater solution contains 2 g of salt dissolved in enough water to make 100 mL of solution. The more solute dissolved, the greater is the concentration of the solution. A saturated solution is one in which no more solute can dissolve. Aqueous (AY-kwee-uhs) solutions—solutions in which water is the solvent—are universally important to living things. Marine microorganisms spend their lives immersed in the sea, an aqueous solution. Most nutrients that plants need are in aqueous solutions in moist soil. Body cells exist in an aqueous solution of intercellu- lar fluid and are themselves filled with fluid; in fact, most chemical reactions that occur in the body occur in aqueous solutions. Copyright © by Holt, Rinehart and Winston. All rights reserved. Liquid water Solid water Ice (solid water) is less dense than liquid water because of the structure of ice crystals. The water molecules in ice are bonded to each other in a way that creates large amounts of open space between the molecules, relative to liquid water. FIGURE 2-12 solvent from the Latin solvere, meaning “to loosen” Word Roots and Origins CHEMISTRY OF LIFE 43 ACIDS AND BASES One of the most important aspects of a living system is the degree of its acidity or alkalinity. What do we mean when we use the terms acid and base? Ionization of Water As water molecules move about, they bump into one another. Some of these collisions are strong enough to result in a chemical change: one water molecule loses a proton (a hydrogen nucleus), and the other gains this proton. This reaction really occurs in two steps. First, one molecule of water pulls apart another water molecule, or dissociates, into two ions of opposite charge: H2O ∏ H OH The OH ion is known as the hydroxide ion. The free H ion can react with another water molecule, as shown in the equation below. H H2O ∏ H3O The H3O ion is known as the hydronium ion. Acidity or alkalin- ity is a measure of the relative amounts of hydronium ions and hydroxide ions dissolved in a solution. If the number of hydronium ions in a solution equals the number of hydroxide ions, the solution is said to be neutral. Pure water contains equal numbers of hydro- nium ions and hydroxide ions and is therefore a neutral solution. Acids If the number of hydronium ions in a solution is greater than the number of hydroxide ions, the solution is an acid. For example, when hydrogen chloride gas, HCl, is dissolved in water, its mol- ecules dissociate to form hydrogen ions, H, and chloride ions, Cl, as is shown in the equation below. HCl ∏ H Cl These free hydrogen ions combine with water molecules to form hydronium ions, H3O. This aqueous solution contains many more hydronium ions than it does hydroxide ions, making it an acidic solution. Acids tend to have a sour taste; how- ever, never taste a substance to test it for acidity. In concentrated forms, they are highly corrosive to some materials, as you can see in Figure 2-13. Bases If sodium hydroxide, NaOH, a solid, is dissolved in water, it dissociates to form sodium ions, Na, and hydroxide ions, OH, as shown in the equation below. NaOH ∏ Na OH Copyright © by Holt, Rinehart and Winston. All rights reserved. Eco Connection onnection Acid Precipitation Acid precipitation, more commonly called acid rain, describes rain, snow, sleet, or fog that contains high levels of sulfuric and nitric acids. These acids form when sulfur dioxide gas, SO2, and nitrogen oxide gas, NO, react with water in the atmosphere to produce sulfuric acid, H2SO4, and nitric acid, HNO3. Acid precipitation makes soil and bodies of water, such as lakes, more acidic than normal. These high acid levels can harm plant and animal life directly. A high level of acid in a lake may kill mollusks, fish, and amphibians. Even in a lake that does not have a very elevated level of acid, acid precipitation may leach aluminum and magnesium from soils, poisoning water- dwelling species. Reducing fossil-fuel consump- tion, such as occurs in gasoline engines and coal-burning power plants, should reduce high acid levels in precipitation. Sulfur dioxide, SO2, which is produced when fossil fuels are burned, reacts with water in the atmosphere to produce acid precipitation. Acid precipitation, or acid rain, can make lakes and rivers too acidic to support life and can even corrode stone, such as the face of this statue. FIGURE 2-13 44 CHAPTER 2 This solution then contains more hydroxide ions than hydronium ions and is therefore defined as a base. The adjective alkaline refers to bases. Bases have a bitter taste; however, never taste a substance to test for alkalinity. They tend to feel slippery because the OH ions react with the oil on our skin to form a soap. In fact, commercial soap is the product of a reaction between a base and a fat. pH Scientists have developed a scale for comparing the relative con- centrations of hydronium ions and hydroxide ions in a solution. This scale is called the pH scale, and it ranges from 0 to 14, as shown in Figure 2-14. A solution with a pH of 0 is very acidic, a solution with a pH of 7 is neutral, and a solution with a pH of 14 is very basic. A solution’s pH is measured on a logarithmic scale. That is, the change of one pH unit reflects a 10-fold change in the acidity or alkalinity. For example, urine has 10 times the H3O ions at a pH of 6 than water does at a pH of 7. Vinegar, has 1,000 times more H3O ions at a pH of 3 than urine at a pH of 6, and 10,000 times more H3O ions than water at a pH of 7. The pH of a solution can be measured with litmus paper or with some other chemical indicator that changes color at various pH levels. Buffers The control of pH is important for living systems. Enzymes can function only within a very narrow pH range. The control of pH in organisms is often accomplished with buffers. Buffers are chemi- cal substances that neutralize small amounts of either an acid or a base added to a solution. As Figure 2-14 shows, the composition of your internal environment—in terms of acidity and alkalinity— varies greatly. Some of your body fluids, such as stomach acid and urine, are acidic. Others, such as intestinal fluid and blood, are

Electrostatics The section of CBSE Class 12 Physics electrostatic potential and capacitance notes mainly deals with the in-depth analysis of electromagnetic phenomena when they are not performing any movements. Additionally, it is divided into ten further sub-topics to study the companion processes of reaching the state. These are - 1. Electric charge In this section of Physics ch 2 Class 12 notes, you get to learn about the basic features of electric charge and its expression in Physics. Along with its basics, the sections help to understand the full potential of charge. Different aspects of Charge included in Class 12 Physics Chapter 2 notes are - Definition Type: Positive and Negative Charge Unit and dimensional formula Point Charge Properties of Charge Comparison of Charge and Mass Methods of Charging Electroscope 2. Coulomb's Law Force is created when charges of opposite signs attract each other, and they repulse if the signs are the same. Coulomb's law tries to define this phenomenon through a mathematical formula, explicitly mentioned in Physics Class 12 notes Chapter 2. Moreover, there is key information about the variation of the constant k and its effect on a medium. Coulomb's law's vector form and the principle of superimposition are also explained in ch 2 Physics Class 12 notes. (Image will be uploaded soon) 3. Electric Field As stated in Class 12 Physics Chapter 2 notes, every positively or negatively charged particle has their respective electric fields. It feels a force at the time of interaction which might be attraction or repulsion. As it arises from electric charge, it is crucial to know about its different parts like - Electric field intensity Relation between electric force and electric field Super imposition of electric field Point charge Continuous charge distributions Properties of Electric Field Lines Motion of Charged Particles in an Electric field Learning more about the electric field from electric potential and capacitance notes Class 12 helps a student to get a grasp of upcoming chapters. 4. Electric Potential Energy When energy helps a charge to move from an electric field, it is known as the Electric Potential Energy. This section of electrostatic chapter Class 12 notes requires a student to study the Electron volt (eV), and the potential energy that an n number of charges can hold. 5. Electric Potential This section of Class 12 Physics Chapter 2 notes focuses on in-depth learning of Electric Potential or Voltage. Basically, it defines the potential movement of energy. 6. Relation between Electric Field and Potential Apart from knowing more about the relationship between the two values, Physics Class 12 Chapter 2 notes also discuss equipotential surfaces. 7. Electric Dipole Essentially, 'Dipoles' are two opposite points of charge represented with q and –q, with their distance between each other being 2a. Electric Dipoles are crucial in your study of Physics Class 12 Chapter 2 notes to learn more about electric fields and their potential. Additionally, Class 12 Physics Chapter 2 notes focus on the influence of electric dipoles on a uniform electric field mainly through Force and Torque, Work, and Potential Energy. In the last part of Electrostatics, further focus is on using the formulas to their fullest potential. It includes subsections of Electric Field, Electric Potential Energy, Electric Potential, and Electric Dipole. In the notes for electrostatic potential and capacitance, you will find proper solutions accompanied by clear and crisp diagrams for better understanding. 8. Gauss's Law Apart from just discussing the Gauss's Law, in Physics Class 12 ch 2 notes there is a thorough explanation of its properties and applications. The Gauss' Law states that net electric flux passing through a hypothetical closed surface is equal to the net electric charge present within the same closed surface. Being a broad part of the whole chapter, you may need to spend a little more time on it. Moving forward, it starts discussing the properties of conductors in relation to Gauss's Law. The Class 12 Physics notes Chapter 2 perfectly defines the journey to Gauss' Law from Coulomb's Law. Here is the Gauss's Law present in the Class 12 Physics ch 2 notes, (image will be uploaded soon) 9. Capacitors There is a dedicated section about Capacitors in the Class 12 Physics Chapter 2 notes elucidating its functions and importance as storage of potential electric energy. After explaining the structure of a capacitor, it points out the different types, parallel plate, spherical and cylindrical. The section of Chapter 2 notes of Physics Class 12 is further divided into subheads like: Properties of an ideal battery Grouping of capacitors Simple circuits (Series and Parallel) Dielectric Van de Graaff generator Combination of drops Charge distribution method Wheatstone Bridge-based circuit Extended Wheatstone Bridge Infinite network of capacitors Redistribution of charge between two capacitors Vedantu prepares the Class 12 Physics Chapter 2 notes with help from subject matter experts. In the PDF, you get a comprehensive idea of the topic along with potential answers to the most asked questions. Furthermore, the detailed explanation on each section and subsections are written in a simple language allows a student to ace their exams with wholesome knowledge. These Physics Chapter 2 Class 12 notes are going to be one of the best supplementary study materials besides a student’s textbooks. Visit the Vedantu website or download the app to get your hands on all important notes! Important Questions A charge of 4 × 10–8C is uniformly distributed on the surface of a spherical conductor, having a radius of 15 cm. Determine the electric field just outside this sphere at a point that is 15 cm from the centre of this sphere. Determine the capacitance given that the distance between the two plates has been reduced by half and the parallel plate capacitor holds a capacitance of 20 pF (where 1pF = 10-12 F) having air between the two plates. What will be the total capacitance of a combination where three capacitors, each having a capacitance of 20 pF, are connected in series. A square having a side of 10 cm has a 500 µC charge at its centre. Determine the work done to move a charge of 10 µC between two points that are diagonally opposite each other on the square. At an equatorial point, what will be the electrostatic potential because of an electric dipole? Calculate the work done to move a test charge, q, through a length of 1 cm along the equatorial axis of an electric dipole? Polarisation A capacitor has its plates enclosed in a medium that can be filled by insulating substances. A net dipole moment is then induced by an electric field in the dielectric. This event causes the field in an opposite direction. Equipotential Surface An equipotential surface is a type of surface where the potential always has a constant value. If considered as a point charge, the concentric spheres that are centred at a particular area of this charge are basically equipotential surfaces. Advantages of Vedantu's Revision Notes: A Comprehensive Resource for Effective Learning There are several reasons why one may refer to Vedantu's revision notes for studying a subject like Electrostatic Potential and Capacitance. Here are some key points: Comprehensive Coverage: Vedantu's revision notes provide a comprehensive coverage of the entire topic, ensuring that all important concepts and subtopics are included. Concise and Organized: The notes are designed to be concise, focusing on the key points and core ideas. They are organized in a structured manner, making it easy for students to navigate and revise the content. Simplified Explanation: The revision notes offer simplified explanations of complex concepts, making them more accessible and easier to understand. This helps students grasp the material more effectively. Key Formulas and Equations: The notes highlight the key formulas and equations relevant to the topic, ensuring that students have a clear understanding of the mathematical aspects of Electrostatic Potential and Capacitance. Examples and Illustrations: Vedantu's revision notes often include examples and illustrations that help clarify concepts and provide practical applications, enabling students to better relate theory to real-world scenarios. Quick Recap: The revision notes serve as a quick recap of the important points, allowing students to review the material efficiently before exams or assessments. Exam-Oriented Approach: Vedantu's revision notes are designed with an exam-oriented approach, focusing on the topics and concepts that are frequently asked in examinations. This helps students prepare effectively and increase their chances of scoring well. Accessible Anytime: Vedantu's revision notes are easily accessible online, allowing students to study at their convenience and revise the material anytime, anywhere.

6.4 The student will investigate and understand that there are basic sources of energy and that energy can be transformed. Key ideas include the sun is important in the formation of most energy sources on Earth; Earth’s energy budget relates to living systems and Earth’s processes; radiation, conduction, and convection distribute energy; and energy transformations are important in energy usage. 6.5 The student will investigate and understand that all matter is composed of atoms. Key ideas include atoms consist of particles, including electrons, protons, and neutrons; atoms of a particular element are similar but differ from atoms of other elements; elements may be represented by chemical symbols; two or more atoms interact to form new substances, which are held together by electrical forces (bonds); compounds may be represented by chemical formulas; chemical equations can be used to model chemical changes; and a few elements comprise the largest portion of the solid Earth, living matter, the oceans, and the atmosphere.

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