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The criss-cross method is an easy way to calculate the average amount and composition of a two-component mixture. Problems that can be calculated as m1n1 m2n2 m (n1 n2) can be calculated according to the cross method. where m represents an average amount of the mixture, and m1 and m2 represent the corresponding amounts of the two components.
For example, M represents the average relative molecular weight, M1 and M2 represent the relative molecular mass of the two components, N1 and N2 represent the share of the two components in the mixture, N1:N2 represents the ratio of the quantity of the two components of the substance in most cases, and sometimes it can also be the ratio of the mass of the two components, and the key to judging is the share of what physical quantity N1 and N2 represent in the mixture, such as the amount of matter, the quantity fraction of the substance, and the volume fraction, then N1:N2 represents the ratio of the quantity of the two components; If the mass, mass fraction, and the mass percentage content of the element, then n1:
n2 denotes the ratio of the masses of the two components. The criss-cross method is often used to calculate:
1) Calculation of mass fraction;
2) calculations on the average relative molecular weight;
3) the calculation of the average relative atomic mass;
4) the calculation of the average molecular formula;
5) Calculation of the heat of reaction;
6) Calculations regarding the reaction of the mixture.
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There are different ways to use it.
a) The cross method in the calculation of mixed gases.
Example] At room temperature, 1 volume of ethylene is mixed with a certain amount of an unknown gaseous hydrocarbon, and the relative density of the mixed gas to hydrogen is measured to be 12, and the volume occupied by this hydrocarbon is obtained.
Analysis] According to the relative density, the average formula quantity of the mixed gas is 24, and the formula quantity of ethylene is 28, so the formula quantity of unknown hydrocarbons must be less than 24, and the hydrocarbon with the formula less than 24 is methane, and the methane is the volume by using the cross method.
2) The cross cross method for calculating the percentage content of isotope atoms.
Example] There are two isotopes of bromine, in nature these two isotopes account for about half of each, and the atomic number of bromine is known to be 35 and the atomic weight is 80, then the neutron number of the two isotopes of bromine is equal to each other.
a (b (c (d
Analysis] The two isotopes account for about half of each, and according to the cross method, the difference between the atomic weights of the two isotopes and the atomic weight of bromine is equal, then their neutron numbers should be 2 apart, so the answer is d
3) The cross method in the calculation of solution preparation.
Example] A student wants to prepare 100 grams of 40% NaOH solution, and there are 10% NaOH solutions and NaOH solids in the laboratory, and asks how many grams of the above substances should be taken?
Analysis] 10% NaOH solution solute is 10, NaOH solid solute is 100, 40% NaOH solution solute is 40, using the cross method: 10% NaOH solution is required.
100 = grams, NaOH solids are 100 = grams.
4) The cross method in the calculation of mixture reactions.
Example] There are 100 grams of lithium carbonate and barium carbonate mixture, and the amount of hydrochloric acid consumed when they react with a certain concentration of hydrochloric acid is the same as that consumed when 100 grams of calcium carbonate reacted with this concentration of hydrochloric acid. Calculate the ratio of the amount of lithium carbonate and barium carbonate in the mixture.
Analysis] The formula of calcium carbonate can be understood as the average formula of lithium carbonate and barium carbonate mixture, and the ratio of lithium carbonate and barium carbonate can be calculated by using the cross method to obtain 97:26
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The chemical cross method is an easy way to calculate the average amount and composition of the two mixtures.
All problems that can be calculated according to m1·n1+m2·n2=m·n can be calculated according to the cross method. m represents the average amount of a mixture, and m1 m2 represents the amount corresponding to the two components. For example, m represents the average relative molecular weight, m1 m2 represents the relative molecular mass of each of the two components, n1 n2 represents the share of the two components in the mixture, and n1:
N2 in most cases denotes the ratio of the quantity of a two-component substance, and sometimes it can also be the ratio of the mass of the two components.
Precautions for using the criss-cross method:
1. When using the cross method, it is necessary to distinguish whether the ratio obtained is the ratio of the quantity of the substance or the ratio of the mass. When the unit attribute value has the quantity factor of the substance, the ratio obtained by the cross method is the ratio of the quantity of the substance; When the value of the unit fraction attribute has a mass factor (such as the calculation of the mass fraction of the solution, etc.), the ratio obtained by the cross method is the mass ratio.
2. The cross method is mainly suitable for choice and fill-in-the-blank questions, and is generally not used in large calculation problems, because it is difficult to describe clearly with limited words in the writing process, so the conventional method is generally used in large calculation problems.
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Introduction to the criss-cross method.
The criss-cross method can be used for solution concentration.
calculations, such as dilution, concentration, or mixing of solutions. Use this method to make the problem solving process simple, fast and correct. The following is an example of how to explain the principle of the cross method.
The percentage concentrations of solutions A and B of the same substance are a and b (a b) respectively, and the solution with a percentage concentration of c is now prepared with these two solutions. Q: What should be the mass ratio of these two solutions?
The solution of the same substance, the mass of the solute before and after preparation is equal, and this principle can be used to solve the solution.
Set M1 and M2 grams of A and B solutions respectively, and the mass of the solution after mixing the two solutions is (m1 m2).Columnar m
In order to facilitate memory and calculation, if C is used to replace A, C is dilute instead of B, C is mixed instead of C, and M is concentrated instead of M1, M
Dilute instead of m2, the above formula is written as the general form of the cross method, and the diagram is shown below:
In the figure, m concentration and m dilute are the mass ratios of solutions A and B.
This method of operation is called the cross method. When using the cross method to calculate, pay attention to the oblique finding of the difference and look at the result horizontally.
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Cross multiplication.
This is a method of writing the chemical formula of a substance using valency, and it is suitable for compounds composed of two elements or two groups. It is based on the principle of valence: the algebraic sum of the total number of positive and negative prices is 0 or the absolute value of the total number of positive and negative prices is equal.
This paragraph is crossed by comparison.
What we often call the cross method is actually the cross comparison method, which is a graphical method. The cross diagram method is actually a simple algorithm instead of the summation formula, which is particularly suitable for the calculation of mixtures of two total quantities and two relationships (i.e., the calculation of 2-2 type mixtures), which is used to calculate the ratio of the two components in the mixture.
This paragraph is crossed and eliminated.
The cross elimination method is referred to as the cross elimination method, which is a type of ion inference problem solution, using "cross elimination" to narrow the scope of unknown substances, so as to use the problem to determine the substance and find the correct answer. In fact, the cross method is a simple form of solving binary equations, if you are really not used to it, you can solve the equation example, but I will tell you about it. For example, if a has a density of 10 and b has a density of 8, and their mixture has a density of 9, you can put 9 in the middle, write 10 and 8 on the left, mark ab, and then subtract 9 respectively to get 11 on the right.
At this time, it is easier than this 1:1 example, but the difficulty is the same, you can experience it yourself, this method is actually very easy to use, saving time, especially when taking the comprehensive test.
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The criss-cross method, if understood thoroughly, is actually not difficult.
The criss-cross method, if understood thoroughly, is actually not difficult.
Go to the chemistry competition book by yourself, and there should be chemical calculations in it.
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