{"id":14938,"date":"2014-05-30T15:05:19","date_gmt":"2014-05-30T15:05:19","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=14938"},"modified":"2026-03-28T10:33:56","modified_gmt":"2026-03-28T15:33:56","slug":"volume-percent-of-a-solution","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/volume-percent-of-a-solution\/","title":{"rendered":"Volume Percent of a Solution"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_2xorwoHbiRM\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_2xorwoHbiRM\" data-source-videoID=\"2xorwoHbiRM\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Volume Percent of a Solution Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Volume Percent of a Solution\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_2xorwoHbiRM:hover {cursor:pointer;} img#videoThumbnailImage_2xorwoHbiRM {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/443-volume-percent-of-a-solution-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_2xorwoHbiRM\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_2xorwoHbiRM\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Volume Percent of a Solution\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_2xorwoHbiRM\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_2xorwoHbiRM\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_2xorwoHbiRM\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction Gnj_Function() {\n  var x = document.getElementById(\"Gnj\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"Gnj_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"Gnj\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_Volume_Percent\" class=\"smooth-scroll\">What is Volume Percent?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_3\" class=\"smooth-scroll\">Example #3<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_4\" class=\"smooth-scroll\">Example #4<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video on volume percent\u2014the concentration of a solute in a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/solutions\/\">solution<\/a> calculated as a percentage of volume!<\/p>\n<h2><span id=\"What_is_Volume_Percent\" class=\"m-toc-anchor\"><\/span>What is Volume Percent?<\/h2>\n<p>\nVolume percent, represented as <span style=\"font-size:110%\">\\(\\frac{v}{v \\text{%}}\\)<\/span>, is commonly used to represent the concentration of binary mixtures of liquids, as liquids are often measured in volume. For example, when you buy isopropanol at the store (rubbing alcohol), you\u2019ll notice that it says 70% (<span style=\"font-size:110%\">\\(\\frac{v}{v}\\)<\/span>), which means by volume. This tells you that the solution is 70% isopropanol.<\/p>\n<h3><span id=\"Volume_Percent_Equation\" class=\"m-toc-anchor\"><\/span>Volume Percent Equation<\/h3>\n<p>\nThe equation for volume percent is pretty straightforward: <\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{v}{v\\%} = \\frac{\\text{volume of solute}}{\\text{volume of solution}}\\)<span style=\"font-size: 85%;\"> \\(\\times 100\\)<\/span><\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h2>\n<p>\nSo, returning to our rubbing alcohol, 70% (<span style=\"font-size:110%\">\\(\\frac{v}{v}\\)<\/span>) means that for every 100 mL of solution, there are 70 mL of the solute, isopropanol.  <\/p>\n<div class=\"examplesentence\">\\(70\\% =\\)<span style=\"font-size: 120%;\">\\(\\frac{\\text{volume of solute}}{100\\text{ mL}}\\)<\/span>\\(\\times 100\\)<br \/>\nVolume of solute = 70 mL<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h2>\n<p>\nLet\u2019s consider a bottle of wine, listed as 12% ABV (alcohol by volume, which is another way of saying volume percent). <\/p>\n<div class=\"examplesentence\">\\(12\\% =\\)<span style=\"font-size: 120%;\">\\( \\frac{\\text{volume of solute}}{750 \\text{ mL}}\\)<\/span>\\( \\times 100\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe bottle is 750 mL, which means the wine contains 90 mL of ethanol.<\/p>\n<p>We\u2019ve demonstrated in these two examples that given the total volume of solution and the volume percent, it\u2019s pretty simple to calculate the volume of solute.  <\/p>\n<h2><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h2>\n<p>\nHowever, if you plan on making a solution with a certain volume percent, you should be aware of a slight caveat when you\u2019re working in the laboratory. Let\u2019s consider another example.   <\/p>\n<p>Let\u2019s say you want to make a 70% <span style=\"font-size:110%\">\\(\\frac{v}{v%}\\)<\/span> solution of ethanol in water. You prepare beakers of 70 mL ethanol and 30 mL water. By mixing them together, you believe this will give you the 70% <span style=\"font-size:110%\">\\(\\frac{v}{v%}\\)<\/span> mixture you desire.  <\/p>\n<p>But when you pour the 70 mL of ethanol and 30 mL of water into your graduated cylinder, you actually find that you\u2019ve come up short! Your graduated cylinder only has 96 mL of solution. How is that possible?<\/p>\n<p>As you mixed the two liquids, the ethanol and water molecules began to interact with each other, packing together in a different way than in either pure ethanol or pure water. This results in a new density of the solution and thus, a volume that does not equal the sum of the two original volumes.<\/p>\n<p>In other words, the volume of solution, the denominator of our volume percent equation, does not equal the volume of solute plus the volume of solvent. In the case of water and ethanol, their mixture has less volume than the sum of the pure liquids.  <\/p>\n<h2><span id=\"Example_4\" class=\"m-toc-anchor\"><\/span>Example #4<\/h2>\n<p>\nSo how do you actually prepare a 70% <span style=\"font-size:110%\">\\(\\frac{v}{v%}\\)<\/span> solution of ethanol in water? Instead of adding the premeasured liquids together, you would fill a graduated cylinder with 70 mL ethanol and then top up to 100 mL with water. This way, you\u2019ve reached a total volume of 100 mL, 70 of which are ethanol, but you added a bit more water than you initially expected. <\/p>\n<p>The difference between the volume of solute plus the volume of solvent and the volume of the solution is typically pretty small, so you\u2019ll often be instructed to assume that they are the same.<\/p>\n<p>For example, you might get a question like, what is the volume percent of ethanol in a mixture of 40 mL ethanol and 80 mL water (assume that the volume of solution is 120 mL).  <\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{v}{v\\%}\\) <span style=\"font-size: 85%;\">\\(=\\)<\/span>\\( \\frac{40\\text{ mL}}{120\\text{ mL}}\\) <span style=\"font-size: 85%;\">\\(\u00d7 100=33.3\\%\\text{ ethanol }\\)<\/span>\\(\\frac{v}{v}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, you should be able to understand what you\u2019re being asked and can easily make the calculations. <\/p>\n<p>Thanks for watching, and happy studying!<\/p>\n<\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/chemistry\/\">Return to Chemistry Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Chemistry Videos<\/p>\n","protected":false},"author":1,"featured_media":95335,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-14938","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-chemistry-instruments-and-calculations","7":"page_type-video","8":"subject_matter-science"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/14938","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=14938"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/14938\/revisions"}],"predecessor-version":[{"id":280505,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/14938\/revisions\/280505"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/95335"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=14938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}