Calculations Associated with Solutions

CHAPTER 6


Calculations Associated With Solutions




PERCENT SOLUTIONS


Solutions may be expressed in other concentrations besides molarity, molality, or normality. In the laboratory, solutions are sometimes expressed in terms of relative percent concentration of solute to solution. There are three types of percent concentrations that may be used in the laboratory. In all three types, the total volume of the solvent is based on a quantity of 100 mL or gram, not 1.00 L, as in molarity or normality concentrations.



Percent Weight/Weight


A percent weight/weight (%w/w) solution is calculated using the following formula:


%W/W=gramofsolute100.0gofsolutionORgram of solute per100.0g of solution


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In this type of solution, the amounts of solute and solvents are weighed individually using a balance. It is important to note that as the total is based on 100.0 g of solution, the amount of solvent that must be weighed is determined by subtracting the quantity of solute needed from 100.0. A solution consists of solute + solvent. Once the amount of solvent is determined, the solvent and solute are combined and mixed together in a flask or beaker. In the clinical laboratory, deionized water is the most frequently used solvent. The %w/w solutions are the most accurate because unlike %w/v, their concentrations do not fluctuate with temperature. However, the %w/w solutions are not commonly prepared in the clinical laboratory.




Percent Weight/Volume


A percent weight/volume (%w/v) solution is calculated by the following formula:


%W/W=gofsolute100mLofsolutionORgofsoluteper100.0mLofsolution


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The %w/v solution is the most frequently used percent solution in the clinical laboratory. For this solution, the amount of solute is weighed on a balance and then placed into a 100-mL volumetric flask in which there is a small amount of solvent to dissolve the solute. Once the solute is dissolved, the remaining solvent (which in most cases in the clinical laboratory is deionized water) is then added to the volumetric flask to the calibrated mark. The Latin term quantis satis, or quantity sufficient (qs) is often used in the laboratory to describe the addition of the solvent to the calibrated mark. For example, you may be instructed to add a determined amount of solute to a volumetric flask and then qs it to the calibration mark with the appropriate solvent.




Percent Volume/Volume


A percent volume/volume (%v/v) solution uses volume, or liquid, measurements for both the solute and the solvent.


A %v/v solution is calculated by the following formula:


%V/V=mLofsolute100mLofsolutionORmilliliterofsoluteper100mLofsolution


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Percent v/v is similar to %w/w in that the total volume of the solution is 100 mL.


Therefore, the amount of solvent is determined by the following formula:


100mLtotalvolumeamountofsolute=amountofsolvent


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Example 6–3

How many milliliters of ethanol (EtOH) are needed to make a 75.0%v/v solution using deionized water as the solvent?


This problem is solved in the same manner as solving for %w/w and %w/v. Using the formula for %v/v and substituting in the appropriate given numbers, the following equation is derived:


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How many milliliters of water are necessary for this solution?


The amount of water needed is determined by the following formula:


Amount of solvent=100amount of soluteX=10075.0X=25.0


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Therefore, 75.0 mL of EtOH would be added to 25.0 mL of deionized water to produce a solution of 75.0%v/v EtOH.




Conversion of Percentage Calculations to Molarity


In the laboratory, sometimes a chemical solution may be labeled in terms of relative percentage but you may need to know the molarity of that solution. By using both molarity and percentage formulas, you can interchange between the two types of concentrations.





Example 6–4

Suppose you found a bottle labeled 0.85%w/v NaCl in your laboratory. What is the molarity of this solution?


To solve this problem, first use the percent formula to determine the concentration of NaCl in the solution. A %w/v solution is calculated by the number of g of solute dissolved in 100 mL of solvent. As we have a 0.85%w/v solution, we know that there are 0.85 g of NaCl dissolved in 100 mL of water. Because molarity is based on the concentration in 1.00 L of solute, we need to determine the quantity of NaCl present in 1.00 L. We can use a simple ratio formula to determine this:


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Using algebra and crossmultiplying we derive the following:


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Next, use the molarity formula to determine the molarity of this solution. We know that there are 8.50 g of NaCl present per liter of solvent in this solution. The molecular weight of NaCl is 58.44. Next, substitute all of the known values to determine the molarity of this solution:


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Therefore, an 0.85%w/v NaCl solution has a molarity of 0.14 mol/L.



Additional Examples




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Therefore, a 40.0%w/v NaOH solution has a molarity of 10.0 mol/L.




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Therefore, a 10%w/v CaCl2 solution has a molarity of 0.90 mol/L.



Example 6–5

What would be the normality of a solution of 15.0%w/v H2SO4?


To solve this problem, remember that


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To determine the amount of g in 1.00 L:


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Crossmultiplying the equations results in the following:


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Next, use the normality formula to determine the normality of the solution.


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Therefore, a 10.0%w/v H2SO4 solution has a normality of 3.06 Eq/L.




ANHYDROUS VERSUS HYDRATED SOLUTIONS


Another type of solution may consist of hydrated chemical salts dissolved in a solvent. As the difference between the hydrous and the anhydrous form of a chemical is the amount of water molecules present in the hydrated form, it may be necessary to be able to interchange between the two. Sometimes, in the laboratory, only one of the forms of a chemical is available. You must be able to interchange the two forms to arrive at the form that you need. The basic formula for interchanging between hydrated and anhydrous chemicals is as follows:


anhydrouschemicalmolecularweighthydratedchemicalmolecularweight=gramofanhydrouschemicalgramofhydratedchemical


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Notice that it is a ratio and proportion calculation. Ratio and proportion is used whenever the same concentration of a solution but different quantities of the solution is necessary. In anhydrous as opposed to hydrated forms of a chemical, the ratio and proportion are used to ensure that the same concentration of the chemical is used regardless of its water content.






Example 6–6

Suppose you needed to make a 12.0%w/v solution of CuSO4, but only CuSO4 · H2O was available. How much of the CuSO4 · H2O should you use? The gram molecular weight of CuSO4 is 159.61, whereas the gram molecular weight of CuSO4 · H2O is 177.63.


The first step is to determine the amount of grams in a 12.0%w/v solution. A 12%w/v solution contains 12.0 g in 100 mL of solvent. Using the formula for interchanging hydrated and anhydrous chemicals, the following equation is derived:


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By crossmultiplying, the following equation is derived:


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Therefore, 13.4 g of CuSO4 · H2O qs to 100 mL of solvent will result in a 12.0 %w/v solution of CuSO4image.



Additional Examples




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Nov 18, 2017 | Posted by in PHARMACY | Comments Off on Calculations Associated with Solutions

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