{"id":53526,"date":"2014-05-31T05:21:33","date_gmt":"2014-05-30T21:21:33","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=53526"},"modified":"2021-10-06T16:18:09","modified_gmt":"2021-10-06T08:18:09","slug":"%e4%b8%89%e7%a8%ae%e5%88%a9%e7%94%a8%e4%be%9d%e6%95%b8%e6%80%a7%e8%b3%aa%e6%b1%82%e5%88%86%e5%ad%90%e9%87%8f%e6%96%b9%e6%b3%95%e7%9a%84%e6%af%94%e8%bc%83%ef%bc%88%e4%b8%8a%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e4%b8%89%e7%a8%ae%e5%88%a9%e7%94%a8%e4%be%9d%e6%95%b8%e6%80%a7%e8%b3%aa%e6%b1%82%e5%88%86%e5%ad%90%e9%87%8f%e6%96%b9%e6%b3%95%e7%9a%84%e6%af%94%e8%bc%83%ef%bc%88%e4%b8%8a%ef%bc%89\/","title":{"rendered":"\u4e09\u7a2e\u5229\u7528\u4f9d\u6578\u6027\u8cea\u6c42\u5206\u5b50\u91cf\u65b9\u6cd5\u7684\u6bd4\u8f03\uff08\u4e0a\uff09"},"content":{"rendered":"<div class=\"pf-content\"><p><span style=\"color: #ff6600;\"><strong>\u4e09\u7a2e\u5229\u7528\u4f9d\u6578\u6027\u8cea\u6c42\u5206\u5b50\u91cf\u65b9\u6cd5\u7684\u6bd4\u8f03\uff08\u4e0a\uff09<\/strong><\/span><br \/>\n<span style=\"color: #008000;\"><strong>\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u5316\u5b78\u7cfb\u517c\u4efb\u6559\u5e2b\u90b1\u667a\u5b8f<\/strong><\/span><\/p>\n<p>\u9ad8\u4e2d\u5316\u5b78\u8ab2\u7a0b\u4ecb\u7d39\u4f9d\u6578\u6027\u8cea(colligative properties)\u6642\uff0c\u7e3d\u6703\u63d0\u5230\u5229\u7528\u6eb6\u6db2\u7684\u6cb8\u9ede\u4e0a\u5347\u6cd5(ebullioscopy)\u3001\u51dd\u56fa\u9ede\u4e0b\u964d\u6cd5(cryoscopy)\u53ca\u6ef2\u900f\u58d3\u6cd5(osmometry)\u7b49\u4e09\u7a2e\u65b9\u6cd5\uff0c\u4f86\u91cf\u6e2c\u975e\u63ee\u767c\u6027\u6eb6\u8cea\u7684\u5206\u5b50\u91cf\u3002<\/p>\n<p>\u96d6\u7136\u524d\u4e8c\u7a2e\u65b9\u6cd5\u5728\u73fe\u4eca\u7684\u5be6\u9a57\u5ba4\u5df2\u7d93\u9bae\u5c11\u4f7f\u7528\uff0c\u4f46\u5728\u5316\u5b78\u53f2\u7684\u4ecb\u7d39\u53ca\u516c\u5f0f\u7684\u63a8\u5c0e\u4e0a\uff0c\u4ecd\u6709\u5176\u5b58\u5728\u7684\u50f9\u503c\u3002\u5118\u7ba1\u6b64\u4e09\u7a2e\u65b9\u6cd5\u5728\u4f7f\u7528\u4e0a\u5747\u6709\u5176\u5171\u540c\u7684\u9650\u5236\uff0c\u5fc5\u9808\u5728\u7a00\u8584\u7684\u6eb6\u6db2\u4e2d\u65b9\u80fd\u9069\u7528\u3002\u552f\u5728\u5be6\u969b\u7684\u64cd\u4f5c\u4e0a\uff0c\u5229\u7528\u6ef2\u900f\u58d3\u6cd5\u6c42\u975e\u63ee\u767c\u6027\u6eb6\u8cea\u7684\u5206\u5b50\u91cf\uff0c\u5176\u6e96\u78ba\u5ea6\u8981\u6bd4\u524d\u4e8c\u8005\u9ad8\uff0c\u672c\u6587\u5206\u70ba\uff08\u4e0a\uff09\u3001\uff08\u4e0b\uff09\u4e8c\u7bc7\uff0c\uff08\u4e0a\uff09\u7bc7\u8a66\u8457\u7d93\u7531\u6ef2\u900f\u58d3\u6cd5\u516c\u5f0f\u7684\u63a8\u5c0e\uff0c\u8b93\u8b80\u8005\u4e86\u89e3\u5176\u4f7f\u7528\u4e0a\u7684\u9650\u5236\uff0c\u53ca\u5176\u539f\u56e0\u70ba\u4f55\uff1f\uff08\u4e0b\uff09\u7bc7\u4ee5\u5be6\u969b\u7684\u4f8b\u5b50\u6bd4\u8f03\u4e09\u8005\u5728\u5be6\u969b\u6e2c\u91cf\u6eb6\u8cea\u5206\u5b50\u91cf\u6642\uff0c\u4f55\u8005\u8f03\u512a\u3002<!--more--><\/p>\n<ul>\n<li><span style=\"color: #000080;\"><strong>\u6ef2\u900f\u58d3\u6cd5\u516c\u5f0f\u7684\u63a8\u5c0e<\/strong><\/span><\/li>\n<\/ul>\n<p>\u7531\u5716\u4e00\u7684\u7c21\u6613\u5be6\u9a57\u88dd\u7f6e\u5716\u53ef\u4ee5\u770b\u51fa\uff0c\u7576\u6eb6\u5291\u5206\u5b50 $$A$$ \u53ef\u4ee5\u81ea\u7531\u7a7f\u904e\u534a\u900f\u819c\u6642\uff0c\u7d14\u6eb6\u5291\u7aef\u7684 $$A$$ \u5206\u5b50\uff0c\u9032\u5165\u6eb6\u6db2\u7684\u901f\u7387\uff0c\u6bd4\u5176\u7531\u6eb6\u6db2\u7aef\u9032\u5165\u6eb6\u5291\u7aef\u5feb\uff0c\u56e0\u6b64\u9020\u6210\u6eb6\u6db2\u7aef\u7684\u6db2\u9762\u5347\u9ad8\uff0c\u76f4\u5230\u5169\u908a\u7684\u901f\u7387\u5e73\u8861\u70ba\u6b62\uff0c\u6b64\u6642\u7684\u9ad8\u5ea6\u7a31\u70ba\u8a72\u6eb6\u6db2\u7684\u6ef2\u900f\u58d3\u3002<\/p>\n<div id=\"attachment_67221\" style=\"width: 410px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2014\/05\/53526_p1.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-67221\" class=\"wp-image-67221\" src=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2014\/05\/53526_p1.png\" alt=\"53526_p1\" width=\"400\" height=\"446\" srcset=\"http:\/\/localhost\/wp-content\/uploads\/2014\/05\/53526_p1.png 686w, http:\/\/localhost\/wp-content\/uploads\/2014\/05\/53526_p1-269x300.png 269w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><p id=\"caption-attachment-67221\" class=\"wp-caption-text\">\u5716\u4e00 \u7c21\u6613\u7684\u6ef2\u900f\u58d3\u5be6\u9a57\u88dd\u7f6e\uff0c\u534a\u900f\u819c\u50c5\u8b93\u6eb6\u5291\u5206\u5b50\u901a\u904e\uff0c\u9020\u6210\u7ba1\u67f1\u5167\u4e4b\u6db2\u9762\u5347\u9ad8\u800c\u7522\u751f\u6ef2\u900f\u58d3<\/p><\/div>\n<p>\u5982\u679c\u6211\u5011\u5c07\u5716\u4e00\u63db\u6210\u5716\u4e8c\uff0c\u4ee5\u53e6\u4e00\u7a2e\u8868\u9054\u65b9\u5f0f\uff0c\u5de6\u908a\u70ba\u7d14\u6eb6\u5291\uff0c\u53f3\u908a\u70ba\u542b\u975e\u63ee\u767c\u6eb6\u8cea\u7684\u6eb6\u6db2\uff0c\u4e2d\u9593\u4ee5\u80fd\u8b93\u6eb6\u5291\u5206\u5b50 $$A$$ \u81ea\u7531\u9032\u51fa\u7684\u534a\u900f\u819c\u9694\u958b\u3002\u7531\u5716\u4e00\u53ef\u77e5\u7d14\u6eb6\u5291\u7684 $$A$$ \u5206\u5b50\u7a7f\u900f\u534a\u900f\u7684\u901f\u7387\u6703\u5927\u65bc\u76f8\u53cd\u7684\u65b9\u5411\uff0c\u56e0\u6b64\u5c07\u7522\u751f\u4e00\u80a1\u58d3\u529b($$\\pi$$)\u4f7f\u53f3\u908a\u7684\u6db2\u9762\u4e0a\u5347\u3002\u5982\u679c\u6b64\u6642\u5728\u53f3\u908a\u65bd\u52a0 $$\\pi$$ \u7684\u58d3\u529b\uff0c\u5247\u4e8c\u908a\u5c07\u7dad\u6301\u5e73\u8861\uff0c\u6b64\u6642\u6eb6\u5291\u5206\u5b50 $$A$$ \u5728\u7d14\u6eb6\u5291\u53ca\u6eb6\u6db2\u5169\u908a\u7684\u5316\u5b78\u80fd\u61c9\u76f8\u7b49\uff08\u4e0b\u5f0f\u4e2d\u4e0a\u6a19\u7684 $$*$$ \u4ee3\u8868\u7d14\u6eb6\u5291\uff09\uff0c\u5373<\/p>\n<p style=\"text-align: center;\">$$\\mu^*_A(p)=\\mu_A(p+\\pi)~~~~~~~~~(1)$$<\/p>\n<p>\u7531\u71b1\u529b\u5b78\u7684\u5b9a\u5f8b\u53ef\u77e5\uff0c\u76f8\u540c\u72c0\u6cc1\u4e0b\uff0c\u7d14\u6eb6\u5291\u7684\u5316\u5b78\u80fd\u6c38\u9060\u9ad8\u65bc\u6eb6\u6db2\u7684\u5316\u5b78\u80fd\uff0c\u5982\u4e0b\u5f0f\u6240\u5217\uff0c<br \/>\n\u5176\u4e2d $$X_A$$\u00a0\u4ee3\u8868\u6eb6\u5291\u7684\u83ab\u8033\u5206\u7387\uff0c\u5176\u503c\u5c0f\u65bc $$1$$\uff0c\u6545 $$\\ln(X_A)&lt;0$$\u3002<\/p>\n<p style=\"text-align: center;\">$$\\mu_A(p+\\pi)=\\mu^*_A(p+\\pi)+RT\\ln X_A~~~~~~~~~(2)$$<\/p>\n<div id=\"attachment_67222\" style=\"width: 410px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2014\/05\/53526_p2.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-67222\" class=\"wp-image-67222\" src=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2014\/05\/53526_p2.png\" alt=\"53526_p2\" width=\"400\" height=\"316\" srcset=\"http:\/\/localhost\/wp-content\/uploads\/2014\/05\/53526_p2.png 789w, http:\/\/localhost\/wp-content\/uploads\/2014\/05\/53526_p2-300x237.png 300w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><p id=\"caption-attachment-67222\" class=\"wp-caption-text\">\u5716\u4e8c \u5de6\u908a\u7684\u7d14\u6eb6\u5291\u548c\u53f3\u908a\u542b\u975e\u63ee\u767c\u6027\u6eb6\u8cea\u7684\u6eb6\u6db2\u4ee5\u534a\u900f\u819c\u9694\u958b\uff0c\u7576\u53f3\u908a\u65bd\u52a0\u58d3\u529b\u03c0\u4f7f\u4e8c\u908a\u5e73\u8861\u6642\uff0c\u6eb6\u5291A\u5728\u5169\u908a\u7684\u5316\u5b78\u80fd\u61c9\u76f8\u7b49<\/p><\/div>\n<p>\u53e6\u5916\uff0c\u6eb6\u5291\u5206\u5b50 $$A$$ \u56e0\u53d7\u5916\u5728\u58d3\u529b $$\\pi$$ \u800c\u6539\u8b8a\u7684\u5316\u5b78\u80fd\uff0c\u53ef\u7d93\u7531\u4e0b\u5217\u57fa\u672c\u516c\u5f0f\u63a8\u51fa<\/p>\n<p style=\"text-align: center;\">$$d\\mu^*=-S_mdT+V_mdp$$<\/p>\n<p>\u5176\u4e2d $$S_m,V_m$$\u00a0\u5206\u5225\u70ba\u6eb6\u5291\u7684\u83ab\u8033\u71b5\u53ca\u83ab\u8033\u9ad4\u7a4d\u3002<br \/>\n\u5728\u5b9a\u6eab\u4e0b\u4e0a\u5f0f\u7b49\u865f\u53f3\u908a\u7b2c\u4e00\u9805\u70ba $$0$$\uff0c\u82e5\u5169\u908a\u7531\u58d3\u529b\u5f9e $$p$$ \u5230 $$p+\\pi$$ \u7a4d\u5206<\/p>\n<p style=\"text-align: center;\">$$\\int_{p}^{p+\\pi} d\\mu^*=\\int_{p}^{p+\\pi} V_mdp$$<\/p>\n<p style=\"text-align: center;\">$$\\mu^*_A(p+\\pi)=\\mu^*_A(p)+\\int_{p}^{p+\\pi} V_mdp~~~~~~~~~(3)$$<\/p>\n<p>\u5c07\u5f0f $$(3)$$ \u4ee3\u5165\u5f0f $$(2)$$ \u5f8c\uff0c\u518d\u4ee3\u5165 $$(1)$$ \u5f0f\uff0c\u53ef\u5f97\u4e0b\u5f0f<\/p>\n<p style=\"text-align: center;\">$$-RT\\ln X_A=\\int_{p}^{p+\\pi} V_mdp~~~~~~~~~(4)$$<\/p>\n<p>\u7531\u65bc\u6eb6\u8cea\u7684\u83ab\u8033\u5206\u7387\u52a0\u6eb6\u5291\u7684\u83ab\u8033\u5206\u7387\u70ba $$1$$\uff0c\u6240\u4ee5\u5c07 $$X_A=1-X_B$$\u00a0\u4ee3\u5165\u4e0a\u5f0f\uff0c\u4e26\u505a\u4e8c\u9805\u5047\u8a2d<\/p>\n<ul>\n<li>$$(\\bf I)$$ \u7576 $$X_B\\ll 1$$\uff0c\u6eb6\u8cea\u7684\u83ab\u8033\u5206\u7387\u9060\u5c0f\u65bc\u6eb6\u5291\uff0c<br \/>\n\u5373\u70ba\u7a00\u8584\u6eb6\u6db2\u6642\uff0c$$\\ln (1-X_B)=-X_B$$\uff08\u53c3\u8003\u8cc7\u65991\uff09<\/li>\n<li>$$(\\bf II)$$ \u5c07 $$V_m$$\u00a0\u5728\u58d3\u529b\u5f9e $$p$$ \u5230 $$p+\\pi$$ \u4e4b\u9593\u8996\u70ba\u5b9a\u503c\uff0c\u5247<\/li>\n<\/ul>\n<p style=\"text-align: center;\">$$RTX_B=V_m(p+\\pi-p)=V_m\\pi$$<\/p>\n<p style=\"text-align: center;\">$$\\displaystyle X_B=\\frac{n_B}{n_A+n_B}$$<\/p>\n<p>\u7531\u65bc $$n_A\\gg n_B$$\uff0c\u6240\u4ee5 $$X_B\\approx \\frac{n_B}{n_A}$$\uff0c\u800c $$V=n_A\\times V_m$$\u3002<br \/>\n\u53e6\u5916\uff0c\u56e0\u70ba\u662f\u7a00\u8584\u6eb6\u6db2\uff0c\u5373\u53ef\u5c07 $$V$$ \u7576\u6210\u6eb6\u6db2\u7684\u9ad4\u7a4d\uff0c<br \/>\n\u56e0\u6b64\u5c07\u00a0$$X_B\\approx \\frac{n_B}{n_A}$$ \u4ee3\u5165\u4e0a\u5f0f\uff0c\u5247\u53ef\u6539\u5beb\u70ba<\/p>\n<p style=\"text-align: center;\">$$\\pi V=n_BRT$$ \u00a0\u6216 \u00a0$$\\pi=M_BRT~~~~~~~~~(5)$$<\/p>\n<p>\u5f0f $$(5)$$ \u5373\u70ba\u51e1\u7279\u4f55\u592b\u65b9\u7a0b\u5f0f\uff08van\u2019t Hoff equation\uff09\uff0c\u5176\u4e2d $$M_B$$\u00a0\u70ba\u9ad4\u7a4d\u83ab\u8033\u6fc3\u5ea6\u3002\u7531\u5f0f\u4e2d\u53ef\u770b\u51fa\u6eb6\u6db2\u7684\u6ef2\u900f\u58d3\uff08$$\\pi$$\uff09\u50c5\u548c\u6eb6\u8cea\u7684\u83ab\u8033\u6578\uff0c\u5373\u7c92\u5b50\u6578\u6709\u95dc\uff0c\u548c\u6eb6\u5291\u7684\u6027\u8cea\u7121\u95dc\u3002<\/p>\n<p>\u7531\u4ee5\u4e0a\u7684\u8a0e\u8ad6\u53ef\u77e5\uff0c\u5229\u7528\u6ef2\u900f\u58d3\u6cd5\u6c42\u975e\u63ee\u767c\u6027\u6eb6\u8cea\u7684\u5206\u5b50\u91cf\u6642\uff0c\u56e0\u70ba\u4f7f\u7528\u4e0b\u5217\u5047\u8a2d\uff1a$$\\ln(1-X_B)\\approx -X_B$$\uff0c\u6240\u4ee5\u53ea\u6709\u5728\u7a00\u8584\u7684\u6eb6\u6db2\u4e2d\u65b9\u80fd\u9069\u7528\uff0c\u82e5\u8d85\u904e\u7279\u5b9a\u6fc3\u5ea6\uff0c\u5c07\u7522\u751f\u4e0d\u53ef\u9810\u6599\u7684\u8aa4\u5dee\u3002\u9664\u4e86\u6ef2\u900f\u58d3\u6cd5\u53ef\u4ee5\u61c9\u7528\u5728\u5be6\u9a57\u4e0a\u6c42\u51fa\u6eb6\u8cea\u7684\u5206\u5b50\u91cf\u5916\uff0c\u6cb8\u9ede\u4e0a\u5347\u6cd5\u3001\u51dd\u56fa\u9ede\u4e0b\u964d\u6cd5\u4e5f\u5e38\u88ab\u63d0\u53ca\uff0c\u7a76\u7adf\u5728\u5be6\u52d9\u4e0a\uff0c\u4f55\u8005\u6bd4\u8f03\u5177\u9ad4\u53ef\u884c\uff0c\u5c07\u5728\uff08\u4e0b\uff09\u7bc7\u4e2d\u8a73\u7d30\u6bd4\u8f03\u3002<\/p>\n<p>\u9023\u7d50\uff1a<a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=53543\">\u4e09\u7a2e\u5229\u7528\u4f9d\u6578\u6027\u8cea\u6c42\u5206\u5b50\u91cf\u65b9\u6cd5\u7684\u6bd4\u8f03\uff08\u4e0b\uff09<\/a><\/p>\n<p>\u53c3\u8003\u8cc7\u6599<\/p>\n<ol>\n<li>\u6cb8\u9ede\u4e0a\u5347\u6cd5\u6c42\u5206\u5b50\u91cf\u7684\u9650\u5236\uff0c\u9ad8\u77bb\u8a08\u756b\u8cc7\u6e90\u5e73\u53f0<\/li>\n<li><a href=\"http:\/\/www.vaxasoftware.com\/doc_eduen\/qui\/tcriosebu.pdf\">http:\/\/www.vaxasoftware.com\/doc_eduen\/qui\/tcriosebu.pdf<\/a><\/li>\n<li>P. W. Atkins, &#8220;Physical Chemistry&#8221;, Oxford University Press, Oxford, 5th ed., p. 221~229 (1994).<\/li>\n<li>\u8449\u540d\u5009\uff0c\u5289\u5982\u71b9\uff0c\u90b1\u667a\u5b8f\uff0c\u5468\u82b3\u5983\uff0c\u9673\u5efa\u83ef\uff0c\u9673\u5049\u6c11\uff0c\u9ad8\u7d1a\u4e2d\u5b78\u5316\u5b78\u9078\u4fee\u4e0a\u518a\uff0c\u5357\u4e00\u66f8\u5c40\uff0c\u7b2c140\uff5e141\u9801\uff0c2013 \u5e74\u3002<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u4e09\u7a2e\u5229\u7528\u4f9d\u6578\u6027\u8cea\u6c42\u5206\u5b50\u91cf\u65b9\u6cd5\u7684\u6bd4\u8f03\uff08\u4e0a\uff09 \u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u5316\u5b78\u7cfb\u517c\u4efb\u6559\u5e2b\u90b1\u667a\u5b8f \u9ad8\u4e2d\u5316\u5b78\u8ab2\u7a0b\u4ecb\u7d39\u4f9d\u6578\u6027\u8cea(co&hellip;<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[66,108,65,62],"tags":[6599,6598,6597],"class_list":["post-53526","post","type-post","status-publish","format-standard","hentry","category-chemistry04-04","category-chemistry00","category-chemistry04-03","category-chemistry04","tag-6599","tag-6598","tag-6597","loop-entry","cat-66","cat-108","cat-65","cat-62","no-thumbnail"],"views":8477,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/53526","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=53526"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/53526\/revisions"}],"predecessor-version":[{"id":87048,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/53526\/revisions\/87048"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=53526"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=53526"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=53526"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}