The floating egg problem

Transcription

1 The floating egg problem ----Can you make an egg float? Background: For many years soap was made at home from a variety of recipes. Animal fat, usually from cattle (also called tallow) was cooked with a lye solution. Lye, though it was mostly simple sodium hydroxide, could not be made from purified chemicals, as we do now. Instead, the solution was obtained from ashes and water. The ashes were treated with hot water, and then the mixture was filtered to obtain a solution. But before this could be used in soap making, one had to check the concentration of the lye solution. One simple test was to try to "just float" a raw egg in the solution. If the egg sank, the concentration of the lye in the solution was too low. The density of a solution affects whether an object floats in that solution. If the egg floated too high, the concentration of the solution was too great, and water was added before adding the fat. To just float in this case means to make the top of the egg just touch the top of the solution, without any significant amount of the egg protruding above the surface of the solution. Because lye is caustic and corrosive, sodium chloride will be substituted in this lab. In this investigation, you will practice with volumetric glassware to improve your technique and to solve an important historical question in practical chemistry by answering "What is the density of an egg?" Firstly, a series of salt solutions are prepared by a variety of volumetric glasses to determine the concentration range which an egg can float. Then, prepare a salt solution with exact concentration in which an egg just floats. You will obtain mass and volume measurements of this solution using a balance to measure the mass and volumetric glasses to measure the volume. The values that you obtain for the mass and volume will be used to calculate the density of the salt solution and, by extension, the density of the egg itself. Hydrometer is also used to measurement the density of this solution. You will compare the density of a fresh egg with that of an egg that is past its prime. Safety note: Sodium chloride solution is not harmful unless it gets into the eyes. If this occurs, flush the eyes with large amount of water for 15 min. All solution may be poured down the drain with water after use. Note: Be sure to record all measurements using the numbers of significant figures allowed by that instrument. 1

2 Purpose: Practice skills of measuring masses on balance, measuring volumes with graduated cylinder, volumetric flask and pipets, and making solutions; To investigate the error associated with the measurements of volume in the chemistry lab Consider the conceptions of accuracy, precision, and data analysis To use significant figures correctly Material available: electric Balances; beaker (50 ml, 100 ml); pipettes(10 ml, 25mL, 50mL) ; pipet bulb; graduated cylinders (10 ml, 50mL); Volumetric flasks(50 ml); Deionized water; Eggs ; Sodium chloride (salt) 2

3 Pre-lab Questions 1. Why is density a physical property useful for identifying an unknown substance? 2. As the density of a given liquid increases, will the hydrometer used to determine it float higher or lower in the liquid? Explain. 3. If a hydrometer touches bottom in a liquid, is its range too high or low for the liquid? Why? 4. In what way dose each of the following affect the calculated density or the precision of the calculated density: (a) the type of the volume measuring device used: 10 ml graduated cylinder, 50 ml graduated cylinder, 100 ml beaker, or pipet? (b) the degree of freshness of the raw egg? 5. A student, who performed this experiment, consistently viewed the meniscus of the liquid from a high angle (not at eye level) when reading the graduated cylinder. Explain how this error would affect both the accuracy and precision of the density result that he obtained when using this device. 6. Determine the number of significant digit of figures below: Calculate these equations using the appropriate number of significant figures g g = 21,500 g 2 58 g = 3

4 Related reading 1. Egg component: To determine the density of an egg, we need to described the components of an egg. It is these components, after all, that give an egg its mass and volume. According to the American Egg Board at IncredibleEgg.org, the main parts of an egg are: * Shell, which is mostly calcium carbonate and makes up 9 to 12 percent of the total weight of the egg (and which is actually very porous so that air can pass through) * Yolk (the yellow part consisting of fats, proteins, minerals and vitamins), which makes up about 34 percent of the liquid weight of the egg * Albumen (the egg white consisting of proteins, among other things), which makes up about 66 percent of the liquid weight of the egg * Air cell, which is a pocket of air found at the large end of the egg There can be some variation of these parts. 2. Density and density measurement: Density is a physical property of a substance that can be determined by scientific experiment. You might have learned that density is mass divided by volume, which means that if you can measure both the mass and the volume of an object, you can calculate its density. A substance will always have the same density no matter the size of the sample, so that density can be used to help identify a substance. Since an egg is an object that has a mass and a volume, you can calculate its density. The mass of the sample can be easily be measured with balance. While the measurement of the volume will be more complicated. The volume of an object can be measured in different ways. One way is to measure length with a ruler, and calculate the volume mathematically. This is easy to do if the shape of an object is something like a cube or a sphere. For objects that have irregular shapes, a common method is to use the water displacement method. Measure the volume of a certain amount of water (say, for example, 70 ml of water), then place the object into the water and see how much water it displaces (if the new volume is 100 ml, then 30 ml of water were displaced and that is the volume of the object). For smaller objects, volume is typically measured in milliliters or cubic centimeters. The hydrometer can measure the density of the liquid directly. An object that is less dense than a liquid will float in that liquid density to a depth such that the mass of the object submerged equals the mass of the of the liquid displaced (Archimedes' Principle). A hydrometer is a tube of constant mass that has been calibrated to measure density by floating 4

5 the hydrometer in liquids of known densities and recording on a scale the fraction of the hydrometer submerged. Any hydrometer can be used over a limited range of densities because the hydrometer must float in the liquid being studied and the hydrometer level must be sufficiently submerged to obtain an on scale reading. Hydrometers may be calibrated in g/ml or some other unit of density. Figure above show how to read when using hydrometers. 3. Precision and Accuracy: Chemists use special volumetric glassware in the chemistry laboratory (rather than the ordinary beakers and flasks) when they need high-precision measurements of the volumes of liquids. Understanding the proper use and limitations of such glassware is important in achieving reliable results. Experimental technique and the inherent accuracy of the glassware both affect experimental results. One of your personal goals for this course is to develop sound experimental techniques. In this experiment you will practice using volumetric glassware and balance to improve your technique and to solve an important historical problem in practical chemistry. In any quantitative operation, one must always be concerned with both the precision and accuracy of the measurements. The precision is determined by how closely two or more measurements of the same quantity agree with each other. Random errors, unpredictable variations in measurements that result from fluctuations such as mechanical vibrations or differences in reading scales, are reflected in the precision of the data. The best way to evaluate the overall precision of an experiment is to repeat the entire experiment several times, varying the amounts of the substances used, but otherwise performing each operation the same way, and then to check the reproducibility of the data. The accuracy of a measurement refers to its degree of correspondence with a true or known value. Systematic errors, which result from such things as defective instrumentation or faulty lab technique, lead to inaccurate measurements. High precision might seem to imply high accuracy in a result, but this is not necessarily the case. If an instrument is improperly calibrated, for example, it may consistently give an inaccurate result with a high precision. Precision is not the same as accuracy. Every measuring device has a degree of precision, or uncertainty, associated with it. The general rule in using such a device is to estimate between the smallest calibrations of the measuring scale in order to obtain a reading with one more digit. The pieces of equipment you will use in the experiment have the following uncertainties: top-loading electric balance: ±0.01 g 10 ml graduated cylinder: ±0.02 ml 50 ml graduated cylinder: ±0.1 ml 25 ml volumetric pipet: ±0.01 ml 50 ml buret: ±0.01 ml 5

6 4. Significant figures: The sensitivity of the instrument and the size of the sample govern the number of significant figures that can be reported. The significant figures in a number consist of all the digits known with certainty to be correct, plus one estimated digit. In other words, the last figure on the right should be the only approximate figure in the number. Always be sure your measurements include the last estimated digit, even if it is zero. It is important that a number which results from a calculation that incorporates more than one type of measurement does not claim a higher precision than was possible with the least precise measurement. In other words, the number of significant figures contained in the result cannot exceed the number of significant figures that are included in the least precise measurement. Keep this in mind when you read the ten-digit display on your calculator! Using the proper number of significant figures is a convenient way to estimate the uncertainty of a calculated result. The uncertainty will always be contained in the last digit of the result. The following are guidelines for using significant figures. 1. All nonzero digits are significant, and zeroes between nonzero digits are significant. Zeroes to the left of the first nonzero digit are not significant. 2. Trailing zeroes after a decimal point are always significant. 3. Trailing zeroes before an implied decimal point are ambiguous and should be avoided by using scientific notation. 4. In addition and subtraction calculations, the result carries the same number of decimal places as the quantity with the fewest decimal places. 5. In multiplication and division calculations, the result carries the same number of significant figures as the factor with the fewest number of significant figures. 6. When rounding to the correct number of significant figures, round down if the last (or leftmost) digit dropped is four or less; round up if the last (or leftmost) digit is five or more. 7. To avoid rounding errors in multistep calculations, round only the final answer do not round intermediate steps. If you write down intermediate steps, keep track of significant figures by underlining the least significant digit. Note: When a problem involves both addition or subtraction and multiplication or division, the answer may have a different number of significant figures than the initial quantities. 5. Preparation of general-purpose solution: Solutions are usually prepared with respect to their molar concentrations (e.g. mol. L -1, mol. dm -3, or mol. m -3 ) or mass concentration (e.g. g. L -1, or kg. m -3 ); both can be regarded as an amount per unit volume, in accordance with the relationship: amount concentration = volume In general there are two levels of accuracy required for the preparation of solution: General-purpose solutions and Analytical solutions. The General-purpose solutions is the solution for chemicals used in qualitative and preparation procedure when the concentration of the chemical need not to be known more than one or two decimal places. For example: 1) solution used in extraction and washing procedures, e.g. hydrochloric acid (0.1 mol. L -1 ), 6

7 sodium carbonate (5% w/v) 2) solutions for chemicals used in preparative experiments where the techniques of purification - distillation, recrystallization, filtration, etc - introduce intrinsic losses of substance that make accuracy to any greater level meaningless. Box below shows the steps involved in making up general-purpose aqueous solution. After weighting out the required mass or volume of chemical use distilled or deionized water or other solvent to make up solutions and stir with a clean glass rod or magnetic stirrers bar until all the chemical is dissolved. 'Obstinate' solutions may require heating, but only do this if you know that the chemical will not be damaged at the temperature used. Use a stirrer-heater to keep the solution mixed as you heat it. Allow the solution to cool to room temperature before you finalize its volume. 7

8 6. Balances and weighing: Electronic single-pan balances with digital readouts are now favored over mechanical types and are common in most laboratories, There are essentially two types of balance: 1) General purpose balances which weigh to the nearest 0.01 g with a capacity of about 200 g, Chemicals may be dispensed for weighing, into a suitable weighing container, directly onto these balances; 2) Analytical four-figure balances for quantitative work, which weigh to the nearest g (0.1 mg) and have a maximum capacity of about 200 g, Chemicals must not be transferred onto the balance at any time and analytical balances usually be used for weighing by difference. Both types are illustrated in Figure below and you should familiarize yourself with their operation before use. Weighing - never weigh anything directly onto a balance's pan: you may contaminate it for others. Use an appropriate weighing container such as a weighing boat, sample tube, weighing paper, conical flask, beaker. 'Weighing paper' - It is common practice to put a piece of paper onto the pan of general-purpose balances, The mass of the paper is then 'tared off before the weighing container is placed on the balance pan. The paper protects the balance pan from corrosion by spillages and also allows you to discard easily any material spilt without affecting the weighing. General-purpose balances The most useful feature of this type of balance is the electronic zero facility (self-taring), which means the mass of the weighing container can be subtracted automatically before weighing chemicals, To operate a standard self-taring balance: 1. Check that it is level, using the adjustable feet to centre the bubble in the spirit level (usually at the back of the machine). For relatively accurate work or when using in a fume cupboard, make sure that the draught shield is in place. 2. Ensure that the balance is switched on: the display should be lit. 3. Place an empty weighing container centrally on the balance pan and allow the reading to stabilize, If the object is larger than the pan, take care that no part rests on the body of the balance or the draught shield as this will invalidate the reading. Press the tare bar to bring the reading to zero. 4. Place the chemical or object carefully in the weighing vessel: (a) Solid chemicals should be dispensed with a suitably sized clean spatula. (b) Non-volatile liquids should be dispensed using a Pasteur pipette but take the weighing container off the balance pan before dispensing; then reweigh the liquid plus container. Repeat until the desired weight is obtained. 5. Allow the reading to stabilize and make a note of the reading. 6. If you have added excess chemical. take great care when removing it. Remove the container from the balance, remove the solid (with a spatula) or liquid (with a Pasteur pipette) and 8

9 reweigh. 7. If you need to clean any deposit accidentally left on or around the balance, switch off the balance. Take care not to exceed the limits for the balance: while most have devices to protect against overloading, you may damage the mechanism. 7. working with liquid:! Reading any volumetric scale - make sure your eye is level with the bottom of the liquid's meniscus and take the reading from this point. Measuring and dispensing liquids The equipment you should choose to measure out liquids depends upon the volume to be dispensed, the accuracy required and the number of times the job must be repeated. Table1 Criteria for choosing a method for measuring out a liquid Usefulness for repetitive Method Best volume range Accuracy measurement Pasteur pipette 1-5 Low Convenient Conical Very Convenient Measuring Medium Convenient Volumetric High Convenient Burette 1-100mL High Convenient Glass 1-100mL High Convenient Mechanical High* Convenient Syringe 0,5-20 Medium** Convenient Microsyringe High Convenient Any(depends on weighing Very Inconvenient accuracy of balance) *If calibrated correctly and used properly; **Accuracy depends on width of barrel: large volumes less accurate; Conical flasks, beakers, measuring cylinders and volumetric flasks measure the volume of liquid contained in them, while burettes, pipettes, pipettors, syringes and micro syringes mostly measure the volume delivered from them: think about the requirements of the experiment. Certain liquids may cause problems:. High-viscosity liquids are difficult to dispense: allow time for the liquid to transfer.. Organic solvents may evaporate rapidly, making measurements inac-curate: work quickly; seal containers quickly.. Solutions prone to frothing (e.g. surfactant solutions) are difficult to measure and dispense: avoid forming bubbles; do not transfer quickly. Volumetric glassware is designed for two quite different purposes. To deliver (TD) an accurate volume of liquid. To contain (TC) an accurate volume of liquid. A container meant to contain an accurately known volume could of course be used to deliver the liquid to another vessel. However, the amount actually delivered would never exactly be equal to the amount originally in the container. Some liquid would inevitably remain behind, clinging to the interior walls. Some liquid also remains behind on the walls 9

10 of a piece of glassware that is TD designed, but the calibration of the TD glassware takes this into account. Pasteur pipettes Hold correctly during use - keep the pipette vertical, with the middle finger gripping the barrel to support the pipette while the thumb and index finger provide controlled pressure on the bulb, and squeeze gently to provide individual drops. To prevent liquid being sucked into the bulb and hence cross-contamination:. Ensure that the capacity of the bulb does not exceed that of the barrel.. Do not remove the tip of the pipette from the liquid while drawing up the liquid; the inrush of air may splash the liquid into the bulb, This is particularly true when you lose patience trying to draw up viscous liquids,. Do not lie the pipette on its side during use. Conversely, if volatile liquids such as dichloromethane (DCM), ethanol, propanone (acetone) or diethylether (ether), for example, are to be dispensed, the warmth of the glass pipette will cause the liquid to squirt from the pipette without any pressure on the bulb. To prevent this, suck up the liquid several times into the pipette so as to cool the glass and then dispense as normal. Conical flasks and beakers These have approximate graduations and should only be used for measuring volumes of solutions/liquids where accuracy is unimportant. Measuring cylinders and volumetric flasks These must be used on a level surface (the laboratory bench) so that the scale is horizontal; you should first fill with solution until just below the desired mark, then fill slowly (e,g, using a Pasteur pipette) until the bottom of the meniscus is level with the mark, Remember to allow time for the solution to run down the walls of the vessel and to bend down so that your eyes are level with the graduation mark(s) and the meniscus. Burettes These must be mounted vertically in a clamp - don't over-tighten the clamp - or in a burette holder, on a stand, First ensure that the tap is closed and, using a funnel, add a little of the solution to be dispensed, rinse the burette and discard the washings through the tap: this is vital in titrations where a little water in the burette will alter the concentration of the solution, Refill the burette with solution, open the tap and allow the liquid to fill the barrel below the tap, then take a meniscus reading, 10

11 noting the value in your notebook, Dispense the solution via the tap and measure the new meniscus reading, The volume dispensed is the difference between the two readings. Pipettes There are various designs, including graduated and bulb (volumetric) pipettes, Take care to look at the volume scale before use: some graduated pipettes empty from full volume to zero, others from zero to full volume; some scales refer to the shoulder of the tip, others to the tip by gravity, Never blowout volumetric (bulb) pipettes, just touch the tip against the inside wall of the vessel. Rinse out pipettes with a little of the solution to be delivered before commencing the accurate measurement. To prevent cross-contamination, never draw the solution into the pipette filler. KEY POINT For safety reasons, it is no longer permissible to mouth pipette - various aids (pipette fillers) are available, such as the rubber-bulb and Pi-Pump'". Pipettors (autopipettors) There are two basic types: 1. Air displacement pipettors. For routine work with dilute aqueous solutions, One of the most widely used is the Gilson Pipetman". 2. Positive displacement pipettors, For non-standard applications, including dispensing viscous, dense or volatile liquids where an air displacement pipettors might create aerosols leading to errors. Air displacement and positive displacement pipettors may be: Fixed volume: capable of delivering a single factory-set volume, Adjustable: where the volume delivered is determined by the operator across a particular range of values, Pre-set: movable between a limited number of values. Multichannel: able to deliver several replicate volumes at the same time. Whichever type of these routine but expensive devices you use, you must ensure that you understand the operating principles of the volume scale and the method for changing the volume delivered - some pipettors are easily misread. A pipettor must be fitted with the correct disposable tip before use and each manufacturer produces different tips to fit particular models, Specialized tips are available for particular applications. If you accidentally draw liquid into the barrel, seek assistance from your demonstrator/ supervisor since the barrel will need to be cleaned before further use (to prevent crosscontamination) and unskilled dismantling of the device will cause irreparable damage. Using syringes - take great care when handling syringe needles. They are very sharp and may be contaminated by Chemicals. 11

12 Syringes Syringes should be used by placing the tip of the needle into the solution and slowly drawing the plunger up to the required point on the scale. Check the barrel to make sure no air bubbles have been drawn up, and expel the solution slowly, touching the needle tip on the side of the vessel to remove any adhering solution, If there is air in the barrel fill past the mark, invert the syringe and push the plunger to the mark so that the air and a little of the solution are expelled into a waste collection vessel. Then dispense the solution, The use of syringes for dispensing air-sensitive reagents is described latterly. Microsyringes should always be cleaned before and after use by repeatedly drawing up and expelling pure solvent. The dead space in the needle can occupy up to 4% of the nominal syringe volume, Some microsyringes have a fine wire attached to the plunger, which fills the dead space. Never pull the plunger out of the barrel. Balances These can be used to weigh accurately how much liquid you have dispensed. Convert mass to volume using the equation: Mass/density = volume e,g, a liquid (9.0g) of density (L2gmL- 1 ) = 7.5mL. Densities of common solvents and common chemicals can be found in Lide (2000), You will also need to know the liquid's temperature, since density is temperature dependent. 12