{"id":2906,"date":"2016-08-24T19:44:11","date_gmt":"2016-08-24T19:44:11","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/?post_type=chapter&#038;p=2906"},"modified":"2016-08-26T18:54:09","modified_gmt":"2016-08-26T18:54:09","slug":"dilution","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/chapter\/dilution\/","title":{"raw":"Dilution","rendered":"Dilution"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<div class=\"x-ck12-data-objectives\">\r\n<ul id=\"x-ck12-Nzc5NTNkYTQwNTAyZmU4NzYyNWU5YTE4YzkyMGY5NmY.-wnk\">\r\n \t<li>Perform calculations involving dilutions.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How do you clean concrete?<\/h3>\r\n[caption id=\"\" align=\"aligncenter\" width=\"400\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212434\/20140811155608084590.jpeg\" alt=\"Diluted muriatic acid (HCl) is used to clean concrete\" width=\"400\" height=\"333\" \/> A soldier cleans concrete. Image from <a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:USMC-07803.jpg\">Wikimedia<\/a>.[\/caption]\r\n<p id=\"x-ck12-MWJlYjI3YjcxMjI3ZGQzNTg0MTYyYjc3ZWE5YmExMGQ.-9w7\">Muriatic acid (another name for HCl) is widely used for cleaning concrete and masonry surfaces. The acid must be diluted before use to get it down to a safer strength. Commercially available at concentrations of about 18%, this compound can be used to remove scales and deposits (usually composed of basic materials).<\/p>\r\n\r\n<\/div>\r\n<h2>Dilutions<\/h2>\r\n<p id=\"x-ck12-MmUwZmNjZjZhNWEyZmE4M2I4M2ZmZTRhOGRhZjkzYTg.-90d\">When additional water is added to an aqueous solution, the concentration of that solution decreases. This is because the number of moles of the solute does not change, while the volume of the solution increases. We can set up an equality between the moles of the solute before the dilution (1) and the moles of the solute after the dilution (2).<\/p>\r\n<p id=\"x-ck12-7zj\"><img id=\"x-ck12-MTM2NjcwNjM4MjY3OA..\" class=\"x-ck12-block-math aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212436\/0fe169785b0deacb8e096951d997a255.png\" alt=\"text{mol}_1=text{mol}_2\" width=\"95\" height=\"17\" \/><\/p>\r\n<p id=\"x-ck12-NmFmMzM5YWNkNmU3NDhiNjQ1OWUyNjU3NWViNjgwNGQ.-an4\">Since the moles of solute in a solution is equal to the molarity multiplied by the liters, we can set those equal.<\/p>\r\n<p id=\"x-ck12-kjd\"><img class=\"x-ck12-block-math aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212436\/c390e6394b3ee9998ce11e2a17eb93a4.png\" alt=\"M_1 times L_1=M_2 times L_2\" width=\"155\" height=\"16\" \/><\/p>\r\n<p id=\"x-ck12-N2NjNzU1MWFjZTlhMmRjNjI2OTcwYTgxYmVmMzQ2MmQ.-foy\">Finally, because the two sides of the equation are set equal to one another, the volume can be in any units we choose, as long as that unit is the same on both sides. Our equation for calculating the molarity of a diluted solution becomes:<\/p>\r\n<p id=\"x-ck12-pwk\"><img class=\"x-ck12-block-math aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212437\/07f6835a15ba95465ec59b284bb1bcea.png\" alt=\"M_1 times V_1 = M_2 times V_2\" width=\"151\" height=\"16\" \/><\/p>\r\n<p id=\"x-ck12-Mzg1MTNjNzBhNWE3YzU5MmUyOTE0ODNiNDIyZjRkZTc.-erl\">Suppose that you have 100. mL of a 2.0 M solution of HCl. You dilute the solution by adding enough water to make the solution volume 500. mL. The new molarity can easily be calculated by using the above equation and solving for <img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212438\/4398a50def640d8316e798060db7f81b.png\" alt=\"M_2\" width=\"23\" height=\"15\" \/> .<\/p>\r\n<p id=\"x-ck12-oua\"><img id=\"x-ck12-MTM2NjcwNjM4MjY3OQ..\" class=\"x-ck12-block-math aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212438\/8df6428e5dad7614ef7beabdaff5d02c.png\" alt=\"M_2=frac{M_1 times V_1}{V_2}=frac{2.0 text{ M} times 100. text{ mL}}{500. text{ mL}}=0.40 text{ M } HCl\" width=\"395\" height=\"40\" \/><\/p>\r\n<p id=\"x-ck12-MWZkYTljNmVkZTVmZjAyNzM3YjI2YWJiYmZmMzliN2I.-fn4\">The solution has been diluted by one-fifth since the new volume is five times as great as the original volume. Consequently, the molarity is one-fifth of its original value.<\/p>\r\n<p id=\"x-ck12-MzI1OWRhMjdjNDBjZDQ3ZWNkNmQxYWYwMzYyNjIyMjU.-krv\">Another common dilution problem involves deciding how much of a highly concentrated solution is requires to make a desired quantity of solution of lesser concentration. The highly concentrated solution is typically referred to as the stock solution.<\/p>\r\n\r\n<h3>Sample Problem: Dilution of a Stock Solution<\/h3>\r\n<p id=\"x-ck12-MjUyYmE2NGYyOWE5YmNiM2ViOTU1MWYzYzgzNmI5MWM.-uhg\">Nitric acid (HNO <sub> 3 <\/sub> ) is a powerful and corrosive acid. When ordered from a chemical supply company, its molarity is 16 M. How much of the stock solution of nitric acid needs to be used to make 8.00 L of a 0.50 M solution?<\/p>\r\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-6ij\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\r\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-nmv\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-ZDRlYTgyYmUzZWUyYjU0YjZhZTZlZDM3ZWY2ZmFmYjY.-go5\">\r\n \t<li>stock HNO <sub> 3 <\/sub> = 16 M<\/li>\r\n \t<li><img id=\"x-ck12-MTQwMDYyMjE0MzAxMA..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212439\/ac38c80da79c41d3c51f69c6df8aca8f.png\" alt=\"V_2=8.00 text{L}\" width=\"91\" height=\"16\" \/><\/li>\r\n \t<li><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212440\/221dbef97bed18141a15fd83a8a79c3f.png\" alt=\"M_2=0.50 text{M}\" width=\"103\" height=\"16\" \/><\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-wac\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\r\n\r\n<ul id=\"x-ck12-jby\">\r\n \t<li><img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212440\/c317c305d11872a4458a92ebd35bb199.png\" alt=\"text{volume stock} text{HNO}_3 (V_1)=? text{L}\" width=\"238\" height=\"18\" \/><\/li>\r\n<\/ul>\r\n<p id=\"x-ck12-NmJmODg4MzI5ODhjZWU2M2JmOTAwNmQxOTRlYjhmMzg.-l9y\">The unknown in the equation is <img class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212125\/29c883aa1a216bc9157974e94c993965.png\" alt=\"V_1\" width=\"16\" height=\"16\" \/> , the volume of the concentrated stock solution.<\/p>\r\n<p id=\"x-ck12-ZmYxNjkxNzA3ODcxNDhkYjhmZGUyOTFlNDk1NmEzZjE.-gsp\"><em> Step 2: Solve. <\/em><\/p>\r\n<p id=\"x-ck12-l9d\"><img class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212441\/f6faf46f6cb23d89e08631c77e2eb88b.png\" alt=\"V_1=frac{M_2 times V_2}{M_1}=frac{0.50 text{ M} times 8.00 text{ L}}{16 text{ M}}=0.25 text{ L}=250 text{ mL}\" width=\"419\" height=\"41\" \/><\/p>\r\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-quj\"><em> Step 3: Think about your result. <\/em><\/p>\r\n<p id=\"x-ck12-ZDJlNDhmY2NkYzIwNmQ3OTc5MTBhMGJlMDk1Y2VlODc.-e7h\">250 mL of the stock HNO <sub> 3 <\/sub> needs to be diluted with water to a final volume of 8.00 L. The dilution is by a factor of 32 to go from 16 M to 0.5 M.<\/p>\r\n\r\n\r\n[caption id=\"attachment_3169\" align=\"alignleft\" width=\"283\"]<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/515\/2016\/08\/25182527\/pipette.jpg\"><img class=\"wp-image-3169\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/515\/2016\/08\/25182527\/pipette.jpg\" alt=\"Scientist holding liquid in a pipette during a transfer.\" width=\"283\" height=\"212\" \/><\/a> Image 1. Volumetric pipette. Image from the <a href=\"https:\/\/www.youtube.com\/watch?v=TffTiRw8cQY\">Teaching and Learning Centre<\/a>.[\/caption]\r\n\r\n[caption id=\"\" align=\"alignright\" width=\"192\"]<img id=\"x-ck12-OTgwNDUtMTM2Mzc3MzgxNC05LTg4LTUz\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212444\/20140811155608356241.jpeg\" alt=\"Micropipettes are used to precisely measure volumes under 1 mL\" width=\"192\" height=\"144\" longdesc=\"Micropipette.\" \/> Figure 2. Micropipette. Image by <a href=\"https:\/\/www.flickr.com\/photos\/rocksee\/2406542538\/\">rocksee<\/a>.[\/caption]\r\n<p id=\"x-ck12-YzAwNjNkY2JkMDBkNjc5MzhhMDRhZTM1MDYyOTBmMDY.-xgj\">Dilutions can be performed in the laboratory with various tools, depending on the volumes required and the desired accuracy. The following images illustrate the use of two different types of pipettes. The images below illustrate the use of two different types of pipettes. In the Image 1, a glass <strong> pipette <\/strong> is being used to transfer a portion of a solution from a cylinder.Volumetric pipette.Use of a pipette rather than a graduated cylinder for the transfer improves accuracy.\u00a0Figure 2\u00a0shows a\u00a0 <strong> micropipette <\/strong> , which is designed to quickly and accurately dispense small volumes. Micropipettes are adjustable and come in a variety of sizes.<\/p>\r\n\r\n<div id=\"x-ck12-NmRjNDE2M2VlYzIyNDFiYjA0ODVlY2FmY2JjNjE4Zjk.-rbg\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul id=\"x-ck12-ZmIyMWFmYmRlNWEwNTZlODc4YjM4NTc4NGNjM2IwNGY.-ufs\">\r\n \t<li>A process is described for calculations of dilutions.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\n<p id=\"x-ck12-ZThkYjdjMTJjNWM3YjlhMmY1YzllNmQzODFiODYwYTI.-vgf\">Read the material and work the problems at the link below:<\/p>\r\n<p id=\"x-ck12-NDIwOWRhOTFjMTFjYTVmZDBlZjEyNTEzZThkZTc3NjM.-v8e\"><a href=\"http:\/\/dl.clackamas.edu\/ch105-04\/dilution.htm\"> http:\/\/dl.clackamas.edu\/ch105-04\/dilution.htm<\/a><\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<ol id=\"x-ck12-MGZkNjUwYzQwYzA2ZjBkYzg1ZGE2MmMyOTIwNDU2ZWI.-63o\">\r\n \t<li>What does not change when additional water is added to a solution?<\/li>\r\n \t<li>What is a stock solution?<\/li>\r\n \t<li>How is a stock solution used?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"x-ck12-data-vocabulary\">\r\n<ul id=\"x-ck12-ZmJkNjU5ZGYwYzk0OGZkM2Q5NTg2MGM0YzBiYmM3OGQ.-gcv\">\r\n \t<li><strong> micropipette: <\/strong> A pipette designed to transfer very small amounts of fluid.<\/li>\r\n \t<li><strong> pipette: <\/strong> A calibrated glass tube for the accurate transfer of liquids.<\/li>\r\n<\/ul>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<div class=\"x-ck12-data-objectives\">\n<ul id=\"x-ck12-Nzc5NTNkYTQwNTAyZmU4NzYyNWU5YTE4YzkyMGY5NmY.-wnk\">\n<li>Perform calculations involving dilutions.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>How do you clean concrete?<\/h3>\n<div style=\"width: 410px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212434\/20140811155608084590.jpeg\" alt=\"Diluted muriatic acid (HCl) is used to clean concrete\" width=\"400\" height=\"333\" \/><\/p>\n<p class=\"wp-caption-text\">A soldier cleans concrete. Image from <a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:USMC-07803.jpg\">Wikimedia<\/a>.<\/p>\n<\/div>\n<p id=\"x-ck12-MWJlYjI3YjcxMjI3ZGQzNTg0MTYyYjc3ZWE5YmExMGQ.-9w7\">Muriatic acid (another name for HCl) is widely used for cleaning concrete and masonry surfaces. The acid must be diluted before use to get it down to a safer strength. Commercially available at concentrations of about 18%, this compound can be used to remove scales and deposits (usually composed of basic materials).<\/p>\n<\/div>\n<h2>Dilutions<\/h2>\n<p id=\"x-ck12-MmUwZmNjZjZhNWEyZmE4M2I4M2ZmZTRhOGRhZjkzYTg.-90d\">When additional water is added to an aqueous solution, the concentration of that solution decreases. This is because the number of moles of the solute does not change, while the volume of the solution increases. We can set up an equality between the moles of the solute before the dilution (1) and the moles of the solute after the dilution (2).<\/p>\n<p id=\"x-ck12-7zj\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM2NjcwNjM4MjY3OA..\" class=\"x-ck12-block-math aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212436\/0fe169785b0deacb8e096951d997a255.png\" alt=\"text{mol}_1=text{mol}_2\" width=\"95\" height=\"17\" \/><\/p>\n<p id=\"x-ck12-NmFmMzM5YWNkNmU3NDhiNjQ1OWUyNjU3NWViNjgwNGQ.-an4\">Since the moles of solute in a solution is equal to the molarity multiplied by the liters, we can set those equal.<\/p>\n<p id=\"x-ck12-kjd\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212436\/c390e6394b3ee9998ce11e2a17eb93a4.png\" alt=\"M_1 times L_1=M_2 times L_2\" width=\"155\" height=\"16\" \/><\/p>\n<p id=\"x-ck12-N2NjNzU1MWFjZTlhMmRjNjI2OTcwYTgxYmVmMzQ2MmQ.-foy\">Finally, because the two sides of the equation are set equal to one another, the volume can be in any units we choose, as long as that unit is the same on both sides. Our equation for calculating the molarity of a diluted solution becomes:<\/p>\n<p id=\"x-ck12-pwk\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212437\/07f6835a15ba95465ec59b284bb1bcea.png\" alt=\"M_1 times V_1 = M_2 times V_2\" width=\"151\" height=\"16\" \/><\/p>\n<p id=\"x-ck12-Mzg1MTNjNzBhNWE3YzU5MmUyOTE0ODNiNDIyZjRkZTc.-erl\">Suppose that you have 100. mL of a 2.0 M solution of HCl. You dilute the solution by adding enough water to make the solution volume 500. mL. The new molarity can easily be calculated by using the above equation and solving for <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212438\/4398a50def640d8316e798060db7f81b.png\" alt=\"M_2\" width=\"23\" height=\"15\" \/> .<\/p>\n<p id=\"x-ck12-oua\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTM2NjcwNjM4MjY3OQ..\" class=\"x-ck12-block-math aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212438\/8df6428e5dad7614ef7beabdaff5d02c.png\" alt=\"M_2=frac{M_1 times V_1}{V_2}=frac{2.0 text{ M} times 100. text{ mL}}{500. text{ mL}}=0.40 text{ M } HCl\" width=\"395\" height=\"40\" \/><\/p>\n<p id=\"x-ck12-MWZkYTljNmVkZTVmZjAyNzM3YjI2YWJiYmZmMzliN2I.-fn4\">The solution has been diluted by one-fifth since the new volume is five times as great as the original volume. Consequently, the molarity is one-fifth of its original value.<\/p>\n<p id=\"x-ck12-MzI1OWRhMjdjNDBjZDQ3ZWNkNmQxYWYwMzYyNjIyMjU.-krv\">Another common dilution problem involves deciding how much of a highly concentrated solution is requires to make a desired quantity of solution of lesser concentration. The highly concentrated solution is typically referred to as the stock solution.<\/p>\n<h3>Sample Problem: Dilution of a Stock Solution<\/h3>\n<p id=\"x-ck12-MjUyYmE2NGYyOWE5YmNiM2ViOTU1MWYzYzgzNmI5MWM.-uhg\">Nitric acid (HNO <sub> 3 <\/sub> ) is a powerful and corrosive acid. When ordered from a chemical supply company, its molarity is 16 M. How much of the stock solution of nitric acid needs to be used to make 8.00 L of a 0.50 M solution?<\/p>\n<p id=\"x-ck12-Y2VlNGQ1OTZkZWQ3ZDY1MzMyNmI1ODhhNWUzY2Q3NmU.-6ij\"><em> Step 1: List the known quantities and plan the problem. <\/em><\/p>\n<p id=\"x-ck12-MmY1NjUwZTQ4NGZhMTk1OTQ5YWM2YzhkMTFkY2E0ZmQ.-nmv\"><span class=\"x-ck12-underline\"> Known <\/span><\/p>\n<ul id=\"x-ck12-ZDRlYTgyYmUzZWUyYjU0YjZhZTZlZDM3ZWY2ZmFmYjY.-go5\">\n<li>stock HNO <sub> 3 <\/sub> = 16 M<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-MTQwMDYyMjE0MzAxMA..\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212439\/ac38c80da79c41d3c51f69c6df8aca8f.png\" alt=\"V_2=8.00 text{L}\" width=\"91\" height=\"16\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212440\/221dbef97bed18141a15fd83a8a79c3f.png\" alt=\"M_2=0.50 text{M}\" width=\"103\" height=\"16\" \/><\/li>\n<\/ul>\n<p id=\"x-ck12-ODgxODNiOTQ2Y2M1ZjBlOGM5NmIyZTY2ZTFjNzRhN2U.-wac\"><span class=\"x-ck12-underline\"> Unknown <\/span><\/p>\n<ul id=\"x-ck12-jby\">\n<li><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212440\/c317c305d11872a4458a92ebd35bb199.png\" alt=\"text{volume stock} text{HNO}_3 (V_1)=? text{L}\" width=\"238\" height=\"18\" \/><\/li>\n<\/ul>\n<p id=\"x-ck12-NmJmODg4MzI5ODhjZWU2M2JmOTAwNmQxOTRlYjhmMzg.-l9y\">The unknown in the equation is <img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212125\/29c883aa1a216bc9157974e94c993965.png\" alt=\"V_1\" width=\"16\" height=\"16\" \/> , the volume of the concentrated stock solution.<\/p>\n<p id=\"x-ck12-ZmYxNjkxNzA3ODcxNDhkYjhmZGUyOTFlNDk1NmEzZjE.-gsp\"><em> Step 2: Solve. <\/em><\/p>\n<p id=\"x-ck12-l9d\"><img loading=\"lazy\" decoding=\"async\" class=\"x-ck12-block-math\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212441\/f6faf46f6cb23d89e08631c77e2eb88b.png\" alt=\"V_1=frac{M_2 times V_2}{M_1}=frac{0.50 text{ M} times 8.00 text{ L}}{16 text{ M}}=0.25 text{ L}=250 text{ mL}\" width=\"419\" height=\"41\" \/><\/p>\n<p id=\"x-ck12-MGZhMzc5YjY2OWU0YzY0ZWM4YjYzZWNhYzc4OTQ3ZDA.-quj\"><em> Step 3: Think about your result. <\/em><\/p>\n<p id=\"x-ck12-ZDJlNDhmY2NkYzIwNmQ3OTc5MTBhMGJlMDk1Y2VlODc.-e7h\">250 mL of the stock HNO <sub> 3 <\/sub> needs to be diluted with water to a final volume of 8.00 L. The dilution is by a factor of 32 to go from 16 M to 0.5 M.<\/p>\n<div id=\"attachment_3169\" style=\"width: 293px\" class=\"wp-caption alignleft\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/515\/2016\/08\/25182527\/pipette.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3169\" class=\"wp-image-3169\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/515\/2016\/08\/25182527\/pipette.jpg\" alt=\"Scientist holding liquid in a pipette during a transfer.\" width=\"283\" height=\"212\" \/><\/a><\/p>\n<p id=\"caption-attachment-3169\" class=\"wp-caption-text\">Image 1. Volumetric pipette. Image from the <a href=\"https:\/\/www.youtube.com\/watch?v=TffTiRw8cQY\">Teaching and Learning Centre<\/a>.<\/p>\n<\/div>\n<div style=\"width: 202px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" id=\"x-ck12-OTgwNDUtMTM2Mzc3MzgxNC05LTg4LTUz\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212444\/20140811155608356241.jpeg\" alt=\"Micropipettes are used to precisely measure volumes under 1 mL\" width=\"192\" height=\"144\" longdesc=\"Micropipette.\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 2. Micropipette. Image by <a href=\"https:\/\/www.flickr.com\/photos\/rocksee\/2406542538\/\">rocksee<\/a>.<\/p>\n<\/div>\n<p id=\"x-ck12-YzAwNjNkY2JkMDBkNjc5MzhhMDRhZTM1MDYyOTBmMDY.-xgj\">Dilutions can be performed in the laboratory with various tools, depending on the volumes required and the desired accuracy. The following images illustrate the use of two different types of pipettes. The images below illustrate the use of two different types of pipettes. In the Image 1, a glass <strong> pipette <\/strong> is being used to transfer a portion of a solution from a cylinder.Volumetric pipette.Use of a pipette rather than a graduated cylinder for the transfer improves accuracy.\u00a0Figure 2\u00a0shows a\u00a0 <strong> micropipette <\/strong> , which is designed to quickly and accurately dispense small volumes. Micropipettes are adjustable and come in a variety of sizes.<\/p>\n<div id=\"x-ck12-NmRjNDE2M2VlYzIyNDFiYjA0ODVlY2FmY2JjNjE4Zjk.-rbg\" class=\"x-ck12-img-thumbnail x-ck12-nofloat\">\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul id=\"x-ck12-ZmIyMWFmYmRlNWEwNTZlODc4YjM4NTc4NGNjM2IwNGY.-ufs\">\n<li>A process is described for calculations of dilutions.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p id=\"x-ck12-ZThkYjdjMTJjNWM3YjlhMmY1YzllNmQzODFiODYwYTI.-vgf\">Read the material and work the problems at the link below:<\/p>\n<p id=\"x-ck12-NDIwOWRhOTFjMTFjYTVmZDBlZjEyNTEzZThkZTc3NjM.-v8e\"><a href=\"http:\/\/dl.clackamas.edu\/ch105-04\/dilution.htm\"> http:\/\/dl.clackamas.edu\/ch105-04\/dilution.htm<\/a><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<ol id=\"x-ck12-MGZkNjUwYzQwYzA2ZjBkYzg1ZGE2MmMyOTIwNDU2ZWI.-63o\">\n<li>What does not change when additional water is added to a solution?<\/li>\n<li>What is a stock solution?<\/li>\n<li>How is a stock solution used?<\/li>\n<\/ol>\n<\/div>\n<div class=\"x-ck12-data-vocabulary\">\n<ul id=\"x-ck12-ZmJkNjU5ZGYwYzk0OGZkM2Q5NTg2MGM0YzBiYmM3OGQ.-gcv\">\n<li><strong> micropipette: <\/strong> A pipette designed to transfer very small amounts of fluid.<\/li>\n<li><strong> pipette: <\/strong> A calibrated glass tube for the accurate transfer of liquids.<\/li>\n<\/ul>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-2906\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Chemistry Concepts Intermediate. <strong>Authored by<\/strong>: Calbreath, Baxter, et al.. <strong>Provided by<\/strong>: CK12.org. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\">http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/\">CC BY-NC: Attribution-NonCommercial<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":29,"menu_order":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Chemistry Concepts Intermediate\",\"author\":\"Calbreath, Baxter, et al.\",\"organization\":\"CK12.org\",\"url\":\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\",\"project\":\"\",\"license\":\"cc-by-nc\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2906","chapter","type-chapter","status-publish","hentry"],"part":2337,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2906","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/users\/29"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2906\/revisions"}],"predecessor-version":[{"id":3417,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2906\/revisions\/3417"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/parts\/2337"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/2906\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/media?parent=2906"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapter-type?post=2906"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/contributor?post=2906"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/license?post=2906"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}