Difference method is a method to solve problems according to some "differences" before and after chemical reaction (such as poor solid quality, poor solution quality, poor gas volume, poor gas substance quantity, etc.). ) is proportional to the change of reactants or products.

In this method, the "difference" is regarded as a term on the right hand side of the chemical equation, and the known difference (actual difference) is directly proportional to the corresponding difference (theoretical difference) in the chemical equation, and other solving steps are exactly the same as those in the chemical equation.

The key to solving problems by difference method is to find out the theoretical differences correctly.

Applicable conditions

(1) The reaction is incomplete or residual.

In this case, the difference reflects the actual reaction and eliminates the influence of unreacted substances on the calculation, so that the calculation can be carried out smoothly.

(2) There is a difference before and after the reaction, which is easy to find. This is the premise of using the difference method. Only when the difference is easy to obtain, use the difference method quickly, otherwise, consider other methods to solve it.

use

a ~ B ~δx

A b a b

c d

Available a/c=(a-b)/d

Knowing a, b and d, we can calculate c=a*d/(a-b).

There is a meaning in the chemical equation:

The chemical equation shows the proportional relationship between substances before and after the reaction.

This is the theoretical basis of the difference method.

certificate

Let the numerical ratio between micro and macro be k (assuming that the unit has been unified).

a ~ B ~δx

A b a b

a*k b*k (a-b)*k

Get a*k=a*[(a-b)]*k/(a-b).

Deduce a/(a*k)=(a-b)/[(a-b)*k]

Replace a*k with c and (a-b)*k with d.

Knowing a, b and d, we can calculate c=a*d/(a-b).

Therefore, the difference method can be proved.

principle

Before and after a chemical reaction, the mass difference of substances is directly proportional to the mass of reactants or products involved in the reaction, which is the principle of chemical calculation based on mass difference.

step

1. Investigate the meaning of the problem and analyze the reasons for the differences.

2. Write the difference on the right side of the chemical reaction equation as a relational quantity.

3. Write the proportional formula and find out the unknown.

classify

Poor quality method

Example: Add a certain amount of copper powder to the dilute nitric acid solution of 1 L and 2 mol/L.. After the full reaction, the mass of the solution increased by13.2g.. Q: How many grams of copper powder are added? (2) How many liters of NO gas can be produced theoretically? (standard conditions)

Analysis: excessive nitric acid cannot be solved by the amount of nitric acid. After copper reacts with nitric acid, the solution will increase in weight due to the formation of copper nitrate, which can be solved by this change.

3cu+8HNO3 = 3cu (NO3) 2+2no =+4h2o gain weight.

192 44.8 636-504= 132

X = 19.2g, Y = 4.48L can be obtained from x grams and y liters of 13.2.

(2) Volume difference method

Example: 10 ml gaseous hydrocarbon is completely burned in 80 ml oxygen, and when it returns to its original state (1.01×105pa, 270°C), the measured gas volume is 70 ml. Find the molecular formula of this hydrocarbon.

Analysis: The total volume of the original mixed gas was 90 ml, but it was 70 ml after the reaction, and the volume was reduced by 20 ml. The remaining gases should be generated carbon dioxide and excess oxygen, and the following calculation can be carried out by using the general formula of hydrocarbon combustion.

The volume of CxHy+(x+ )O2 → xCO2+H2O decreases.

1 1+

10 20

Y=4, and the molecular formula of hydrocarbon is C3H4 or C2H4 or CH4.

(3) the difference method of substance

Example: white solid PCl5 volatilizes and decomposes when heated: PCl5 (gas) = PCl3 (gas) +Cl2. Now, 5.84g of PCl5 is put into a 2.05l vacuum sealed container. When it reaches equilibrium at 2770C, the pressure in the container is1.01×105pa.

Analysis: The amount of substance in the original PCl5 was 0.028 mol, and the amount of substance increased by 0.022 mol when the reaction reached equilibrium, calculated according to the chemical equation.

The amount of PCl5 = PCl3+Cl2 substance increases.

1 1

X 0.022

There is 0.022 mole of PCl5 decomposed, so the result is 78.6%.

example

One. Put 6. 1g dry and pure mixture of potassium chlorate and manganese dioxide into a test tube and heat it. When it is completely decomposed and cooled, the remaining solid mass is 4.2g How many grams of potassium chlorate are there in the original mixture?

[Analysis] According to the law of conservation of mass, the reduced mass of the mixture after heating is the generated oxygen mass (w -W surplus =WO2), and KClO3 can be obtained from the generated O2.

[Solution] Let the mass in the mixture be xKClO3.

Two. Put the iron sheet with the mass of 10g into 50g copper sulfate solution, take it out later, wash it, dry it in the air, and weigh it. When the mass of the iron sheet increases to 10.6g, how many grams of copper is precipitated? What is the mass fraction of solute in the original copper sulfate solution?

[Analysis] In this reaction, elemental iron becomes ferrous ions and enters the solution, which reduces the mass of the iron sheet, while copper ions are replaced and attached to the iron sheet. Theoretically, every 56g of iron should be able to replace 64g of copper and iron sheet after reaction, and the net added mass is 64-56=8g. At present, the weight gain of iron sheet is 10.6- 10=0.6g, which is not the quality of precipitated copper, but the quality of precipitated copper is worse than that of iron participating in the reaction. According to this difference, it can be simply calculated.

[Solution] Copper precipitate with mass x and yCuSO4 participate in the reaction.

Three. Put a small piece of sodium into 50gFeCl3 _ 3 solution, after the reaction is complete, filter to get 45.9g brown solution, and the mass of sodium put in is

A, 4.6g b, 4. 1 g c, 6.9g d, 9.2g.

[Analysis] When Na is put into FeCl3 _ 3 solution, the following reaction occurs.

6Na+2 FeCl 3+6H2O = 6 NaCl+2Fe(OH)3↓+3 H2↓

If 2mol FeCl3 _ 3 _ 3 reacts with 6molH2O, 6molNaCl will be generated, and the quality of the solution will be reduced by 82g. At this time, the Na participating in the reaction is 6mol.

When the mass of the solution decreases by 4. 1g, the Na should be 0.3moL and the mass should be 6.9g, and the answer is (c).

Four. At the same temperature and pressure, a bottle filled with O2 * * * weighs 1 16g, a bottle filled with CO2 * * weighs 122g and a bottle filled with gas * * * weighs14g, so the relative molecular weight of gas is.

a、28 B、60 C、32 D、 14

[Analysis] According to "at the same temperature, pressure and volume, the mass ratio of different gases is equal to their molar mass ratio", the difference of gas mass is directly proportional to the difference of formula quantity. So the mass of this bottle can be solved directly by the proportional formula without calculation:

(122-116)/(44-32) = (122-114)/(44-m (gas))

The solution is that m (gas) =28. So the answer is (a)

Five. Hydrogen was introduced into 10g copper oxide. After heating for a period of time, the mass of the remaining solid was 8.4g, and the composition and mass of the remaining solid were determined.

[Resolution] If the mass of the remaining solid is 8.4g, the mass of oxygen will be lost:10-8.4 =1.6g.

The mass of copper produced by reduction is1.6× 64/16 = 6.4g.

The composition of the remaining solid is copper oxide 8.4-6.4 = 2g copper 6.4g.

Six. Put 10g iron sample into a sufficient amount of copper sulfate solution, measure the solid mass of 10.8g after full reaction, and calculate the purity of iron in the iron sample (assuming that impurities in the sample do not react with copper sulfate and are insoluble in water).

[Analysis] When obtaining 0.8g, the iron consumption is 0.8/(64-56) = 0. 1mol.

The mass of iron is 56× 0.1= 5.6g.

The purity of iron is 5.6/ 10 = 56%.

Seven. Put a certain amount of iron into 100g dilute sulfuric acid, and after full reaction, the mass of the solution is105.4g. Find the mass of the added iron.

[Resolution] Weight gain105.4-100 = 5.4g.

The amount of iron is 5.4/(56-2) = 0. 1mol.

The mass of iron is 0.1× 56 = 5.6g.

extremum method

It is an important mathematical thought and analysis method. The so-called "extreme value method" in chemistry is the problem of calculating or judging the composition of a mixture because of insufficient data. The name, mass fraction and volume fraction of each substance in the mixed system are determined by using the method of extreme hypothesis (that is, for a certain component or for a reaction that has just been completed), which makes some abstract and complicated problems concrete and simplified, and can achieve twice the result with half the effort.

Conversion method

definition

Transformation method In physics, some invisible phenomena or physical quantities that are not easy to measure directly are usually recognized through some very intuitive phenomena or indirectly measured through physical quantities that are easy to measure. This method of studying problems is called transformation method. This method has been applied in many places in the research and experiment of physics concept law in junior middle school.

App application

Measuring instruments: stopwatch, ammeter, voltmeter, resistance meter, spring dynamometer, barometer, micro-manometer, thermometer, tray balance, electric energy meter and measuring pen. ...

Physical experiment: explore the causes of sound, explore the characteristics of liquid pressure, and explore the factors that affect the electric heat generated by conductors. ...

example

The deformation or change of motion state of an object can prove that some objects are stressed; The experiment of Madburg Hemisphere can prove the existence of atmospheric pressure. The appearance of fog can prove that the air contains water vapor; The formation of shadows can prove that light travels along a straight line; Eclipses can prove that the moon is not a light source; Oster experiment can prove that there is a magnetic field around the current; Compass refers to the north and south that can prove the existence of geomagnetic field; Diffusion phenomenon can prove that molecular motion is irregular; Lead block experiment can prove that there is gravity between molecules; If a moving object can do external work, it can prove that it has energy and so on.

Cross method (Note: only applicable to the mixture of two substances M A: molar mass M B: molar mass M Mix: molar mass N of the mixture formed by A and B: amount of substance B.

According to:

Hybrid merger-hybrid merger

M- mixing

B: m, b, m, a, m.

Draw:

N A: N B =(M mixed -M B): (M A -M mixed)

{M, a, m and m, b must be quantities of the same nature (that is, if they are molar masses, they must all be molar masses, if they are formula quantities, they must all be formula quantities). The relationship between X, Y and M: X, Y and M can be mutually calculated in the chemical reaction formula (for example, in the chemical reaction formula, the amount of substance N and the thermal change Q in the reaction can be mutually calculated, then the ratio of Q is Q A/Q B =(N N- mixing < N A, the ratio of N A /n B =(Q mixing -q mixing) /(Q A-q mixing) Q.

First, cross multiplication

This is a method of writing the chemical formula of a substance with valence, which is suitable for compounds composed of two elements or two groups. Its principle is the law of price number: the algebraic sum of the total number of positive prices and the total number of negative prices is 0 or the absolute value of the total number of positive prices and the total number of negative prices is equal. Now let's take a look at its operation steps with the following example.

Second, the cross-comparison method

The cross method we often talk about is actually the cross comparison method, which is a graphic method. In fact, the cross diagram method is a simple algorithm to replace the summation formula. It is especially suitable for calculating the mixture of two quantities and two relationships (that is, the calculation of 2-2 mixture) and calculating the ratio of two components in the mixture.

Third, the cross elimination method

Cross elimination method, referred to as cross elimination method, is a solution to the problem of ion inference. Using "cross-elimination method" can narrow the range of unknown substances, so as to determine substances under given conditions and find out the correct answer.

In fact, the intersection method is a simple method to solve binary linear equations. If you are really not used to it, you can solve the equation, but I will tell you. For example, the density of A is 10 B, and the density of their mixture is 9, so you can put 9 in the middle, write 10 and 8 on the left, and then subtract 9 respectively to get the ratio of 1 and 1 on the right. 438+0: 1 This example is relatively simple, but the difficulty is the same. Please experience for yourself. This method actually saves time, especially when it comes to comprehensive examination.

(A) the cross method in the calculation of mixed gas

Example At room temperature, 1 volume of ethylene is mixed with a certain amount of gaseous unknown hydrocarbon, the relative density of mixed gas and hydrogen is measured as 12, and the volume of the hydrocarbon is calculated.

According to the calculation of relative density, the average molecular formula of mixed gas is 24, and the molecular formula of ethylene is 28, so the molecular formula of unknown hydrocarbons must be less than 24, and the hydrocarbons less than 24 are only methane. By using the cross method, we can find that the volume of methane is 0.5.

(2) Cross method for calculating the atomic percentage of isotopes.

There are two isotopes of bromine. In nature, these two isotopes account for about half. It is known that bromine has an atomic number of 35 and an atomic weight of 80, so the neutron number of two isotopes of bromine is equal to.

(A)79、8 1 (B)45、46 (C)44、45 (D)44、46

According to the cross method, the difference between the atomic weights of two isotopes and bromine is equal, so their neutron numbers should be different by 2, so the answer is D.

(3) Cross method in solution preparation calculation

Example A Students should prepare100g of 40% NaOH solution, and there are 10% NaOH solution and NaOH solids in the laboratory. How many grams of each of the above substances should this student take?

The analysis shows that the solute of 10%NaOH solution is 10, the solid solute of NaOH is 100, and the solute of 40%NaOH solution is 40. The required 10% NaOH solution was obtained by orthogonal method.

× 100 = 66.7g, and NaOH solid is×100 = 33.3g ..

(4) Cross method in calculation of mixed reaction.

For example,100g mixture of lithium carbonate and barium carbonate consumes the same amount of hydrochloric acid when they react with hydrochloric acid of a certain concentration as when100g calcium carbonate reacts with hydrochloric acid of this concentration. Calculate the molar ratio of lithium carbonate to barium carbonate in the mixture.

The formula amount of calcium carbonate can be understood as the average formula amount of the mixture of lithium carbonate and barium carbonate, and the ratio of lithium carbonate to barium carbonate can be calculated by cross method, which is 97:26.

Conservation method

The principle of conservation method is to use the principle of conservation of mass. In chemical reactions, the sum of the masses of all substances before and after the reaction is constant, which is applicable under any conditions.