Introduction We are going to have to do this one in two stages. We don’t know enough (yet) to give a full treatment of the problem, but it’s too important to not make a start! Acid catalysis is widely used to increase the rates of...
Acid Catalysis in Organic Reactions Part 1
Acid Catalysis in Organic Reactions Part 2
Answer 1 Here is the equilibrium again. [image] We know that...
Acid Catalysis in Organic Reactions Part 2
Introduction We started looking at this problem in Basics 22. Now we have looked at the thermodynamics of reactions involving charged species (Basics 35), we can consider the implications of acid catalysis with a strong acid and with a weak acid.... This...
This chapter explains the acid-base equilibrium. This involves the transfer of protons in line with the Brønsted–Lowry theory. A strong acid or strong base is fully ionized in an aqueous solution, while weak acids or bases are only partially ionized in an aqueous solution. Acid-base titrations measure the unknown concentration of one solution by reaction with another standard solution with a familiar concentration. The chapter also notes how indicators are typically water-soluble weak organic acids with varying colours at different pH values. It explores the alternative theory of acid-base reactions proposed by Gilbert Lewis: a Lewis acid is an electron-pair acceptor, while a Lewis base is an electron-pair donor.
Rearranging equations with more complicated functions
This chapter illustrates the process of performing simple rearrangement using the BODMAS rule. When rearranging, we identify the presenting function and perform its inverse. The chapter then looks at rearrangements involving brackets. A bracket is the collection of algebraic terms sandwiched between symmetrical symbols. It contains more than one term because it makes no sense to use bracket symbols to ‘group together’ a single term. We cannot move any of the content from within the bracket. Rather, we move the entire bracket as a complete and whole unit. Indeed, we treat everything grouped between the bracket symbols as a self-contained whole. The chapter also considers the process of rearranging exponentials and logarithms, as well as rearrangements involving powers, roots, and trigonometry.
So, you’ve got to the end. Hopefully you have enjoyed reading this book. More importantly, I hope you have understood all of the explanations and learned quite a lot of organic chemistry. Did you ‘just’ read this book? If you did, then that’s okay. The...
This chapter focuses on alcohols (ROH) which have at least one hydroxyl group bonded to a carbon atom. Alcohols are known to undergo two reactions similar to the reactions of halogenoalkanes. Additionally, esters are formed through an alcohol's reaction to carboxylic acids. Alcohols also undergo oxidation reactions. The chapter explores the main manufacturing processes for ethanol which are fermentation and the direct hydration of ethene. It also considers the nucleophilic substitution and oxidation reactions of alcohols. The elimination reactions coincide with alcohol being dehydrated through heating with acid. However, conditions depend on the specific alcohol involved in the process as some of the alcohols could produce more than a single product.
Aldehydes and Ketones
This chapter describes aldehydes and ketones. Aldehydes have one alkyl group and one hydrogen atom attached to the carbonyl carbon. Ketones have two alkyl groups and resist oxidation. Both aldehydes and ketones contain the carbonyl group which has a carbon atom doubly bonded to an oxygen atom. Fehling's solution and Tollens' reagent can also help determine the differences between aldehydes and ketones. Oxidation can also help the reduction of aldehydes and ketones to primary and secondary alcohols respectively. The chapter also explains nucleophilic addition, condensation reactions, and alpha carbon reaction of aldehydes and ketones.
Introducing notation, symbols, and operators
This chapter discusses mathematical symbols. Mathematical symbols are all operators. In mathematics, the instructions giving us the result we want are contained within the operator which describes an action performed on numbers or other elements. The operator may be regarded as a function, map, or transformation, in the sense that it ‘maps’ elements from one set to elements from another set. Simple operators tell us what operation to perform. Ultimately, an operator must operate on something, which is known as the argument. The chapter then looks at the Delta operator, which tells us to subtract the initial value of the argument from its final value, the Sigma operator, which tells us to add up a series of terms, and the Pi operator, which is a shorthand symbol that tells us to multiply together a series of terms. It also considers other operators encountered in chemistry.
The correct order to perform a series of operations: BODMAS
This chapter examines the correct order to perform a series of operations. When a calculation involves more than one operator, the resultant value depends on the order in which we employ the various operators. Only if we perform the operations in the correct order will the answer be correct. The BODMAS scheme is the simplest way to remember the correct order in which to perform a calculation comprising several operations. The letters in BODMAS stand for Brackets, Of, Division, Multiplication, Addition, and Subtraction. Brackets have the highest priority because we regard everything inside a bracket as separate and self-contained. Meanwhile, the word ‘of’ points toward more complicated operators such as powers and roots.
This chapter details the process of simplifying equations. Collecting together similar terms is one of the easiest ways of simplifying an equation. ‘Similar terms’ means algebraic portions that have the same form or content. We collect terms together because the process simplifies otherwise complicated expressions. Indeed, collecting terms saves time and allows us to simplify our mathematics. ‘Collecting terms’ is a form of factorizing. Another powerful way of simplifying equations is through cancelling. When we cancel, we look for similar terms on the top and bottom of a fraction. The terms will not cancel completely if one is a multiple of the other. In such cases, cancelling will leave a factor.
Fractions and percentages
This chapter focuses on fractions and percentages. A fraction involves one quantity divided by another. The part of the fraction above the solidus line is called the numerator, and the part below the denominator. The denominator sometimes represents the total number possible, and the numerator represents the overall proportion under scrutiny. We can simplify many fractions by cancelling portions of the numerator and denominator. Another way to simplify a fraction is turning it into a decimal. We obtain a numerical value of a fraction by dividing the value of the numerator by the value of the denominator. Long division is thus the first method of converting a fraction into a decimal. The chapter then explains the process of multiplying, adding, subtracting, and dividing fractions. It also considers the concept of a percentage, which relates to the hundredth part of a thing.
Rearranging simple equations
This chapter assesses the process of rearranging simple equations, starting with a focus on the importance of the equals sign. The equals sign lies at the heart of all our mathematics: an equation is only complete when it contains an equals sign to relate the expressions on either side of the equation. An equation is balanced when the variables and numbers on the left of the equals sign have the same overall value as the collection of variables and numbers written to its right. Thus, we can change the magnitude of the variables and numbers on the left-hand side of an equation provided we do exactly the same to the right-hand side. The chapter then looks at the process of rearranging equations that have one operator; rearranging equations that have many operators, using the BODMAS scheme; and rearranging equations with negative coefficients.
Multiplying brackets and factorizing
This chapter addresses the process of multiplying brackets and factorizing. The acronym BODMAS tells us that brackets have the highest priority in rearrangements and algebra. The correct way to multiply out a bracket is to multiply each term within the bracket by the factor positioned outside it. When two brackets are positioned side by side, we multiply them term by term. The chapter then looks at the process of squaring a bracket by multiplying it with itself, as well as squaring larger brackets and obtaining coefficients using Pascal's triangle. The term ‘perfect square’ refers to the product of a bracket multiplied by itself. Finally, the chapter details the process of factorizing simple expressions, the difference between two squares, by completing a square, quadratic equations, and by using ‘the quadratic formula’.
Solving simultaneous linear equations
This chapter describes the process of solving simultaneous linear equations. ‘Linear’ means the equations have variables of the form x and y associated with a straight line rather than curved lines — finding the common value when one or more of the lines is curved requires a different procedure. Solving simultaneous linear equations involves elimination and substitution. We can achieve elimination by subtracting like terms from between the two equations. The chapter then looks at the situation in which there are two equations and two unknowns. It considers the process of solving simultaneous linear equations graphically, with algebra, with negative coefficients, with factors, and with generalized equations.
This chapter focuses on functions of only one variable. It shows graphical representations of functions and explains the cartesian coordinate system, including the x-coordinate or abscissa and the y-coordinate or ordinate. The chapter then discusses how the structure of an algebraic expression is simplified by the process of factorization. Furthermore, it tackles inverse functions and polynomials. The chapter also discusses rational functions, differentiating proper and improper functions. Lastly, it explains partial fractions, emphasizing that the decomposition into partial fractions is an important tool in the solution of some differential equations in the theory of reaction rates, and in integration in general.
Introduction An adjacent double bond can influence the outcome of a substitution reaction in several ways. The purpose of this chapter, as always, is to explore fundamental principles. Therefore, we will establish, and then build on, what we know.
Always Draw Structures with Realistic Geometry
In the previous chapter, I mentioned the importance of forming good habits. I want to formalize this by including short chapters focused only on this one theme. Here is the first one!
Amines and Amino Acids
This chapter describes the mechanisms of amines and amino acids. It also notes the two common naming systems of amines, which are known to be one class of organic compounds with nitrogen atoms. Amines are classified in terms of their general formulas, alkyl group, and hydrogen atoms attached to the nitrogen atom. The Gabriel synthesis is a method of successfully making a primary amine. Amino acids have two function groups: an amino group and a carboxylic acid group. Amino acids also polymerize to construct polypeptides. The chapter discusses the effects of pH and zwitterions as well.
The Point of The Exercise During various chemical transformations, the stereochemistry of a given stereogenic centre may change. If it does, you need to know about it. The labels are very useful for keeping track. Let’s not have any illusions about this. If you give...