Determination of Percentage Composition of Sugar Solution from Viscosity
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Name: D.O.E Section: D.O.S Class Roll No: Stream: University Roll No: DETERMINATION OF PERCENTAGE COMPOSITION OF SUGAR SOLUTION FROM VISCOSITY THEORY: The coefficient of viscosity (η) of a liquid is defined as the tangential force per unit area required maintaining unit velocity gradient between two successive layers of a liquid, which are unit distance apart from each other .The unit of co- efficient of viscosity is dyne-sec\cm2 (poise). The co-efficient of viscosity of liquid can be determined by comparing its coefficient of viscosity with the known coefficient of viscosity of a liquid. Generally water is taken as the known liquid for comparison. As this method requires the comparison with another liquid, it is a relative method. In relative method for determination of coefficient of viscosity (η) of a liquid, Poiseuille’s equation can be used. Poiseuille’s equation η =πPr4t\8vl…………. (1) Where v=volume of the liquid following through a capillary tube of length (l) in‘t’ sec. The radius of the tube is ‘r’ cm and ‘P’ is the driving pressure in dyne\cm2. P can be replaced by hρg, where h= difference in height between the levels of the liquid in the two limbs, g= acceleration due to gravity and ρ is the density of the liquid. Now if the same capillary and the same volume of liquids are used, then for the two liquids the following equation can be deduced. η1\η2=ρ1t1\ρ2t2 …………….. (2) Where, ρ1 and ρ2 are the densities and t1 and t2 are time of flow for the two liquids. So if η2 is known, then by determining t1and t2 ,ρ1 and ρ2 , η1 can be calculated. η1=η2 x ρ1t1\ρ2t2 ……………… (3) In the present study we are measuring the relative viscosity in comparison of viscosity of water. So as η2 the viscosity of water and it’s density (ρ2) is known (from the chart), then by measuring t2 it’s time of flow and ρ1, t1 the density and time of flow of other liquids, viscosity can be calculated. Times of flow of the liquids are determined using Oswald’s viscometer and stopwatch. Densities are determined using specific gravity bottle. The density of water varies from 0.99987 to 0.98807 gm/c.c in the temperature range 00C to 500C and can be taken as 1 gm/c.c , the equation then becomes η1 = η2 x ρ1t1\ t2 centipoise ……………(4). PROCEDURE: 1. Determination of density of liquid using specific gravity bottle: The specific gravity bottle is cleaned, dried and weighed empty. Then it is filled with water and weighed. Then the bottle is filled with stock solution and then unknown solution and weighed. The densities of other solutions are then determined by calculations. 2. The time of flow of same volume of each liquid is determined using an Ostwald’s Viscometer. The time of flow of same volume of water is determined using same Viscometer. The data thus collected is put into the equation (4) which is the working formula. 3. Preparation of solution: Stock solution: 10% sugar solution is prepared at first. Then 6% and 3%solution are prepared from the stock solution in the following way. % of solution Volume of stock Volume of Water Total volume solution of solution 6% 18c.c 12c.c 30c.c 3% 9c.c 21c.c 30c.c 4. Graph: Coefficient of viscosity of each solution is plotted against conc. of each solution. From the graph, conc. of unknown solution can be determined Coefficient of viscosity(η) unknown conc. of sugar solution (%) RESULT: 1. Recording of temperature: Initial temperature(0C) Final temperature(0C) Mean temperature(0C) 2. Preparation of solution: % of solution Volume of stock Volume of Water Total volume solution (ml) of solution (ml) (ml) 3. Recording of weight for determination of densities: Wt. of bottle with lid Wt. of empty Wt. of unknown Wt. of 10% solution+ + bottle with lid solution + Wt. of wt. of bottle with lid Wt. of water (gm) x bottle with lid (gm) z (gm) y (gm) p 4. Recording of time flow % of solution Time of flow Mean time (sec) (sec) Water i) ii) 3% i) ii) 6% i) ii) Unknown i) ii) 10% i) ii) 5. Determination of coefficient of viscosity of each solution using equation (4) % of solution Density (gm/c.c.) Coefficient of viscosity(centipoises) Water 10% 6% 3% Unknown Calculation: Wt. of water=(y-x) gm=……………………gm Wt. of 10% solution= (z-x) =…………………gm Wt. of unknown solution= (p-x) =…………………gm Density of 10% solution (q) = (z-x)\(y-x) x Dw=…………….. gm\ml Density of unknown solution(r) = (p-x)\(y-x)xDw=……………….. gm\ml Density of 6% solution= (18xq+12xDw)\30=s gm\ml=………………… gm\ml Density of 3% solution= (9xq+21xDw)\30=t gm\ml=………………… gm\ml 10%=w x (q\Dw) x (time of flow of 10% solution\time of flow of water)=a Centipoises =…………….. centipoises 6%=w x (s\Dw) x (time of flow of 6% solution\time of flow of water) =b centipoises =……………… centipoises 3%=w x (t/Dw) x (time of flow of 3% solution\time of flow of water) =c centipoises =……………… centipoises unknown=w x (r/Dw)x (time of flow of unknown solution\time of flow of water)=d centipoises=……......... centipoises DISCUSSION: The viscosity of a solution depends on the concentration of the solute present in it and also on the temperature of the solution. So prior to the experiment all the apparatus were well cleaned with distilled water so that no impurities be present in it. If the temperatures of measurement are not fixed, the viscosity of the solutions at different temperature will be different. So all the viscosity measurement of the solutions are performed under same temperature. The measurement of time flow was done correctly. The viscometer was cleaned after every single measurement. Exactly same volume of solvent / solution were used in the viscometer, neither the relative viscosity measured will be erratic. For measurement of densities, the specific gravity bottle was dried well, filled fully with fluid and lid were introduced. Any error in measuring weight, the overall experiment will be erratic. So; proper care was taken while measuring the fluid flow as well as density measurement. CONCLUSION: From the graph the concentration of sugar in the supplied unknown sugar solution is found to be ( ………… ) % at ………………0C. CHART Density, viscosity datas of water at different temperature Temperature( 0C) Density (gm/c.c) Coefficient of viscosity(centipoise) 0 0.99987 1.787 10 0.99973 1.307 15 0.99913 1.139 20 0.99823 1.002 25 0.99707 0.8904 30 0.99567 0.7974 35 0.99406 0.7194 40 0.99224 0.6529 45 0.99024 0.5960 50 0.98807 0.5468 .