{"id":45454,"date":"2019-08-23T17:12:32","date_gmt":"2019-08-23T16:12:32","guid":{"rendered":"https:\/\/blogs.bmj.com\/bmj\/?p=45454"},"modified":"2019-08-30T13:13:58","modified_gmt":"2019-08-30T12:13:58","slug":"jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action","status":"publish","type":"post","link":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/","title":{"rendered":"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action"},"content":{"rendered":"<p><span style=\"font-weight: 400\"><a href=\"https:\/\/blogs.bmj.com\/bmj\/files\/2014\/12\/jeffrey_aronson.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-32935\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2014\/12\/jeffrey_aronson.jpg\" alt=\"\" width=\"135\" height=\"170\" \/><\/a>As I discussed <\/span><a href=\"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/09\/jeffrey-aronson-when-i-use-a-word-nothing-is-not-a-poison\"><span style=\"font-weight: 400\">two weeks ago<\/span><\/a><span style=\"font-weight: 400\">, Paracelsus\u2019s well-known statement, first published in his <\/span><i><span style=\"font-weight: 400\">Sieben Defensiones<\/span><\/i><span style=\"font-weight: 400\"> in 1564, that \u201conly the dose determines that a thing is not a poison\u201d suggested, when taken with other parts of his text, some familiarity with the concept of dose-responsiveness, a concept that permeates modern drug development and use.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Three hundred years later, on 15 March 1864, the Norwegian chemist Peter Waage (1833\u20131900) and his brother-in-law, the mathematician and chemist Cato Maximilian Guldberg (1836\u20131902) (<em>Figure 1<\/em>) published a paper in which they propounded what eventually came to be known as the Law of Mass Action.<\/span><\/p>\n<p><span style=\"font-weight: 400\"><a href=\"https:\/\/blogs.bmj.com\/bmj\/files\/2019\/08\/Jeff-aronson-law-of-mass-fig-1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-45456 alignright\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2019\/08\/Jeff-aronson-law-of-mass-fig-1.jpg\" alt=\"\" width=\"227\" height=\"394\" \/><\/a>Guldberg and Waage\u2019s 1864 paper, written in Norwegian, was largely ignored, and they published it again in French in 1867, as <\/span><i><span style=\"font-weight: 400\">Etudes sur les affinit\u00e9s chimiques<\/span><\/i><span style=\"font-weight: 400\">. Even then, however, the idea had to be rediscovered in 1877 by the Dutch chemist Jacobus van \u2018t Hoff (1852\u20131911; <em>Figure 2<\/em>), who classified chemical reactions and defined their orders. To focus attention on their work, and to establish priority, Guldberg &amp; Waage then published a more complete version in German, as \u201cUntersuchungen \u00fcber die chemischen Affinit\u00e4ten\u201d (1879).<\/span><\/p>\n<p><span style=\"font-weight: 400\">The problem that had occupied Guldberg and Waage was to give a mathematical description of the affinities that drive chemical reactions, which I discussed <\/span><a href=\"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/16\/jeffrey-aronson-when-i-use-a-word-affinity\"><span style=\"font-weight: 400\">last week<\/span><\/a><span style=\"font-weight: 400\">. This involved both the rates of the reactions, which they described as chemical dynamics, and, for reversible reactions, the final equilibrium between the forward reaction and the backward reaction, which they designated chemical statics.<\/span><\/p>\n<p><span style=\"font-weight: 400\">The upshot of their analyses was the conclusion that the velocity of a reversible chemical reaction at equilibrium is proportional to the concentrations of the substances undergoing the reaction. If there is a series of intermediate reactions whose form is not known, it may not be possible to calculate the rate of each reaction, even when the overall reaction is known. However, the law governing such reactions at equilibrium does not depend on any intermediate steps, only on the concentrations of the initial reactants and the final products.<\/span><\/p>\n<p><span style=\"font-weight: 400\"><a href=\"https:\/\/blogs.bmj.com\/bmj\/files\/2019\/08\/Jeff-aronson-law-of-mass-fig-2-2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-45462\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2019\/08\/Jeff-aronson-law-of-mass-fig-2-2.jpg\" alt=\"\" width=\"201\" height=\"265\" \/><\/a>Although Guldberg &amp; Waage called their discovery a law, they did not name it specifically: \u201cLorsque deux corps A et B se transforment en deux corps nouveaux A&#8217; et B&#8217;, nous appelons vitesse de la r\u00e9action la quantit\u00e9 de A&#8217; + B&#8217; form\u00e9e dans l&#8217;unit\u00e9 de temps et nous \u00e9tablissons la loi: que la vitesse est proportionnelle \u00e0 la force totale de A et B.\u201d<\/span><\/p>\n<p><span style=\"font-weight: 400\">However, soon after the publication of their German paper, the term \u201cLaw of Mass Action\u201d started to appear. In 1879, for example, Matthew Moncrieff Pattison Muir published an annotation of Guldberg and Waage\u2019s 1867 paper, which had been donated to the library of the Chemical Society [of London] in its year of publication, in which he described its contents in detail. \u201cThe law of mass action formulated [by Guldberg &amp; Waage],\u201d he wrote, \u201cwas applied in the authors\u2019 \u2018\u00c9tudes\u2019 to the cases of chemical action already cited and also to the case of ether formation\u201d <\/span>(<em>J Chem Soc Abstr 1879; 36: 580-6<\/em>).<\/p>\n<p><span style=\"font-weight: 400\">From all this it may appear that \u201cLaw of Mass Action\u201d is a misnomer, since the law deals with concentrations, not masses. However, that is not the case. In the first part of their paper, headed \u201cTh\u00e9orie des affinit\u00e9s\u201d, Guldberg and Waage wrote \u201cLes quantit\u00e9s d&#8217;un corps qui se trouvent dans lcc du volume total se nomment la masse active du corps\u201d (\u00a74) and \u201cSi tous les corps forment une solution homog\u00e8ne, la masse active d&#8217;un corps se trouve en divisant la quantit\u00e9 absolue du corps par le volume total de la dissolution\u201d (\u00a77). In other words \u201cactive mass\u201d is the term they used to describe the effective concentration of a solution. This term, no longer used, was meant to refer to the concentration of a substance that was involved in a chemical reaction, on the assumption that that might be less than the total concentration of substance present in the solution, not all of which might be available to react. It was first recorded in English in the same paper by Muir referred to above: \u201cActive mass of a substance is defined as the amount of that substance in the unit-volume of the chemical system within which the chemical change proceeds.\u201d<\/span><\/p>\n<p><span style=\"font-weight: 400\">So the word \u201cmass\u201d in the Law of Mass Action is shorthand for \u201cactive mass\u201d.<\/span><\/p>\n<p><em><strong>Jeffrey Aronson<\/strong>\u00a0is a clinical pharmacologist, working in the Centre for Evidence Based Medicine in Oxford&#8217;s Nuffield Department of Primary Care Health Sciences. He is also president emeritus of the British Pharmacological Society.<\/em><\/p>\n<p><strong>Competing interests:<\/strong> None declared.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>As I discussed two weeks ago, Paracelsus\u2019s well-known statement, first published in his Sieben Defensiones in 1564, that \u201conly the dose determines that a thing is not a poison\u201d suggested, [&#8230;]<\/p>\n<p><a class=\"btn btn-secondary understrap-read-more-link\" href=\"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/\">More&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":38359,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5762],"tags":[],"class_list":["post-45454","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-jeff-aronsons-words"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action - The BMJ<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action - The BMJ\" \/>\n<meta property=\"og:description\" content=\"As I discussed two weeks ago, Paracelsus\u2019s well-known statement, first published in his Sieben Defensiones in 1564, that \u201conly the dose determines that a thing is not a poison\u201d suggested, [...]More...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/\" \/>\n<meta property=\"og:site_name\" content=\"The BMJ\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/bmjdotcom\/\" \/>\n<meta property=\"article:published_time\" content=\"2019-08-23T16:12:32+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-08-30T12:13:58+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/02\/Jeffrey-Aronson.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"540\" \/>\n\t<meta property=\"og:image:height\" content=\"350\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"BMJ\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@bmj_latest\" \/>\n<meta name=\"twitter:site\" content=\"@bmj_latest\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"BMJ\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/\"},\"author\":{\"name\":\"BMJ\",\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/#\\\/schema\\\/person\\\/ba3da426ed20e8f1d933ca367d8216fe\"},\"headline\":\"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action\",\"datePublished\":\"2019-08-23T16:12:32+00:00\",\"dateModified\":\"2019-08-30T12:13:58+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/\"},\"wordCount\":760,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/files\\\/2017\\\/02\\\/Jeffrey-Aronson.jpg\",\"articleSection\":[\"Jeff Aronson's Words\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/\",\"url\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/\",\"name\":\"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action - The BMJ\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/files\\\/2017\\\/02\\\/Jeffrey-Aronson.jpg\",\"datePublished\":\"2019-08-23T16:12:32+00:00\",\"dateModified\":\"2019-08-30T12:13:58+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/#primaryimage\",\"url\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/files\\\/2017\\\/02\\\/Jeffrey-Aronson.jpg\",\"contentUrl\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/files\\\/2017\\\/02\\\/Jeffrey-Aronson.jpg\",\"width\":540,\"height\":350},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/2019\\\/08\\\/23\\\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/#website\",\"url\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/\",\"name\":\"The BMJ\",\"description\":\"Helping doctors make better decisions.\",\"publisher\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/#organization\",\"name\":\"The BMJ\",\"url\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/files\\\/2018\\\/05\\\/The-BMJ-logo.jpg\",\"contentUrl\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/files\\\/2018\\\/05\\\/The-BMJ-logo.jpg\",\"width\":852,\"height\":568,\"caption\":\"The BMJ\"},\"image\":{\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/bmjdotcom\\\/\",\"https:\\\/\\\/x.com\\\/bmj_latest\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/#\\\/schema\\\/person\\\/ba3da426ed20e8f1d933ca367d8216fe\",\"name\":\"BMJ\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/b4d8f39281bcae118348a1c027347b8e53b82d42520e774a8b50dd9a6ac6c01d?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/b4d8f39281bcae118348a1c027347b8e53b82d42520e774a8b50dd9a6ac6c01d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/b4d8f39281bcae118348a1c027347b8e53b82d42520e774a8b50dd9a6ac6c01d?s=96&d=mm&r=g\",\"caption\":\"BMJ\"},\"sameAs\":[\"https:\\\/\\\/blogs.bmj.com\\\/\"],\"url\":\"https:\\\/\\\/blogs.bmj.com\\\/bmj\\\/author\\\/admin\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action - The BMJ","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/","og_locale":"en_US","og_type":"article","og_title":"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action - The BMJ","og_description":"As I discussed two weeks ago, Paracelsus\u2019s well-known statement, first published in his Sieben Defensiones in 1564, that \u201conly the dose determines that a thing is not a poison\u201d suggested, [...]More...","og_url":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/","og_site_name":"The BMJ","article_publisher":"https:\/\/www.facebook.com\/bmjdotcom\/","article_published_time":"2019-08-23T16:12:32+00:00","article_modified_time":"2019-08-30T12:13:58+00:00","og_image":[{"width":540,"height":350,"url":"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/02\/Jeffrey-Aronson.jpg","type":"image\/jpeg"}],"author":"BMJ","twitter_card":"summary_large_image","twitter_creator":"@bmj_latest","twitter_site":"@bmj_latest","twitter_misc":{"Written by":"BMJ","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/#article","isPartOf":{"@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/"},"author":{"name":"BMJ","@id":"https:\/\/blogs.bmj.com\/bmj\/#\/schema\/person\/ba3da426ed20e8f1d933ca367d8216fe"},"headline":"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action","datePublished":"2019-08-23T16:12:32+00:00","dateModified":"2019-08-30T12:13:58+00:00","mainEntityOfPage":{"@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/"},"wordCount":760,"commentCount":0,"publisher":{"@id":"https:\/\/blogs.bmj.com\/bmj\/#organization"},"image":{"@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/#primaryimage"},"thumbnailUrl":"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/02\/Jeffrey-Aronson.jpg","articleSection":["Jeff Aronson's Words"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/","url":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/","name":"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action - The BMJ","isPartOf":{"@id":"https:\/\/blogs.bmj.com\/bmj\/#website"},"primaryImageOfPage":{"@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/#primaryimage"},"image":{"@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/#primaryimage"},"thumbnailUrl":"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/02\/Jeffrey-Aronson.jpg","datePublished":"2019-08-23T16:12:32+00:00","dateModified":"2019-08-30T12:13:58+00:00","breadcrumb":{"@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/#primaryimage","url":"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/02\/Jeffrey-Aronson.jpg","contentUrl":"https:\/\/blogs.bmj.com\/bmj\/files\/2017\/02\/Jeffrey-Aronson.jpg","width":540,"height":350},{"@type":"BreadcrumbList","@id":"https:\/\/blogs.bmj.com\/bmj\/2019\/08\/23\/jeffrey-aronson-when-i-use-a-word-the-law-of-mass-action\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/blogs.bmj.com\/bmj\/"},{"@type":"ListItem","position":2,"name":"Jeffrey Aronson: When I Use a Word . . . The Law of Mass Action"}]},{"@type":"WebSite","@id":"https:\/\/blogs.bmj.com\/bmj\/#website","url":"https:\/\/blogs.bmj.com\/bmj\/","name":"The BMJ","description":"Helping doctors make better decisions.","publisher":{"@id":"https:\/\/blogs.bmj.com\/bmj\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/blogs.bmj.com\/bmj\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/blogs.bmj.com\/bmj\/#organization","name":"The BMJ","url":"https:\/\/blogs.bmj.com\/bmj\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/blogs.bmj.com\/bmj\/#\/schema\/logo\/image\/","url":"https:\/\/blogs.bmj.com\/bmj\/files\/2018\/05\/The-BMJ-logo.jpg","contentUrl":"https:\/\/blogs.bmj.com\/bmj\/files\/2018\/05\/The-BMJ-logo.jpg","width":852,"height":568,"caption":"The BMJ"},"image":{"@id":"https:\/\/blogs.bmj.com\/bmj\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/bmjdotcom\/","https:\/\/x.com\/bmj_latest"]},{"@type":"Person","@id":"https:\/\/blogs.bmj.com\/bmj\/#\/schema\/person\/ba3da426ed20e8f1d933ca367d8216fe","name":"BMJ","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/b4d8f39281bcae118348a1c027347b8e53b82d42520e774a8b50dd9a6ac6c01d?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/b4d8f39281bcae118348a1c027347b8e53b82d42520e774a8b50dd9a6ac6c01d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/b4d8f39281bcae118348a1c027347b8e53b82d42520e774a8b50dd9a6ac6c01d?s=96&d=mm&r=g","caption":"BMJ"},"sameAs":["https:\/\/blogs.bmj.com\/"],"url":"https:\/\/blogs.bmj.com\/bmj\/author\/admin\/"}]}},"_links":{"self":[{"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/posts\/45454","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/comments?post=45454"}],"version-history":[{"count":0,"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/posts\/45454\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/media\/38359"}],"wp:attachment":[{"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/media?parent=45454"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/categories?post=45454"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.bmj.com\/bmj\/wp-json\/wp\/v2\/tags?post=45454"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}