"Cross method" is a common method to solve problems in middle school chemical calculation, especially in solving some calculation problems that do not need the selectivity of calculation process and fill in the blanks. The significance of the proportional relationship after crossing is a blind spot for many students. Only by clarifying the principle of "crossover method" can we solve the problem quickly.

First, the mathematical principle of "cross method"

Physical quantities can be divided into two categories: one is non-additive, such as density, concentration and molar mass. , called "intensity quantity"; Another kind of physical quantity is additive, such as mass, volume, quantity of matter, etc. This physical quantity is called "width quantity".

A mixture consists of two components, a 1 and a2 (a1>; A2) is a certain strength of the two components, a is a certain strength of the mixture, and x 1 and x2 are a certain width of the two components in the mixture. If the following equation is satisfied: a1x1+a2x2 = a (x1+x2), then X 1 (A65438) can be known.

Any quantity satisfying the above equation can be expressed by "crossing method" as follows:

a 1a-a2x 1

Answer? =

a2a 1-ax2

The average molar mass of the mixed gas formed by H2 and NH3 is 14 mol- 1. Find the molar ratio of H2 and NH3.

The analysis (1) is solved by "mathematical method";

Let the amount of H2 be x 1mol and the amount of NH3 be x2mol, then: 2x1+17x2 =14 (x1+x2), and the solution is:

(2) Using "cross method" to solve:

23 1? x 1

14=? =

17 12? 4x2

Second, the meaning of "cross method" ratio-"look at the law of denominator"

When we clarify the mathematical principle of "cross method", there will naturally be such a question: What does the ratio of the above width mean? What does it have to do with strength? Solving this problem is the key for us to use the "cross method" correctly. Because of the existence of "strength x width", we can know that the meaning of width is related to the physical meaning of strength.

For example, the molar mass is equal to the mass of the substance divided by the mass of the substance, and its corresponding width should be the mass of the substance, that is, the physical quantity represented by the denominator of the molar mass, and the ratio after crossing is the ratio of the masses of the two components (as in the above example).

As can be seen from the above, the proportional relationship after crossing is the ratio of widths represented by the denominator of strength.