Campbell and Kartzmark (9) report the relative viscosities at 25' C over the complete concentration range. Relative volatility is the ratio of the volatilities of two components It indicates how easy or difficult a particular separation by distillation will be b b a a ab x P x P . When a multi-component mixture is distilled, the overhead fraction and the bottoms fraction typically contain much more than one or two components. Volatility of a = pa / xa. Ethanol yield wich used analysis used spectrofotometer pharo 100. Find the T-x-ydata. NMR Chemical Shifts of Common Laboratory Solvents as Trace Impurities. Influence of Relative Air Humidity on Evaporation of Water-Ethanol The calculator below can be used to calculate ethanol dynamic or kinematic viscosity at given temperatures and atmospheric pressure. The transition of a liquid to a gas is called vaporization. 3. If the price of a . Answer: Given: Specific gravity of water at 20C s1 = 0.9982 Specific gravity of methanol at 20C s2 = 0.7917 Wt% of water w1 = 20% Wt% of methanol w2 = 80% Let mass of mixture m = 100 g Mass of water m1. DETAILED DESCRIPTION OF DRAWING AND EXPERIMENT. (Iu;CaK] vy73,"!,ag;pw$d>>a! for the ethanol-water system at atmospheric pressure. A comparative presentation of the relative volatility curve estimated by the NRTL model with the relative volatility of the experimental equilibrium data (Kamihama et al. 1. Definitions Introduction Like the HOH bond in water, the ROH bond is bent, and alcohol molecules are polar. volatility is the relative rate at which the price of a security moves up and down. The major attractive forces between molecules in a liquid are calledhydrogen bonds. kindly explain step wise i read from internet but didnt under stood anything. As gas concentrations accumulate in the air, the distance separating individual molecules decreases until Van der Waals and hydrogen bonds can drive clusters of molecules back into liquid form (condensation). C6H5OH. Powered by WordPress / Academica WordPress Theme by WPZOOM. To determine the relative volatility of an ideal binary mixture the volatility of a component is first defined as the ratio of its partial pressure to its liquid mole fraction: \displaystyle \text{volatility} = \frac{p_{i}}{x_{i}}. It is an object of this invention to suggest at least one further extractive distillation solvent for the separation of ethanol and water from mixtures thereof. If the molecules interact through hydrogen bonding, a relatively large quantity of energy must be supplied to break those intermolecular attractions. 0000008342 00000 n However, I have the stumbling block that I need the relative volatility of both components and I need the mole fraction of each substance in the liquid and vapour stages. endobj The pi bonds in the benzene ring attracts the. Treatment of 96% ethanol with molecular sieves gives anhydrous alcohol, the sieves having adsorbed water from the mixture. In an ideal liquid-vapor systems relative volatility remain constant, in the entire temperature range. AE AL AM AT AU AZ BA BB BG BR BY CA CH CN CR CU CZ DE DK DM EE ES FI GB GD GE GH GM HR HU ID IL IN IS JP KE KG KP KR KZ LC LK LR LS LT LU LV MA MD MG MK MN MW MX NO NZ PL PT RO RU SD SE SG SI SK SL TJ TM TR TT TZ UA UG US UZ VN YU ZA ZW, Designated state(s): Novel distillation process for effective and stable separation of high VLE data of binary mixtures is often presented as a plot, as shown in the figure on the right. The relative volatility is computed as an average, where the Wikipedia article suggests that you can take a simple geometric mean of the relative volatility at the top and bottom to get the average relative volatility. My problem is where do we get these mole fraction figures from? This helps engineers optimize the separation process while keeping operating costs low. As the length of the chain increases, however, the solubility of alcohols in water decreases; the molecules become more like hydrocarbons and less like water. A method as claimed in claim 1 or claim 2, in which the amine is 1 ,3-diaminopentane. Detailed usage of activity coefficients is outside the scope of this article as they are not well suited to simple calculations and are best left to computer simulation packages. Methyl Ethyl Ketone | C4H8O - PubChem The Alcohol Pharmacology Education Partnership is powered by WordPress at Duke WordPress Sites. The separation was effected by using a suitable chlorinated hydrocarbon as an extractive distillation. x 0000003698 00000 n Separation of azeotropic mixtures (ethanol and water) enhanced by deep 0000003010 00000 n A first thermometer 26 is adapted to read the temperature of the liquid contained in the flask 12, and a second thermometer 28 is adapted to read the temperature of the vapour in the tube 14. A STUDY OF THE REVERSING OF RELATIVE VOLATILITIES BY EXTRACTIVE DISTILLATION by An-I Yeh A thesis submitted in partial fulfillm ent of the requirements for the degree of Doctor of Philosophy in Chemical Engineering MONTANA STATE UNIVERSITY Bozeman, Montana April 1986 r APPROVAL of a thesis submitted by An-I Yeh Specifically, the concentration of furfural decreased from 1.25 g/L . Composition changes and relative volatility. 0000008321 00000 n i have to calculate relative voltility. As has been stated in US Patent 5,800,681 (Berg) extractive distillation is the method of separating close boiling compounds from each other by carrying out the distillation in a multiplate rectification column in the to the azeotropic mixture to alter the relative volatility of the key component without additional azeotrope formation (Perry et al., 1992; Black and Distler, 1972). Scientists commonly use the boiling point of a liquid as the measure of volatility. The outlet 18 has an electromagnetic closure mechanism 20. Usually the extractive distillation solvent is introduced a few plates from the top of the column to ensure that none of the extractive distillation solvent is carried over with the lowest boiling component. Generally, entrainer . For distilling such a mixture, the distillation column may be designed (for example) to produce: Such a distillation column is typically called a depropanizer. Breaking an azeotrope A common approach involves the use of molecular sieves. Relative volatility of a mixture changes with the mixture composition. [2], The values of Alcohols can be considered derivatives of water (H2O; also written as HOH). stripping, Distillation or related exchange processes in which liquids are contacted with gaseous media, e.g. I believe ethanol forms an azeotrope with water. qOniOQrD8 'twj[8Cap'{0l ivc t'M,S p` RejpC1GI{n$ Ethanol is a primary alcohol that is ethane in which one of the hydrogens is substituted by a hydroxy group. An ethanol/water liquid mixture with a molar ratio of 1.25:1 has a relative volatility of 1.71. Separation of ethanol and water from mixtures thereof by extractive Sand in water St Is Ice To Water Endothermic Or Exothermic . Hb```f``Id`e` @16LL v2W{>$/^qcrWgFQUYYWslwm1M?-h [vqysjzy ,.LJ@ - )[@Dar"`k% Pa`Y," AB`1Qk|a ,D!Ud2.`2n+=G0c/~a+ E f& 0 2v endstream endobj 106 0 obj 343 endobj 75 0 obj << /Type /Page /Parent 70 0 R /Resources 76 0 R /Contents [ 81 0 R 83 0 R 85 0 R 87 0 R 93 0 R 95 0 R 97 0 R 99 0 R ] /MediaBox [ 0 0 595 842 ] /CropBox [ 0 0 595 842 ] /Rotate 0 >> endobj 76 0 obj << /ProcSet [ /PDF /Text ] /Font << /TT2 78 0 R /TT4 89 0 R /TT6 91 0 R >> /ExtGState << /GS1 101 0 R >> /ColorSpace << /Cs6 77 0 R >> >> endobj 77 0 obj [ /ICCBased 100 0 R ] endobj 78 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 243 /Widths [ 250 0 0 0 0 833 778 0 333 333 500 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 0 564 0 0 921 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 722 611 0 0 0 0 0 0 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 333 444 444 0 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 760 0 400 0 0 0 0 0 0 0 0 0 310 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 444 0 0 0 0 0 0 0 444 0 0 0 278 0 0 0 0 0 500 ] /Encoding /WinAnsiEncoding /BaseFont /DPGODB+TimesNewRoman /FontDescriptor 79 0 R >> endobj 79 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -568 -307 2000 1007 ] /FontName /DPGODB+TimesNewRoman /ItalicAngle 0 /StemV 94 /XHeight 0 /FontFile2 102 0 R >> endobj 80 0 obj 568 endobj 81 0 obj << /Filter /FlateDecode /Length 80 0 R >> stream Separation of ethanol and water from mixtures thereof by extractive distillation. Basics of General, Organic, and Biological Chemistry (Ball et al. In what order does the acidity increase in water, ethanol and - Quora Scientists commonly use the boiling point of a liquid as the measure of volatility. Less hydrogen bonding is expected between molecules of a volatile liquid compared with other less volatile liquids. A method as claimed in claim 1 or claim 2, in which the amine is diaminobutane. The temperature of the liquid phase in the bulb flask 12 is continuously monitored by the thermometer 26, and the temperature of the vapour phase in the tube 14 is continuously monitored by the thermometer 28. Distillation 1, which is based on the relative volatility differences between components in a mixture, is one of the most important separation technologies.However, it is difficult to separate . The invention suggests a method of separation of ethanol and water by distilling a mixture of ethanol/water by way of an extractive distillation process in the presence of an extractive distillation solvent selected from the group consisting of an amine and a chlorinated hydrocarbon. The plot could also be made for volume percent in the liquid vs volume percent in the vapor and the equilibrium Figure 1. Volatility is found by calculating the annualized standard deviation of daily change in price. Azeotropic distillation using benzene or cyclohexane is commonly used to effect the separation. The separation was effected by using a suitable chlorinated hydrocarbon as an extractive distillation solvent. This free course, The science of alcohol, looks at the science behind the processes of brewing,. Its presence on each plate of the rectification column alters the relative volatility of the close boiling compounds in a direction to make the separation on each plate greater and thus require either fewer plates to effect the same separation or make possible a greater degree of separation with the same number of plates. Attractive forces between molecules are what holds materials together, and. 0000006284 00000 n It has a role as an antiseptic drug, a polar solvent, a neurotoxin, a central. Instant ice packs an Rheem Fury Gas Water Heaters . This simulation applies a DePriester chart, a set of nomograms, to find the vapor-liquid equilibrium ratio (the gas phase mole fraction divided by the liquid phase mole fraction, known as the K-value) for a series of hydrocarbons. H\SMs0WQb!Ydjc! The diagram shows mole percent ethanol in the liquid (X axis) vs mole percent ethanol in the vapor (Y axis). The relative volatility of binary liquid mixtures. {\displaystyle \alpha } Separation of acetic acid and ethanol from wastewater by - Springer Azeotrope separation of ethyl propionate and ethanol by extractive To the azeotropic mixture to. Relative volatility of ethanol (1) to water (2) at 101.3 kPa at different IL concentrations: , x 3 = 0; , x 3 = 0.05; , x 3 = 0.10; , x 3 = 0.15; solid lines, correlated using the NRTL model.. Explain why the boiling points of alcohols are higher than those of ethers and alkanes of similar molar masses. In order to carry out extractive distillation with high relative volatility, a new operating flowsheet is proposed including three columns: an extractive distillation column, s solvent recovery column, and a concentrator. In ethanol-rich mixtures containing 30-70 mol % DMF, the lowest relative volatility of ethanol to water is 1.3 and . Equilibrium data may be obtained by experiment, by thermodynamic calculation, or in published sources. The liquid and vapour molar fractions were determined to be as follows: This translates to a relative volatility of 2.4 for the system ethanol/water in the ternary system shown above, the ethanol being the distillate. The designer would designate the key components governing the separation design to be propane as the so-called light key (LK) and isobutane as the so-called heavy key (HK). 0000005353 00000 n (@B F)CpQC%+! 8]$2" "4>c;W;7HSAMS(|AC)UW]E[8UWE yA |j=4{? bottom product. With no . Relative volatility - YouTube An ethanol/water liquid mixture with a molar ratio of 4:1 has a relative volatility of 1.12. In this work, the relative volatility of ethanol and water at the azeotropic point was increased from. operating pressure is 1 atm. [15,16] which includes an entrainer to increase the relative volatility of the key components of the feed without forming a new azeotrope [17,18]. 2: Hydrogen Bonding between Methanol Molecules and Water Molecules. A further liquid phase sample conduit 24 leads into the tube 14. The liquid and vapor phases for a mixture of ethanol and water with an overall composition of 60 mole percent ethanol at 175 F and . Replacing a hydrogen atom from an alkane with an OH group allows the molecules to associate through hydrogen bonding (Figure \(\PageIndex{1}\)). Using Raoults law the liquid and vapour mole fractions can then be related to each other via the relative volatility: \displaystyle \alpha = \left(\frac {y_{a}}{1-y_{a}}\right) \left(\frac{1-x_{a}}{x_{a}}\right), \displaystyle y_{a} = \frac{\alpha x_{a}}{1+(\alpha-1)x_{a}}, \displaystyle x_{a} = \frac{ y_{a}}{\alpha+(1-\alpha)y_{a}}. K What is the relative volatility of ethanol? Consider the resources attached to support your work . Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. From yild research wich used, than liquid-vapor equilibrium date binary system ethanol-water direction azeotropic point at ethanol composition 0.98 mol fraction, A liquid with a low boiling point will begin to boil faster than liquids with higher boiling points. Methanol and ethanol form an ideal solution. In this work, the relative volatility of ethanol and water at the azeotropic point was increased from 1.00 to 4.70 with 0-51.0 mass % ChCl/urea (1:2, mol/mol), with ChCl/urea showing a remarkable entrainer performance in this separation. To the azeotropic mixture to. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. crystallisation, Separation; Purification; Stabilisation; Use of additives by change in the physical state, e.g. for stabilisation, Separation; Purification; Use of additives, e.g. Definition [ edit] For a liquid mixture of two components (called a binary mixture) at a given temperature and pressure, the relative volatility is defined as When their liquid concentrations are equal, more volatile components have higher vapor pressures than less volatile components. ethanol-water volatility, causing water to be removed as the top product and ethanol, mixed with solvent, to be withdrawn as the bottom product. Relative volatility - Typeset.io Also, the ethanol/water system is a typical industrial azeotropic mixture. #4 chemeng2014 Brand New Member Members 9 posts Posted 17 March 2019 - 06:22 PM Thanks all, very useful. K {\displaystyle \alpha } ethanol-water separation because of the low energy consump- . It is commonly used in the design of absorption and separation processes such as distillation as it allows the difficulty of separating components to be quickly assessed. Azeotropic distillation would be an attractive method of effecting the separation of ethanol from isopropanol if agents can be found that (1) will create a large apparent relative volatility between ethanol and isopropanol and (2) are easy to recover from ethanol. Alcohol is more volatile than water, because its vapour pressure is 2.5 times greater than water. The values in the table below except as noted have been extracted from online and hardbound compilations . Check to see if the data. In the drawing there is shown a schematic view of an experimental apparatus for testing an extractive distillation solvent for separating ethanol and water from mixtures thereof in accordance with the invention. 0000013253 00000 n While in nonideal systems, relative volatility does not remain constant. Alcohol plays a considerable part in the daily lives of humanity and has done for thousands of years. PDF Chapter 18 Ethanol distillation: the fundamentals - Queen's U Ethanol boils at 78.4 C. and isopropanol at 82.4 C. The relative volatility between these two is 1.14 which makes it very difficult to separate them by conventional rectification. Relative volatility is a comparative measure of the vapour pressures of components in a liquid mixture. How long has Coney Island in Fort Wayne Open? 0000056370 00000 n The mixture is boiled and condensed for several hours, normally 5 to 6 hours. In that context, a lighter component means a component with a lower boiling point (or a higher vapor pressure) and a heavier component means a component with a higher boiling point (or a lower vapor pressure). Volatility of b = pb / xb. To the azeotropic mixture to. for stabilisation by physical treatment by distillation, Separation; Purification; Use of additives, e.g. For the ethyl acetate/water mixture, the membranes showed a very high selectivity to water (> 300) and the permeate was 50--100 times enriched in water relative to the feed. Temperature o C for ethanol: 48.4: 62.5: 78.4: 97.5: Temperature o C for methanol: 34.8: 49.9: 64.7: 84: What value of relative volatility will . ABV dependent volatility of fusel oils - Home Distiller endstream endobj startxref This page titled 14.3: Physical Properties of Alcohols is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Anonymous via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. H|Tr0}+:* I@ _R$d@ q`o7i;1+Vg9;8t(Sx>M~:a#kgC The liquid and vapour phases were analysed. For those without a chemistry background, at that point (~95% water), water and ethanol would evaporate at the same rate, thus the vapor you collect would have 5% ethanol still. All of these methods utilize two distillation columns. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . {\displaystyle K} Relative volatilities are used in the design of all types of distillation processes as well as other separation or absorption processes that involve the contacting of vapor and liquid phases in a series of equilibrium stages. PDF Lecture 5 Single equilibrium stages (1) - CHERIC Once enough energy is supplied to break apart the bonds between molecules, the molecules are free to expand and escape the liquid surface in the form of a gas. [OB\(.djSs}. -|H#Ep4p?.=5[xcJXkRn][ceeP|Mz\1+X3oUu ' 0 endstream endobj 84 0 obj 745 endobj 85 0 obj << /Filter /FlateDecode /Length 84 0 R >> stream [11] R . Where p is the partial pressure of the component and x is the liquid mole fraction. A. N. Campbell, E. M. Kartzaiark, and J. T. Ri. Gieskes Composition changes and relative volatility. Whether or not a liquid will vaporize depends upon the chemical properties of the liquid. The process of evaporation and condensation is repeated until equilibrium is reached between the vapour and liquid phases. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Separation of Acetic Acid from Water Using Ethyl Acetate Entrainer 2-TTh9 ~VUG%B3^@RtU. The extractive distillation procedure is as follows: A liquid mixture is prepared consisting of ethanol, water and an extractive distillation solvent. 2002; Iwakabe et al. Ethyl acetate forms a positive azeotrope with water that boils at 70.4 C (with azeotropic composition 35.9% mole water and 64.1% mole ethyl acetate). The higher the relative volatility, the easier the separation would be. The liquid and vapour molar fractions were determined to be as follows: Table 2: This translates to a relative volatility of 1.33 for the system water/ethanol in the ternary system shown above, the water being the distillate. The system water-chloroform shows a large miscibility gap at 25' C, the limits being 0.8 ~t7~ water and 99.4 wt% water according to Brancker, . Separation of azeotropic mixtures (ethanol and water) enhanced by deep eutectic solvents - ScienceDirect Fluid Phase Equilibria Volume 448, 25 September 2017, Pages 128-134 Separation of azeotropic mixtures (ethanol and water) enhanced by deep eutectic solvents Yong Peng a b , Xiuyang Lu c , Baojian Liu a , Ju Zhu a Add to Mendeley Solvent Polarity Table. Chemistry of water-ethanol mixture - HubPages Separation of ethanol, isopropanol and water mixtures by azeotropic BRIEF DESCRIPTION OF DRAWING. \displaystyle y_{i} = \frac{\gamma_{i}p_{i}x_{i}}{P}. 0000001121 00000 n What size tire is on a 2011 Toyota Corolla. 1. ixw}j/YJ8[/)fKrJHPy0*n)l)TtY{j.&_q^2 &r.RNFfh@r#I,ax?pn^u6nn8ZJRR)-C t6'V@pV:I8+-5S By convention, relative volatility is usually denoted as Volatile liquids, including ethanol, vaporize with relative ease. remaining water. 2012; Wang al. Relative Volatility Of Ethanol And Water. x (ethanol)=0.95. The hydrogen atom of the hydroxyl group (OH) in ethanol increases the potential for hydrogen bonding between neighboring ethanol molecules. Compute vapor-liquid equilibrium data and prepare plots of x-y and T-x-y at 1 atm pressure. The OH bond is fairly strong and will not dissociate , to give an acid H3O+ ion in water. The calculator below can be used to calculate ethanol dynamic or kinematic viscosity at given temperatures and atmospheric pressure. A1, Designated state(s): Volatile liquids have low boiling points. That means that processframework, simplifiedprocess package, involves processaims, parts heatexchange equipments pumpsrelative . The separation was effected by using a suitable amine as an extractive distillation solvent. is a unitless quantity. Density (25C) 787.0 kg/m3. The boiling point of 78.5C for ethanol is significantly higher compared with -24.8C for methoxymethane. It is commonly used in the design of absorption and separation processes such as distillation as it allows the difficulty of separating components to be quickly assessed. stream 218 0 obj <>/Filter/FlateDecode/ID[<50D74B322C62339F236D4C8C5662F0B0>]/Index[204 30]/Info 203 0 R/Length 84/Prev 992574/Root 205 0 R/Size 234/Type/XRef/W[1 3 1]>>stream Where p is the partial pressure of the component and x is the liquid mole fraction. What is the geometric average relative volatility of ethanol-water I am designing a distillation column to seperate ethanol and water up to azeotropic composition. Kind code of ref document: The separation of ethanol and water is complicated due to the existence of an azeotrope. for stabilisation by physical treatment, Separation; Purification; Use of additives, e.g. <> I am designing a distillation column to seperate ethanol and water up to azeotropic composition. 2a indicate that squared relative diameter (d/d 0) 2 of water droplets decreases linearly with time at all values of relative air humidity. The relative volatility of ethanol-water decreases with solvent present at low ethanol concentrations. The relative volatility of ethanol-water decreases with solvent present at low ethanol concentrations. Table 1 shows the relative volatility required-to obtain 99% purity. The main finding is that the addition of DMF breaks the ethanol/water azeotrope. Relative Volatility Of A Binary Mixture - Student The data on ethanol-water vapor-liquid equilibrium in the presence of cellulase enzyme, nutrients, yeast, and rice straw indicated a substantial increase in ethanol concentration in vapor phase at reduced pressures. K PDF Starches and Sugars Future Demand for Ethanol and Adhesives Depend on The calculator below can be used to calculate ethanol dynamic or kinematic viscosity at given temperatures and atmospheric pressure. Relative Volatility Calculation - Cheresources.com Community From base legs 47.0 inches. 0000006061 00000 n The experimental data presented in Fig. Separation of ethanol mixtures by extractive distillation 3 0 obj The novel effective and stable distillation series only changed the streams of the water and butanol columns' distillates. To the azeotropic mixture to. [$F #QXf,?B*rbWLWpW`F(:x*Ndv$e6Wecx:_.8[pZ&iJg y6: Ethyl formate is much more volatile than the other two. In addition to the Thermodynamics Research Center (TRC) data available from this site, much more physical and chemical property data is available from the following TRC products: Volatility of a Liquid - The Alcohol Pharmacology Education Partnership endobj y Separation of ethanol from isopropanol by azeotropic distillation / Reviewthe properties of different chemical bonds. Alkanes with one to four carbon atoms are gases at room temperature. Ethylene glycol has been proposed in the literature as an extractive distillation solvent for the system ethanol/water. Eventually, vaporization and condensation reach a state of equilibrium-no particles are lost, instead the gas phase is constantly being recycled into the liquid phase (think about a simmering pot of water with a lid on). When a binary mixture is distilled, complete separation of the two components is rarely achieved. )kq7LF)uE[Yl0G;=7B;(M]iumb@gM_?-\v-:(WwObe;ZD\Llep\J-JN,'}gj$bn-#w8v Kd nKGOhsD\+h/TL"69z)+#g3a\FLFF*%p$Dh*5k]]`^hRxyT^,RN;$$Ybr}2Zv.T^1}[ endstream endobj 82 0 obj 712 endobj 83 0 obj << /Filter /FlateDecode /Length 82 0 R >> stream