Activity form: debate
Activity flow:
1, personnel distribution: divided into moderators, positive side (learning chemistry well requires learning mathematics well) and negative side (learning chemistry well has nothing to do with learning mathematics well). There are three debaters for and against each.
2. What happened: (1) The moderator spoke, explaining the people on both sides of the debate and their views; (2) 3 minutes for the first debate; (3) the other party speaks for 3 minutes; (This is the keynote speech of both sides. ) (4) The pros and cons ask questions to each other for one *** 10 minute. . (5) make a statement in the last 2 minutes; (6) The other party makes a statement within the last 2 minutes; (7) The host invited the judges to comment; The debate is over.
Activity description, each speech needs the consent of the host, and the host should maintain order.
References:
Chemistry application needs mathematics more.
Chemistry is a very extensive science. According to the research scope, it includes organic chemistry, inorganic chemistry, biochemistry, physical chemistry and analytical chemistry. Coupled with engineering applications, chemical engineering is a very extensive field.
These subjects will be more or less applied to some mathematics; So when you ask a chemist what is the use of mathematics in chemistry, you may get many completely different answers-almost entirely based on personal experience. In this case, the author's views will naturally be influenced by personal views and have preferences. But the purpose of Science Monthly is not only to take root in science, but also to pay attention to the relationship between mathematics and chemistry education. Especially at present, the policy of college chemistry education seems to focus on cultivating generalists in chemistry, so when we talk about this topic, we will try our best to find the mathematics that everyone thinks is needed in modern chemistry.
Chemistry has always been an experimental science, and in the foreseeable future, it will still focus on experiments. What does mathematics have to do with it? There are two aspects to this problem.
On the one hand, modern chemistry gradually explores the composition, structure and reaction of matter from the microscopic direction, that is, from the atomic point of view, so it is greatly influenced by modern physics (both theoretically and experimentally), mainly due to the application of quantum mechanics and statistical mechanics, and the language tends to be mathematical.
On the other hand, the practical application of chemistry now requires more and more strict quantitative knowledge. For example, analytical chemistry and even chemical engineering calculation, we all need more and more accurate chemical calculation work, which involves more applied mathematics.
Therefore, the application of mathematics in chemistry can be roughly divided into two levels, one is linguistic level and the other is technical level. The former uses mathematical language to discuss chemical problems, focusing on concepts, while the latter uses mathematical techniques to do more complicated calculations. This paper will discuss them with examples and summarize their problems in chemistry education. Of course, the above classification is not very strict. Many things (such as statistics) are used at two levels. The application of mathematics itself is alive, and its classification is only for the convenience of this paper.
As for learning mathematics well, can you become an excellent chemist? My opinion is negative. Whether using mathematical language or mathematical technology, it is only a tool in chemistry, and it cannot replace chemistry itself. This is just like a person who can speak ten languages is not necessarily a linguist, and a master glass blower is not necessarily a good chemical experimenter. On the other hand, a very capable chemist is not necessarily good at mathematics. What is important is the comprehensive understanding and application of chemical knowledge, and mathematics should only be one of the auxiliary tools. But it is undeniable that when a chemist's mathematical ability is stronger, the more problems he can deal with. In the future interdisciplinary integration, mathematics will undoubtedly be a more important weapon.
Mathematicization of chemical language
A very important problem in chemistry is to discuss the relationship between the formation of chemical bonds and molecular structure. Since the end of19th century, people have been discussing the bonding between atoms. At first, people just drew the molecular structure diagram; For example, the structure of mercury chloride is Cl-Hg-Cl, and the chemical bond between mercury and chlorine is represented by only one line, so the structure of chemical bond and the configuration of electrons in atoms are completely unclear. The true three-dimensional shape of mercuric chloride is also unclear. The chloride formed by similar bivalent barium (Ba) is obviously very different from mercury chloride in chemical and physical properties, but why it is different is not clear, and chemists still lack a complete theory to understand it. After 1925, due to the development of quantum mechanics, it has been rapidly applied in chemistry. Now even high school chemistry textbooks introduce orbital domain, mixed orbital domain and atomic structure.
Take the above example, the outermost electronic configuration of mercury and barium atoms is 6s2, but the difference is that the lowest empty orbital domain of mercury atom is 6p. When mercury and chlorine atoms form mercuric chloride molecules, the mixed orbital domain used by mercury is sp, and the structure of mercuric chloride is linear. The lowest empty orbital domain of barium is 5d. When barium chloride molecules are formed with chlorine atoms, a considerable part of D orbital domains are also mixed into the mixed orbital domains used by barium, so barium chloride has a nonlinear structure, and the included angle between two Ba-Cl bonds is less than 180 (note 1). Examples like this are common in modern chemistry. To understand these, we must know the mathematical representation of orbital domain, its symmetry and so on. This involves the application of linear algebra, partial differential equations and group theory in mathematics. It is worth noting that in the above examples, mathematics is usually not used as a calculation tool (Note 2), but as a qualitative discussion method, which is very important.
For another example, since the 1960s, polymer chemistry has made great progress, and new polymers have been continuously invented and become an important part of our daily life. These polymers have the same characteristics in solution, that is, there may be many forms of continuous arrangement of atoms in space, even if their molecular weight and chemical structure are completely the same. As shown in figure 1, there are two different conformations); Six carbon moieties in polyethylene molecules. For the whole polymer, the number of different configurations can reach astronomical figures, so we have to use statistical methods to express its shape or size.
For example, the quantity often used to discuss polymer properties is the average of the square of the distance r between two ends of the polymer, which is usually proportional to the molecular weight. The properties of many polymers, such as elasticity, diffusion coefficient and astigmatism coefficient, are closely related to their values, so in order to explain his results, the experimenter must express the physical and chemical properties of polymers in statistical language. More detailed calculation of polymers from the basic chemical structure of molecules requires more statistical data. One of the reasons why P.J.Flory, the winner of the Nobel Prize in Chemistry in previous years, won the prize is his contribution to polymer statistics.
Mathematical technology of chemical calculation
The previous examples show that many important problems in chemistry have been expressed in mathematical language, and the focus is mainly on establishing ideas. On the other hand, traditional chemistry involves calculation in research and application. Although these calculations are applied to different levels of mathematics with the complexity of the problem, basically, mathematics is just a tool to help us solve the problem, which has little to do with the chemical problem itself. For example, if we want to know the rate of the following reactions,
Browse the original text (1)
Where K 1 is the rate constant of the right reaction and K2 is the rate constant of the reverse reaction. The reaction rate can be expressed by the following differential equation:
d[AC]/dt = k 1[AB][CD]-K2[AC][BD](2)
d[AB]/dt =-k 1[AB][CD]-K2[AC][BD]
Coupled with the equilibrium relationship between substances, the reaction rate can be calculated. This mathematical problem is very simple, but the real world reaction is often much more complicated.
If the above reaction is affected by temperature, we need to consider the heat conduction of the reaction, and the diffusion of the substance itself also affects the concentration. If the reaction mechanism becomes more complicated and the equations written are often nonlinear, then the solution of the reaction rate will become a very difficult mathematical problem, and it is necessary to deal with multivariable nonlinear partial differential equations. These problems are often faced by chemical engineers. It is no wonder that in recent years, the mathematics content in chemical engineering courses is gradually deepening.
Mathematics Education in Chemistry
Examples of several mathematical problems in chemistry and their characteristics have been mentioned earlier. Even from these examples, we can see that mathematics is widely used in chemistry, such as differential equations, linear algebra, vector analysis, group theory, statistics and so on. So do all chemistry students have to learn? Who will teach? I think this must be based on human experience.
There are applied chemistry departments and agrochemical departments related to chemistry departments in China. In the college curriculum standards, it is really difficult to meet the same needs by offering the special course "Chemical Mathematics". At present, according to the regulations of the Ministry of Education, chemistry students must take the course of "Chemical Mathematics", which has just been implemented. This may be a good opportunity. We might as well discuss the necessity and content of this course.
Who teaches the questions first, the math teacher or the chemistry teacher? Then there is the issue of content scope. Now other departments that use mathematics generally have their own teachers to teach mathematics, such as electrical engineering and chemical engineering, leaving professional mathematicians aside; The course of "Chemical Mathematics" seems to follow this trend. But as far as chemistry is concerned, most chemists can only be regarded as amateur mathematicians at most. Can this achieve many goals of mathematics education? As mentioned earlier, the application of mathematics in chemistry is conceptual and linguistic. When we learn a language, we don't care too much about its application scope, so it seems that mathematics teaching doesn't have to care too much about what it needs to be applied to!
As for the content of chemical mathematics, I think it should at least include some concepts of differential equation, vector analysis and linear algebra. As for further things, it depends on the needs of various subjects. For example, in applied chemistry, we should do more numerical analysis and strengthen partial differential equations, while physical chemistry or inorganic chemistry, group theory is a very important tool.
Note 1: This is about gaseous barium chloride molecules.
Note 2: Detailed calculation is the work of professional theoretical chemists, and the mathematics used is more complicated.
Science Monthly Magazine, Jinshengtai Information Enterprise Co., Ltd. and Cultural Enterprise Co., Ltd. All rights reserved.
At present, the college entrance examination tends to downplay calculation in science subjects (of course, analytic geometry is inevitable)
Therefore, poor mathematics does not affect the study of chemical physics.
Especially chemistry.
When physics involves comprehensive problems after the third year of high school, there may be some calculations that need to be completed with the help of mathematical skills, but the requirements will never reach the level of "can't be done because of poor mathematics"-it's just hard to think of it.
Don't be discouraged.
I just like math, but I am taller than those who are good at math! Lift your chin!
Chemistry doesn't use mathematics too much, physics uses mathematics more in the calculation process, but most of them use a lot of calculations, so it won't be difficult to solve the Ossetia problem, but if you want to minimize the bad influence, then do more calculations. After all, although these three disciplines are closely related, their essence is still different.
This is very important, but mathematics is farther away from chemistry and closer to physics.