{"id":7612,"date":"2021-06-08T21:57:01","date_gmt":"2021-06-08T21:57:01","guid":{"rendered":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/dilutions-and-concentrations\/"},"modified":"2021-10-04T23:26:27","modified_gmt":"2021-10-04T23:26:27","slug":"dilutions-and-concentrations","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/dilutions-and-concentrations\/","title":{"raw":"Dilutions and Concentrations","rendered":"Dilutions and Concentrations"},"content":{"raw":"[latexpage]\r\n
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Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

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  1. Learn how to dilute and concentrate solutions.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nOften, a worker will need to change the concentration of a solution by changing the amount of solvent. Dilution<\/strong>\u00a0is the addition of solvent, which decreases the concentration of the solute in the solution. Concentration<\/strong>\u00a0is the removal of solvent, which increases the concentration of the solute in the solution. (Do not confuse the two uses of the word concentration<\/em> here!)\r\n\r\nIn both dilution and concentration, the amount of solute stays the same. This gives us a way to calculate what the new solution volume must be for the desired concentration of solute. From the definition of molarity, which is:\r\n

    [latex]\\text{molarity}=\\dfrac{\\text{moles of solute}}{\\text{litres of solution}}[\/latex]<\/p>\r\nwe can solve for the number of moles of solute:\r\n

    [latex]\\text{moles of solute}=(\\text{molarity})(\\text{litres of solution})[\/latex]<\/p>\r\nA simpler way of writing this is to use M<\/em> to represent molarity and V<\/em> to represent volume. So the equation becomes:\r\n

    [latex]\\text{moles of solute}=MV[\/latex]<\/p>\r\nBecause this quantity does not change before and after the change in concentration, the product MV<\/em> must be the same before and after the concentration change. Using numbers to represent the initial and final conditions, we have:\r\n

    [latex]M_1V_1=M_2V_2[\/latex]<\/p>\r\nas the dilution equation<\/strong>. The volumes must be expressed in the same units. Note that this equation gives only the initial and final conditions, not the amount of the change. The amount of change is determined by subtraction.\r\n

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    Example 11.21<\/p>\r\n\r\n<\/header>\r\n

    \r\n\r\nIf 25.0 mL of a 2.19 M solution are diluted to 72.8 mL, what is the final concentration?\r\n\r\nSolution<\/em>\r\nIt does not matter which set of conditions is labelled 1 or 2, as long as the conditions are paired together properly. Using the dilution equation, we have:\r\n

    [latex](2.19\\text{ M})(25.0\\text{ mL})=M_2(72.8\\text{ mL})[\/latex]<\/p>\r\nSolving for the second concentration (noting that the millilitre units cancel):\r\n

    [latex]M_2=0.752\\text{ M}[\/latex]<\/p>\r\nThe concentration of the solution has decreased. In going from 25.0 mL to 72.8 mL, 72.8 \u2212 25.0 = 47.8 mL of solvent must be added.\r\n\r\nTest Yourself<\/em>\r\nA 0.885 M solution of KBr whose initial volume is 76.5 mL has more water added until its concentration is 0.500 M. What is the new volume of the solution?\r\n\r\nAnswer<\/em>\r\n135.4 mL\r\n\r\n<\/div>\r\n<\/div>\r\nConcentrating solutions involves removing solvent. Usually this is done by evaporating or boiling, assuming that the heat of boiling does not affect the solute. The dilution equation is used in these circumstances as well.\r\n

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    Chemistry Is Everywhere: Preparing IV Solutions<\/h1>\r\nIn a hospital emergency room, a physician orders an intravenous (IV) delivery of 100 mL of 0.5% KCl for a patient suffering from hypokalemia (low potassium levels). Does an aide run to a supply cabinet and take out an IV bag containing this concentration of KCl?\r\n\r\nNot likely. It is more probable that the aide must make the proper solution from an IV bag of sterile solution and a more concentrated, sterile solution, called a stock solution<\/em>, of KCl. The aide is expected to use a syringe to draw up some stock solution and inject it into the waiting IV bag and dilute it to the proper concentration. Thus the aide must perform a dilution calculation.\r\n\r\n[caption id=\"attachment_3249\" align=\"aligncenter\" width=\"302\"]\"Medical Medical personnel commonly must perform dilutions for IV solutions.[\/caption]\r\n\r\nIf the stock solution is 10.0% KCl and the final volume and concentration need to be 100 mL and 0.50%, respectively, then it is an easy calculation to determine how much stock solution to use:\r\n

    [latex]\\begin{array}{rcl}\r\n(10\\%)V_1&=&(0.50\\%)(100\\text{ mL}) \\\\\r\nV_1&=&5\\text{ mL}\r\n\\end{array}[\/latex]<\/p>\r\nOf course, the addition of the stock solution affects the total volume of the diluted solution, but the final concentration is likely close enough even for medical purposes.\r\n\r\nMedical and pharmaceutical personnel are constantly dealing with dosages that require concentration measurements and dilutions. It is an important responsibility: calculating the wrong<\/em> dose can be useless, harmful, or even fatal!\r\n\r\n<\/div>\r\n

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    Key Takeaways<\/p>\r\n\r\n<\/header>\r\n

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