Chromatography is a good method for separating and identifying compounds. In chromatography, substances with different properties can be separated by the different partition ratios of compounds in the stationary phase/mobile phase. A very important value for judging the separation efficiency of chromatography is the $Rf$ value (retardation factor), which is the ratio of the distance of the separated substance to the origin to the distance of the solvent front to the origin. In addition to changing the developing solvent, there is also a common technique in the laboratory to separate two compounds on a thin-layer chromatography plate to clarify the composition of the system: after performing one $TLC$ separation, the solvent is evaporated, and then another development is performed (assuming the solvent front reaches the same height). It is known that there are two compounds in the system, and their Rf values in the developing solvent are $a$ and $b$ respectively ($0<a<b<1$).
The following statements are correct:
1. To achieve better separation with secondary development, it is required that $a<b<0.5$
2. If a=0.3, b=0.6, the separation effect of secondary development is better than that of single development.
3. If a=0.3, b=0.4, the separation effect of tertiary development is better than that of secondary development.
4. If a=0.2, b=0.3, the separation effect of tertiary development is better than that of secondary development.
5. Tertiary separation is better than secondary separation, requiring $a+b<0.67$
6. Tertiary development achieves better separation requires: $a^2+b^2+ab-3a-3b+1>0$
色谱法是分离鉴定化合物的一种好方法。在色谱中，通过化合物在固定相/流动相中不同的分配比例，可以分离不同性质的物质。判断色谱的分离效率的一个很重要的数值是$Rf$值（比移值），其大小为分离物到起点的距离与溶剂前沿到起点的距离之比。除了改变展开剂，在实验室中还有一种常用的技巧在薄层色谱板上分离两个化合物以明确体系的组成：在进行一次$TLC$分离之后，挥干溶剂，此后再进行一次爬板（假定溶剂前沿达到同一高度）。已知体系中有两种化合物，它们的在展开剂中的Rf值分别为$a$和$b$（$0<a<b<1$）。
下面说法中正确的是：
1. 使用二次爬板要取得更好的分离效果，要求$a<b<0.5$
2. 若a=0.3, b=0.6, 二次爬板的分离效果比一次爬板更好。
3. 若a=0.3, b=0.4, 三次爬板的分离效果比二次爬板更好。
4. 若a=0.2, b=0.3, 三次爬板的分离效果比二次爬板更好。
5. 三次分离比二次分离效果更好，要求$a+b<0.67$
6. 三次爬板分离效果更好要求：$a^2+b^2+ab-3a-3b+1>0$
All other options are incorrect
2.4.6.
1.3.4.
2.4.5.
3.4.
4.5.
2.6.
2.4.
其他选项均不正确
2.4.6.
1.3.4.
2.4.5.
3.4.
4.5.
2.6.
2.4.
Assume the moving distance of the solvent front is $L$, then the moving distance of the first compound is $aL$, and the moving distance of the second compound is $(1-a)aL$.

$Rf'=2a-a^2 $

Better separation effect refers to being separated further apart in the $TLC$ plate, with a larger difference in $Rf$ values.

$∆Rf'=-2a+2b-b^2+a^2=(b-a)(2-a-b)>b-a$

Then the requirement is: $a+b<1$

<Checkpoint>[The requirement for better separation effect with double development: $a+b<1$](1)</Checkpoint>

Statement 1. Using double development to achieve a better separation effect requires $a<b<0.5$, which does not conform.
In statement 2, if a=0.3, b=0.6, a+b<1, which is correct, the separation effect of double development is better than that of single development.
Statement 1 is incorrect, and statement 2 is correct.

<Checkpoint>[Statement 1 is incorrect](0.5)</Checkpoint>

<Checkpoint>[Statement 2 is correct](0.5)</Checkpoint>

For triple development, $Rf'=1-(1-a)^3=3a-3a^2+a^3$

To make the separation effect of the triple development method better, it needs to satisfy:

$∆Rf'=(b-a)(3-3b-3a+b^2+a^2+ab)>(b-a)(2-a-b)$

The condition can be obtained as $a^2+b^2+ab-2a-2b+1>0$, or rearranged as $(a + b - 1)^2 > ab$

<Checkpoint>[The requirement for better separation effect with triple development: $a^2+b^2+ab-2a-2b+1>0$, or rearranged as $(a + b - 1)^2 > ab$](1)</Checkpoint>

If a=0.3, b=0.4, the separation effect of triple development is better than that of double development. $a^2+b^2+ab-2a-2b+1=-0.03<0$ Statement 3 is negative when substituted, incorrect.

If a=0.2, b=0.3, the separation effect of triple development is better than that of double development. $a^2+b^2+ab-2a-2b+1=0.19>0$ Statement 4 is positive when substituted, correct.

<Checkpoint>[Statement 3 is incorrect](0.5)</Checkpoint>

Statement 4 is positive, correct.

<Checkpoint>[Statement 4 is correct](0.5)</Checkpoint>

Statement 5 is not equivalent to the conclusion, and in statement 6, the coefficient before a and b changes from 2 to 3, both are incorrect.

<Checkpoint>[Statement 5 is incorrect](0.5)</Checkpoint>

<Checkpoint>[Statement 6 is incorrect](0.5)</Checkpoint>

Therefore, statements 2 and 4 are correct, choose H
假定溶剂前沿移动距离为$L$，则第一次化合物移动距离为$aL$，第二次移动的距离为$(1-a)aL$。

$Rf'=2a-a^2 $

分离效果更好，指的是在$TLC$板中分得更开，$Rf$值差距更大。

$∆Rf'=-2a+2b-b^2+a^2=(b-a)(2-a-b)>b-a$

则要求：$a+b<1$

<Checkpoint>[二次爬板分离效果更好要求：$a+b<1$](1)</Checkpoint>

与陈述1. 使用二次爬板要取得更好的分离效果，要求$a<b<0.5$不符合，
陈述2中若a=0.3, b=0.6, a+b<1，正确，二次爬板的分离效果比一次爬板更好。
陈述1错误，陈述2正确

<Checkpoint>[陈述1错误](0.5)</Checkpoint>

<Checkpoint>[陈述2正确](0.5)</Checkpoint>

对于三次爬板，$Rf'=1-(1-a)^3=3a-3a^2+a^3$

要让三次爬板法的分离效果更好，需要满足：

$∆Rf'=(b-a)(3-3b-3a+b^2+a^2+ab)>(b-a)(2-a-b)$

可以得到条件为$a^2+b^2+ab-2a-2b+1>0$，或整理为$(a + b - 1)^2 > ab$

<Checkpoint>[三次爬板分离效果更好要求：$a^2+b^2+ab-2a-2b+1>0$，或整理为$(a + b - 1)^2 > ab$](1)</Checkpoint>

若a=0.3, b=0.4, 三次爬板的分离效果比二次爬板更好。$a^2+b^2+ab-2a-2b+1=-0.03<0$ 陈述3带入发现为负数，错误。

若a=0.2, b=0.3, 三次爬板的分离效果比二次爬板更好。$a^2+b^2+ab-2a-2b+1=0.19>0$ 陈述4带入发现为正数，正确

<Checkpoint>[陈述3错误](0.5)</Checkpoint>

陈述4是正数，正确。

<Checkpoint>[陈述4正确](0.5)</Checkpoint>

陈述5与结论并不等价，陈述6在a和b的系数前从2变成了3，两个都是错误的。

<Checkpoint>[陈述5错误](0.5)</Checkpoint>

<Checkpoint>[陈述6错误](0.5)</Checkpoint>

因此，陈述2、陈述4正确，选H