Problemformulering
Gør rede for, hvad man forstår ved begreberne pH samt puffersystem, og udled pufferligningen.
Gør rede for, hvordan man kan omskrive pufferligningen til en funktion, Y (pH), der har Bjerrumdiagrammet som graf, herunder skal de enkelte trin i omskrivningen forklares.
Gør rede for den geometriske betydning af den anden afledede for en given funktion, og vis både teoretisk og eksperimentelt (ved logistisk regression på data), at Y pH = 0 netop når pH = pK .
Optimer dit sprog - Læs vores guide og scor topkarakter
Uddrag
Resume
Denne opgave belyser nogle grundlæggende bestanddele indenfor syre-base kemi nemlig – pH, puffersystemer, bjerrumdiagrammer.
Der bliver udført en udledning af pufferligningen derudover påvises to forskellige former af pufferligningen. Den ene af disse benyttes til at beregne y>s"-værdier af vores eksperimentelle data.
Endnu, anvendes denne til at udregne pK>s"-værdien for ethansyre, når der er ækvivalente mængder af ethansyre/acetat-ion i opløsningen, hvor der gælder pH = pK>s".
På baggrund af disse data udføres et bjerrumdiagram, som undersøges matematisk. En omskrivelse af pufferligningen til en funktion y>s"(pH) udledes også.
Puffervirkningen eftervises eksperimentelt med bufferopløsningen CH>3-COOH og CH>3-COO/, som viser at pH stabiliseres efter der bliver tilsat den stærke syre HCl.
Den eksperimentelle pK>s"-værdi for ethansyre er 4,67 sammenlignet med den teoretiske pK>s"-værdi på 4,76. Den procentvise afvigelse på -1,89% skyldes en ændring i bufferopløsningen samt diverse usikkerheder og fejlkilder.
The aim of this assignment is to examine the mathematic in Edwin A. Abbott’s novel Flatland – A Romance of Many Dimensions. Therefore, this investigation focuses on both mathematical model-ling and English literature.
The focus of the English approach to the topic is the criticism of society in the Victorian era, and the symbolic use of mathematical functions as a literary instrument. It discusses gender roles, inequality of social classes and the Victorian view on abnormalities.
The focus of the mathematical approach is multidimensionality and non-Euclidean geometry, which can help us to understand the geometry of Flatland.
It presents an in-depth explanation and de-scription of the shape of the n-cube, how a hypersphere passing through our space will look like to us and how to calculate distances in Flatland if it was to be stretched over a sphere.
In addition the assignment as a whole discusses how the new discoveries of science and mathematics are used as a symbol of the changes in structure of society and the new Victorian way of thinking.
In conclusion, Abbott criticizes the Victorian England through his two-dimensional world of Flat-land, and he uses the new mathematical ideas as a symbol of the new cultural development.
This thesis looks at the Victorian society in the late 19th century, with a main focus on the class society that existed, and the conditions of women in the society.
Also this project examines a range of mathematical terms, mainly conic section and the theorems of Miquel.
Based on the book Flatland – a Romance of Many Dimensions by Edwin Abbott Abbott, this paper investigates the similarities between the world presented to us by Abbott in Flatland and norms of the society that Abbotts was a part of when he wrote the book in 1884.
The analysis of the book is mainly focused on two things: the role of women in the world of Flatland contra the role of women in the Victorian society and class society that dominated the Victorian England, which is also portrayed in Flatland.
The connection between the mathematical section of the study and the analysis of the book is found within the book.
The mathematical subjects, which are processed in the study, are linked together with the math, that Abbott introduces us to in his book.
Flatland is about a world in two dimensions instead of three, which means that the life in Flatland is a lot different from the life we know. This is where Abbott uses math as a tool to help explain the world of Flatland.
When working with conic section, the book ‘Geometri og keglesnit’ by Jens Carstensen, that goes through this subject and the theorems of Miquel, was used as a main source.
The information on the Victorian society, which was needed, was found through various educational webpages. The study includes an analysis, an interpretation and a perspective on the book Flatland.
In addition it includes a section that explains the term conic section and proofs of the creation of various shapes through conic section as well as an examination of Miquels theorems about triangles.
Skriv et svar