Question

20£®ÓÐÁ½ÖÖº¬ÑõËáH_nXO_2n-1ºÍH_n+1YO_2n£¬ÆäʽÁ¿·Ö±ðΪMºÍN£¬Ôò
£¨1£©XÔªËØÏà¶ÔÔ­×ÓÖÊÁ¿ÎªM-33n+16£¬YÔªËØÏà¶ÔÔ­×ÓÖÊÁ¿ÎªN-33n-1£»
£¨2£©XÔªËØ»¯ºÏ¼ÛΪ+£¨3n-2£©£¬YÔªËØ»¯ºÏ¼ÛΪ+£¨3n-1£©£»
£¨3£©H_nXO_2n-1ÄÜÉún-1ÖÖËáʽÑΣ¬1molH_n+1YO_2nºÍ$\frac{n+1}{2}$molBa£¨OH£©₂ÍêÈ«Öкͣ»
£¨4£©ºÍµÈÎïÖʵÄÁ¿µÄNaOHÍêÈ«ÖкÍÉú³ÉÕýÑÎʱ£¬ËùÏûºÄÁ½ÖÖËáÎïÖʵÄÁ¿µÄ±ÈΪ£¨n+1£©£ºn£¬ÖÊÁ¿±ÈΪM£¨n+1£©£ºnN£®

Answer 1

·ÖÎö £¨1£©¸ù¾ÝÁ½ÖÖº¬ÑõËáH_nXO_2n-1ºÍH_n+1YO_2nµÄʽÁ¿¼°×é³É¼ÆËã³öX¡¢YµÄÏà¶Ô·Ö×ÓÖÊÁ¿£»
£¨2£©¸ù¾Ý»¯ºÏÎïÖÐ×Ü»¯ºÏ¼ÛΪ0¼ÆËã³öX¡¢YµÄ»¯ºÏ¼Û£»
£¨3£©º¬ÑõËáH_nXO_2n-1×î¶àÄܹ»µçÀë³ön¸öÇâÀë×Ó£¬ÔòÄܹ»Éú³Én-1ÖÖËáʽÑΣ»1molH_n+1YO_2n×î¶àµçÀë³ö£¨n+1£©molÇâÀë×Ó£¬½áºÏÖкͷ´Ó¦ÊµÖʼÆËã³öÏûºÄÇâÑõ»¯±µµÄÎïÖʵÄÁ¿£»
£¨4£©¸ù¾ÝÖкͷ´Ó¦ÊµÖʼ°Á½ÖÖº¬ÑõËáµÄ×é³ÉÈ·¶¨ÆäÎïÖʵÄÁ¿Ö®±È£»¸ù¾ÝʽÁ¿¼°ÎïÖʵÄÁ¿Ö®±ÈÈ·¶¨ÆäÖÊÁ¿Ö®±È£®

½â´ð ½â£º£¨1£©º¬ÑõËáH_nXO_2n-1ºÍH_n+1YO_2nµÄʽÁ¿·Ö±ðΪMºÍN£¬ÔòXµÄÏà¶Ô·Ö×ÓÖÊÁ¿Îª£ºM-1¡Án-16¡Á£¨2n-1£©=M-33n+16£»
YµÄÏà¶Ô·Ö×ÓÁ¿Îª£ºN-1¡Á£¨n+1£©-16¡Á2n=N-33n-1£¬
¹Ê´ð°¸Îª£ºM-33n+16£»N-33n-1£»
£¨2£©º¬ÑõËáH_nXO_2n-1ÖУ¬XµÄ»¯ºÏ¼ÛΪ£ºX+1¡Án+£¨-2£©¡Á£¨2n-1£©=0£¬½âµÃ£ºX=+£¨3n-2£©£»
»¯ºÏÎïH_n+1YO_2nÖУ¬YµÄ»¯ºÏ¼ÛΪ£ºY+1¡Á£¨n+1£©+£¨-2£©¡Á2n=0£¬½âµÃ£ºY=+£¨3n-1£©£¬
¹Ê´ð°¸Îª£º+£¨3n-2£©£»+£¨3n-1£©£»
£¨3£©º¬ÑõËáH_nXO_2n-1×î¶àÄܹ»µçÀë³ön¸öÇâÀë×Ó£¬ÔòÄܹ»Éú³ÉËáʽÑεÄÖÖÀàΪ£ºn-1ÖÖ£»
1molH_n+1YO_2n×î¶àµçÀë³ö£¨n+1£©molÇâÀë×Ó£¬1molH_n+1YO_2nÍêÈ«·´Ó¦ÏûºÄmolBa£¨OH£©₂µÄÎïÖʵÄÁ¿Îª£º$\frac{n+1}{2}$mol£¬
¹Ê´ð°¸Îª£ºn-1£»$\frac{n+1}{2}$£»
£¨4£©ÉèÇâÑõ»¯ÄƵÄÎïÖʵÄÁ¿Îª1mol£¬ÖкÍ1molNaOHÏûºÄËáH_nXO_2n-1µÄÎïÖʵÄÁ¿ÍþÎ䣺$\frac{1mol}{n}$=$\frac{1}{n}$mol£¬ÏûºÄH_n+1YO_2nµÄÎïÖʵÄÁ¿Îª$\frac{1}{n+1}$mol£¬Ôò¶þÕßµÄÎïÖʵÄÁ¿Ö®±ÈΪ£º$\frac{1}{n}$mol£º$\frac{1}{n+1}$mol=£¨n+1£©£ºn£»
º¬ÑõËáH_nXO_2n-1ºÍH_n+1YO_2nµÄʽÁ¿·Ö±ðΪMºÍN£¬ÔòÏûºÄ¶þÕßµÄÖÊÁ¿Ö®±ÈΪ£ºM£¨n+1£©£ºnN£¬
´ð°¸Îª£º£¨n+1£©£ºn£»M£¨n+1£©£ºnN£®

µãÆÀ ±¾Ì⿼²é½ÏΪ×ۺϣ¬Éæ¼°»¯ºÏ¼Û¼ÆËã¡¢Öкͷ´Ó¦µÄ¼ÆËã¡¢Ïà¶Ô·Ö×ÓÖÊÁ¿µÄ¼ÆËãµÈ֪ʶ£¬ÌâÄ¿ÄѶÈÖеȣ¬Ã÷È·»¯ºÏÎïÖи÷ÔªËصÄ×Ü»¯ºÏ¼ÛΪ0Ϊ½â´ð¹Ø¼ü£¬×¢ÒâÕÆÎÕÖкͷ´Ó¦ÊµÖÊ£¬ÊÔÌâÅàÑøÁËѧÉúµÄ»¯Ñ§¼ÆËãÄÜÁ¦£®