两溶液等体积混合后溶液中溶质的质量分数

两溶液等体积混合后溶液中溶质的质量分数 湖北长阳二中 (443500) 田双彪 化学学习中我们常常遇到一类要计算两溶液等体积混合后溶液中溶质的质量分数的选 -3择题，如:把质量分数为70%的硝酸溶液(密度为1.40gcm)加入等体积水中，稀释后硝酸溶液中溶质的质量分数是( ) A、等于35% B、大于35% C、小于35% D、无法估算 这类题目，直接按质量分数的定义进行解答时，就是设原硝酸溶液的体积为VmL,稀释 1.40，70%V，1.40，70%后溶液中溶质的质量分数为:×100%=>35%，选(B)。 V，1.40，V1.40，1 但通常我们不这样解答，而是假设加入的水与硝酸溶液等质量,这时溶液中溶质的质量分数为原来的二分之一，即35%。考虑到题目所给的是加入与硝酸溶液等体积的水，由于水的-3-3密度(1gcm)小于硝酸的密度(1.40gcm)，水的质量自然小于硝酸溶液的质量，即分母比假设的要小，故混合液中溶质的质量分数应大于35%，这种较巧妙。 -3-3再如，已知25%的氨水的密度为0.91gcm,5%的氨水的密度为0.98gcm,若将上述两溶液等体积混合，所得氨水中溶质的质量分数是( ) A、等于15% B、大于15% C、小于15% D、无法估算 此题，就不能再用上述方法巧算了，尽管若是两溶液等质量混合，混合液中溶质的质量分数是15%。但这时是两溶液等体积混合，与两溶液等质量混合相比，不仅溶液的质量改变了，溶质的质量也改变了，即分子分母同时增大或减小，其值到的是增大还是减小是不能随便下结论的。 为了弄清这类题目，我们不仿把上面的问题一般化以后，用数学方法来。如:质量分数为 ω的某溶液(密度为ρ),与质量分数为ω的同类溶液(密度为ρ，且ρ?ρ)112212等体积混合后,其混合液中溶质的质量分数ω与混合前各溶液中溶质的质量分数的算术平均 12,，,值的大小关系如何。 2 解析:设两溶液的体积都为VmL，由题意可知: ,,,,V11，V22ω= V,1，V,2 ,,,,11，22= ,1，,2 ,,,,,,1(1，2)，2(2,1)= 2,1，(,2,,1) ,,2,1,,,，，122,1= ,,,21，2,1 adership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, 2, to further improve research, solve thoroughly, not solid, the effect is not obvious. The major issues and enterprises it is a matter of security bureau year development, the vital interests of the problem, determine the research topic, by members of the Party led research. Basic research to see the truth, to the truth, do not say hello, not pre arranged. After the investigation to submit the research report. 3, insist on grassroots party members take the lead in implementing the line. <. In the construction of work style building long-term mechanism views > and < on the depth of the grassroots, the people, promoting harmony activities notice >, more mines and enterprises, solve the masses of grassroots leaders, mine is not enough. 4, contact a crowd. Combined with the "grassroots cadres contact farmers" activities and each cadres to contact a people, by ,1若ω=0，即溶液加等体积溶剂稀释时，有 ω= 2,,,21，2,1 ,,11当ρ<ρ时，ω=< 12,,,212，2,1 即密度比溶剂小的溶液加等体积溶剂稀释后，其混合液中溶质的质量分数小于原溶液的一半。如:25,的氨水加等体积水稀释后，混合液中溶质的质量分数小于12.5%。 ,,11当ρ>ρ 时，ω=> 1 2,,,212，2,1 即密度比溶剂大的溶液加等体积溶剂稀释后，其混合液中溶质的质量分数大于原溶液的一半。如:30,的硝酸加等体积水稀释后，混合液中溶质的质量分数大于15%。 这样我们解决了溶液稀释后，混合液中溶质的质量分数ω的取值问题。 若ω?0，即两同类溶液等体积混合时，混合液中溶质的质量分数ω的取值问题又怎2 么样呢,我们不仿用最基本的数学方法来比较一下: 12,，,令 ?=ω- 2 ,,,,12,，,11，22 =(-) 2,1，,2 ,,,,,,,,,,,,211，222,11,12,21,22 = 2(,1，,2) ,,,,,,,,11，22,12,21 = 2(,1，,2) ,,,,,,,,11，22,12,21 = 2(,1，,2) ,,,,(1,2)(1,2) = 2(,1，,2) 12,，,当ω>ω且ρ >ρ 或ω<ω且ρ<ρ时?>0则有ω> 121212122 12,，,当ω>ω且ρ<ρ 或ω<ω 且ρ>ρ时?<0则有ω< 12121212 2 对于上述数方法得到的结论，我们还可以再用十字交叉法加以验证，由于等体积混合时溶液密度大的质量大，故 adership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, 2, to further improve research, solve thoroughly, not solid, the effect is not obvious. The major issues and enterprises it is a matter of security bureau year development, the vital interests of the problem, determine the research topic, by members of the Party led research. Basic research to see the truth, to the truth, do not say hello, not pre arranged. After the investigation to submit the research report. 3, insist on grassroots party members take the lead in implementing the line. <. In the construction of work style building long-term mechanism views > and < on the depth of the grassroots, the people, promoting harmony activities notice >, more mines and enterprises, solve the masses of grassroots leaders, mine is not enough. 4, contact a crowd. Combined with the "grassroots cadres contact farmers" activities and each cadres to contact a people, by 当 ω>ω且ρ>ρ或ω<ω且ρ<ρ时，有 12121212 ωω-ω ω ω -ω 1 212 ω ,1或 ω ,1 ω ω -ω ω ω- ω212 1 ,1，,2解得结果均为:ω, 2 当 ω ,ω 且ρ >ρ 或ω ,ω 且ρ<ρ 时，有 12121212 ωω- ω ω ω- ω 1 2112 ω ,1 ω ,1 ωω- ω ω ω-ω 2 12 1 ,1，,2解得结果均为:ω, 2 由此，我们可以得到关于两同类溶液等体积混合后溶液中溶质的溶质质量分数的两条规律，即: (1)溶液中溶质的质量分数与溶液的密度成单调递增函数关系的两同类溶液等体积混合，其混合溶液中溶质的质量分数大于混合前各溶液中溶质的质量分数的算术平均值(简:你大我也大，则大)。 (2)溶液中溶质的质量分数与溶液的密度成单调递减函数关系的两同类溶液等体积混合，其混合溶液中溶质的质量分数小于混合前各溶液中溶质的质量分数的算术平均值(简:你大我却小，则小)。 这两条规律不仅适用加水稀释、两溶液混合(水体系或非水体系)，即使是固体、气体作分散剂的分散系或两纯物质等体积混合照相样适用(分散系中加等体积分散剂或两纯物质混合，我们可把分散剂或其中一种纯物质中溶质的质量分数视为0)。总之，只要混合后体系可视为一个分散系，即可以看作一种物质分散到另一种物质里形成的混合物，我们都可以应用这两条规律进行比较判断。 为了帮助我们更好地理解上述两条规律的化学意义，我们不仿把等体积混合看作是分两 12,，,步来实现的，即先把两溶液等质量混合质量分数为，然后再加密度大的那种溶液，2 12,，,其混合液的质量分数ω又应介于和密度大的溶液的溶质质量分数之间，即 2 12,，,当 ω >ω 且ρ >ρ 时，第一步等质量混合时，ω=，第二步为满足等体12122 12,，,积混合需加密度大的即质量分数为ω的溶液，这时有,ω,ω 112 12,，,当 ω <ω 且ρ<ρ 时，第一步等质量混合时，ω=，第二步为满足等体积12122 12,，,混合需加密度大的即质量分数为ω的溶液，这时有 ,ω,ω22 2 12,，,当 ω ,ω且ρ >ρ时，第一步等质量混合时，ω=，第二步为满足等体1212 2 12,，,积混合需加密度大的即质量分数为ω的溶液，这时有ω ,ω, 112 adership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, 2, to further improve research, solve thoroughly, not solid, the effect is not obvious. The major issues and enterprises it is a matter of security bureau year development, the vital interests of the problem, determine the research topic, by members of the Party led research. Basic research to see the truth, to the truth, do not say hello, not pre arranged. After the investigation to submit the research report. 3, insist on grassroots party members take the lead in implementing the line. <. In the construction of work style building long-term mechanism views > and < on the depth of the grassroots, the people, promoting harmony activities notice >, more mines and enterprises, solve the masses of grassroots leaders, mine is not enough. 4, contact a crowd. Combined with the "grassroots cadres contact farmers" activities and each cadres to contact a people, by ,1，,2当ω ,ω 且ρ<ρ 时，第一步等质量混合时，ω=，第二步为满足等体积12122 ,1，,2混合需加密度大的即质量分数为ω的溶液，这时有 ω ,ω, 222 通过上面的分析比较，使我们知道要解决两同类溶液等体积混合后，溶液中溶质的质量分数ω的取值问题有规律: 溶质密度比溶剂大的两同类溶液等体积混合，其混合液的溶质质量分数大于两溶液溶质质量分数的算术平均值。若水为溶剂，则是密度ρ>1的两同类溶液等体积混合，其混合液的溶质质量分数大于两溶液的算术平均值。 溶质密度比溶剂小的两同类溶液等体积混合，其混合液的溶质质量分数大于两溶液溶质质量分数的算术平均值。若水为溶剂，则是密度ρ<1的两同类溶液等体积混合，其混合液的溶质质量分数小于两混合液的算术平均值。 附习题: -3-31(10,的酒精溶液(,0.9819gcm)与50,的酒精溶液(ρ,0.9138gcm)等体积混合后，所得溶液中溶质的质量分数为( ) A(等于30, B(大于 30, C(小于30, D(无法估算 -3-32(40,的醋酸溶液(ρ,1.049gcm)与60,的醋酸溶液(ρ,1.064gcm)等体积混合后，所得溶液中溶质的质量分数为( ) A(等于50, B(大于 50, C(小于50, D(无法估算 -3-33(2,的KCO溶液(ρ,1.016gcm)与8,的KCO溶液(ρ,1.071gcm)等体积混2323 合后，所得溶液中溶质的质量分数为( ) A(等于5, B(大于 5, C(小于5, D(无法估算 -3-34(8,的溶液(ρ,1.046gcm)与12,的(NH)SO溶液(ρ,1.069gcm)等体积混424 合后，所得溶液中溶质的质量分数为( ) A(等于10, B(大于 10, C(小于10, D(无法估算 5(把乙醇加入等体积水混合后，溶液中溶质的质量分数为( ) A(等于50, B(大于 50, C(小于50, D(无法估算 6(把纯硫酸加入等体积水混合后，溶液中溶质的质量分数为( ) A(等于50, B(大于 50, C(小于50, D(无法估算 -37(把40,的酒精溶液(ρ,0.9352gcm)加入等体积水混合后，溶液中溶质的质量分数为( ) A(等于20, B(大于 20, C(小于20, D(无法估算 -38(把62,的硫酸溶液(ρ,1.520gcm)加入等体积水稀释后，溶液中溶质的质量分数为( ) A(等于31, B(大于 31, C(小于31, D(无法估算 9(把30,的氨水(氨水的密度比水小)加入等体积水稀释后，溶液中溶质的质量分数为( ) A(等于15, B(大于15 , C(15小于, D(无法估算 10(把质量分数为x的硫酸溶液和质量分数为3x的硫酸溶液(质量分数大的硫酸的密度大)等体积后，溶液中溶质的质量分数为( ) A(等于3x B(大于 3x C(小于 3x D(无法估算 adership: Luo Mingjun, rectification time: before September 25th, insist for a long time) 1, 2, to further improve research, solve thoroughly, not solid, the effect is not obvious. The major issues and enterprises it is a matter of security bureau year development, the vital interests of the problem, determine the research topic, by members of the Party led research. Basic research to see the truth, to the truth, do not say hello, not pre arranged. After the investigation to submit the research report. 3, insist on grassroots party members take the lead in implementing the line. <. In the construction of work style building long-term mechanism views > and < on the depth of the grassroots, the people, promoting harmony activities notice >, more mines and enterprises, solve the masses of grassroots leaders, mine is not enough. 4, contact a crowd. Combined with the "grassroots cadres contact farmers" activities and each cadres to contact a people, by