The reciprocal of the density of a substance is called its , a representation commonly used in . Density is an in that increasing the amount of a substance does not increase its density; rather it increases its mass.
Changes of density
In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures.
The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10−6 bar−1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10−5 K−1. This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires a temperature increase on the order of thousands of degrees Celsius.
In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is
CHAPTER TWO
Theory:
Archimedes’ Principle states that any object completely or partially submerged in a fluid is
buoyed up by a force with magnitude equal to the weight of the weight of the fluid displaced by the
object:
B = ρfluid Vfluid g ,
where ρfluid is the density of the fluid and Vfluid is the volume of the displaced fluid. In this lab, all the forces and weights are measured in the unit of grams using the triple beam balance, then the above equation becomes:
B = ρfluid Vfluid .
When measuring the weight of an object completely submerged in a fluid,the volume of the displaced fluid is equal to the volume of the object, and the reading on the balance ( Win-fluid), the buoyant force, and its weight in air (Win-air) should satisfy the following equation:
B = Win-air - Win-fluid = ρfluid Vobject .
Thus, the volume of the object can be determined as:
Vobject = (Win-air - Win-fluid)/ ρfluid ,
and the density and the specific gravity of the object are, respectively:
ρobject = Win-air / Vobject = ρfluid Win-air / (Win-air - Win-fluid),
s.g. = ρobject / ρwater .
Mathematically, density is defined as mass divided by volume:
where ρ is the density, m is the mass, and V is the volume. From this equation, mass density must have units of a unit of mass per unit of volume. As there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use.
The SI unit of kilogram per cubic metre (kg/m³) and the cgs unit of gram per cubic centimetre (g/cm³) are probably the most common used units for density. (The cubic centimeter can be alternately called a millilitre or a cc.) 1000kg/m³ equals one g/cm³. In industry, other larger or smaller units of mass and or volume are often more practical and US customary units may be used. See below for a list of some of the most common units of density. Further, density may be expressed in terms of weight density (the weight of the material per unit volume) or as a ratio of the density with the density of a common material such as air or water.
Measurement of density
The density at any point of a homogeneous object equals its total mass divided by its total volume. The mass is normally measured with an appropriate scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. For determining the density of a liquid or a gas, a hydrometer or dasymeter may be used, respectively. Similarly, hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object.
If the body is not homogeneous, then the density is a function of the position. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: ρ(r)= dm/dV, where dV is an elementary volume at position r. The mass of the body then can be expressed as
Density of solutions
The density of a solution is the sum of mass (massic) concentrations of the components of that solution.
Mass (massic) concentration of a given component ρi in a solution can be called partial density of that component.
Expressed as a function of the densities of pure components of the mixture and their volume participation, it reads:
Density of composite material
In the United States, ASTM specification D792-00[11] describes the steps to calculate the density of a composite material.
where:
ρ is the density of the composite material, in g/cm3
and
Wa is the weight of the specimen when hung in the air
Ww is the weight of the partly immersed wire holding the specimen
Wbρ is the weight of the specimen when immersed fully in distilled water, along with the partly immersed wire holding the specimen
is the density in g/cm3 of the distilled water at testing temperature (for example 0.9975 g/cm3 at 23 °C)
common units
The SI unit for density is:
kilograms per cubic metre (kg/m³)
Litres and metric tons are not part of the SI, but are acceptable for use with it, leading to the following units:
kilograms per litre (kg/L)
grams per millilitre (g/mL)
metric tons per cubic metre (t/m³)
Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m³). Liquid water has a density of about 1 kg/dm³, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm³.
kilograms per cubic decimetre (kg/dm³)
grams per cubic centimetre (g/cc, gm/cc or g/cm³)
megagrams per cubic metre (Mg/m³)
Specific gravity is the ratio of the density (mass of a unit volume) of a substance to the density (mass of the same unit volume) of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance is nearly always water for liquids or air for gases. Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always 1 atm equal to 101.325 kPa. Temperatures for both sample and reference vary from industry to industry. In British brewing practice the specific gravity as specified above is multiplied by 1000.[1] Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, hydrocarbons, sugar solutions (syrups, juices, honeys, brewers wort, must etc.) and acids.
Specific gravity, as it is the ratio of densities, is a dimensionless quantity. Specific gravity varies with temperature; reference and sample must be compared at the same temperature, or corrected to a standard reference temperature. Substances with a specific gravity of 1 are neutrally buoyant in water, those with SG greater than one are denser than water, and so (ignoring surface tension effects) will sink in it, and those with an SG of less than one are less dense than water, and so will float. In scientific work the relationship of mass to volume is usually expressed directly in terms of the density (mass per unit volume) of the substance under study. It is in industry where specific gravity finds wide application, often for historical reasons.
True specific gravity, can be expressed mathematically as:
where is the density of the sample and is the density of water.
The apparent specific gravity is simply the ratio of the weights of equal volumes of sample and water in air:
where represents the weight of sample and the weight of water, both measured in air.
It can be shown that true specific gravity can be computed from different properties:
where is the local acceleration due to gravity, is the volume of the sample and of water (the same for both), is the density of the sample, is the density of water and represents a weight obtained in vacuum.
API Gravity
- API gravity represents a dimensionless property similar to specific gravity. The measure itself derives from specific gravity (see Reference 3): API = (141.5 / SG) - 131.5. Note that because specific gravity appears in the denominator of the equation, API gravity and specific gravity exhibit an inverse relationship: A liquid with high specific gravity will exhibit low API gravity and vice-versa
CHAPTER THREE
EXPERIMENTATION
The experiment carried under room temperature at 34oC, was aimed at determining the density/specific gravity of five varying samples (PMS, DPK, Crude Oil, PKO, and Soap Solution) using two different measuring apparatus; a weighing balance and a measuring cylinder applying the Archimedes principle of floatation to obtain values in ml and then subsequently in grams.
PROCEDURE
- The weights (sliders) on the beam of the weighing balance apparatus was set to zero before measurements. A dry empty pycometer was then placed on the scale pan to obtain its weight for which results were recorded after careful observations of the beam’s calibrations in grams.
-
The weight was determined by locking three different sets of weights (sliders) on their respective number-calibrations (in grams), for which the beam was balanced. The values which these weights rested on at beam-balance were then added up to give the mass of the empty pycometer.
- The weights on the beam were set back to zero and the pycometer lifted off the pan to restart the process but this time to measure the mass of the pycometer filled with a sample; DPK in this case.
- 50 milliliters of DPK was measured with a cylinder and poured into the pycometer, then corked with a small glass-like capillary tube. A small volume of the liquid sample (DPK), which was spilled as a result of the pressure from corking the pycometer, was noted as negligible. The DPK-filled pycometer; a combined weight of both the pycometer and the DPK fluid, was then placed on the pan scale for the second time to acquire readings in grams.
-
The same method for measurement, as explained in the earlier paragraphs, was used to accurately determine the mass of the DPK-filled pycometer and then subsequently recorded.
The above elaborated procedures for the determination of were further carried out for three more samples; PMS, Crude Oil, and PKO to determine their masses. First, the masses of the empty pycometers were measured, followed by the combined masses of the pycometers and samples and then subsequently, the individual masses of the fluid samples were calculated.
In the supplementary method involving the application of the Archimedes principle of floatation –
-
The measuring cylinder was filled with water and the initial volume was observed and recorded. A piece of string was then tied around a dry empty pycometer and attached to the retort stand so that it dropped directly into the measuring cylinder enough to submerge itself in the containing water so that the volume increased. The new volume of water was then noted and recorded in milliliters. The difference between the initial volumes of the water before the introduction of the empty pycometer and after the submergence of the pycometer was also calculated and recorded in grams as the mass of the empty pycometer.
- The pycometer was then gradually pulled out of the cylinder and an initial volume was noted once more. The process mentioned above was repeated but this time with the pycometer filled with 50 milliliters of a liquid sample (DPK).
-
The DPK-filled pycometer was submerged in the containing volume of water which consequently effected a change in the initial volume. The new volume was recorded in milliliters and the difference in the initial and new volume was calculated and subsequently noted in grams as the combined mass of the pycometer and liquid sample.
Results
N.B : volume used for all sample is 50cm3
For weighing balance
Discussion of result
From the result I obtained, I observed that DPK is the densest of the five samples, followed by PMS, crude oil, PKO and soap solution respectively. Density is dependent on the mass and volume of the substance which are in turn affected by temperature and pressure. But since the experiment was done using liquids it is imperative to note that the effect of pressure on the density of a liquid is negligible. The effect of an increase in temperature of a liquid is a decrease in density.
Also values obtained from the weighing balance method and the direct method differed significantly – from calculations the average percentage difference between the results obtained from both methods was found to be 9.7 %
CHAPTER FOUR
Conclusion
At the end of the experiment, it was found that the soap solution had the highest density. Also, values obtained from the weighing balance method and the direct method differed significantly – from calculations the average percentage difference between the results obtained from both methods was found to be 9.7 % . More so, it can be concluded that the density of a fluid is a function of its temperature, mass and volume.
RECOMMENDATION
This experiment was more challenging and difficult majorly due to; 1. Erratic power supply in the laboratory.
2. Poor ventilation.
3. Over-population in the laboratory.
4. Inadequate time.
So I suggest that constant power supply be made available by the next practical class. Also the windows should be well opened to allow adequate ventilation, and for the grouping each group should have fewer students. I also recommend more time for each of the practical.
References:
1.Archimedes, A Gold Thief and Buoyancy - by Larry "Harris" Taylor, Ph.D.
2. CRC Press Handbook of tables for Applied Engineering Science, 2nd Edition, 1976, Table 1-59
3. Extreme Stars: White Dwarfs & Neutron Stars, Jennifer Johnson, lecture notes, Astronomy 162, Ohio State University. Accessed on line May 3, 2007.
4. Edition of Department of Physical Chemistry: Laboratory Practice in Physics for
Students of Pharmacy. Faculty of Pharmacy, Comenius University, Bratislava, UK
1991.
5. Fact or Fiction?: Archimedes Coined the Term "Eureka!" in the Bath, Scientific American, December 2006.
6. Kopecký, F.: Physics for Students of Pharmacy I. Bratislava, UK 1999. 184 s. (in Slovak).
7. Nuclear Size and Density, HyperPhysics, Georgia State University. Accessed on line June 26, 2009.
8. Oremusová J., Vojteková M.: Density determination of liquids and solids. Manual
for laboratory practice. (in Slovak)
Manual written by RNDr.J.Gallová, CSc.
English version prepared by N. Kučerka, PhD.
9. The first Eureka moment, Science 305: 1219, August 2004.
10. Vitruvius on Architecture, Book IX, paragraphs 9-12, translated into English and in the original Latin.
APPENDIX I
CALCULATIONS
Calculation of Density/Specific Gravity and API Using Figures Measured From the Weighing Balance Apparatus
Workings on the Actual Masses of the Samples
The actual mass of a sample is obtained from the relationship;
(Mass of Sample + pycometer) – (Mass of empty pycometer)
for PMS
Mass of empty pycometer = 24.63g
Mass of PMS + pycometer = 62.30g
Actual weight of PMS = (62.30 – 24.63) g = 37.67g
for DPK
Mass of empty pycometer = 24.77g
Mass of PMS + pycometer = 61.95g
Actual weight of DPK = (61.95 – 24.77) g = 37.18g
for CRUDE OIL
Mass of empty pycometer = 24.85g
Mass of PMS + pycometer = 63.87g
Actual weight of CRUDE OIL = (63.87 – 24.85) g = 39.02g
for PKO
Mass of empty pycometer =
Mass of PMS + pycometer =
Actual weight of PKO = (–) g = g
Workings on Densities/Specific Gravities of the Samples
The density of a sample is calculated based on the formula;
Density = Actual mass of sample
Volume of sample
Also,
Specific Gravity, S.G (dimensionless) = Density of substance
Density of Water
for PMS
Actual mass of sample = 37.67g
Volume of sample = 50ml
Therefore, Density = 37.67 = 0.7534g/ml
50
And S.G = 0.7543 = 0.7534
for DPK
Actual mass of sample = 37.18g
Volume of sample = 50ml
Therefore, Density = 37.18 = 0.7436g/ml
And S.G = 0.7436 = 0.7436
for CRUDE OIL
Actual mass of sample = 39.02g
Volume of sample = 50ml
Therefore, Density = 39.02 = 0.7804g/ml
And S.G = 0.7804 = 0.7804
for PKO
Actual mass of sample = 37.67g
Volume of sample = 50ml
Therefore, Density = 37.67 = 0.7534g/ml
And S.G = 0.7543 = 0.7534
Workings on the API Gravities of the Samples
From the relationship, API = 141.5 – 131.5
S.G
where S.G is the specific gravity of a substance.
The API gravities can thus be calculated:
For the direct method
for PMS
S.G of sample = 0.7000g/ml
Therefore, API = 141.5 – 131.5 = 70.64
for DPK
S.G of sample = 0.8000g/ml
Therefore, API = 141.5 – 131.5 = 45.38
for CRUDE OIL
S.G of sample = 0.8400g/ml
Therefore, API = 141.5 – 131.5 = 36.95
for PKO
S.G of sample = 0.9000g/ml
Therefore, API = 141.5 – 131.5 = 25.72
for SOAP SOLUTION
S.G of sample = 0.9400g/ml
Therefore, API = 141.5 – 131.5 = 19.03
For the weighing balance method
for PMS
S.G of sample = 0.7534g/ml
Therefore, API = 141.5 – 131.5 = 56.32
0.7534
for DPK
S.G of sample = 0.7436g/ml
Therefore, API = 141.5 – 131.5 = 58.79
0.7436
for CRUDE OIL
S.G of sample = 0.7804g/ml
Therefore, API = 141.5 – 131.5 = 49.81
0.7804
for PKO
S.G of sample = 0.7534g/mlTherefore, API = 141.5 – 131.5 = 187.82
Appendix II
Question 1
From the calculation above, PMS has the highest API.
While DPK has the highest price in the market.
Question 2
From the experiment carried out and from calculations, PMS was found to be the lightest of the crudes, and DPK is the heaviest.
Question 3
The specific gravity (relative density) of gasoline ranges from 0.71 – 0.70, higher densities of oil residue have a greater volume of aromatics.
Fig.1 hydrometer
A hydrometer measures the difference in gravity (density) between pure water and water with sugar dissolved in it by flotation. The hydrometer is used to gauge the fermentation progress by measuring one aspect of it, attenuation. Attenuation is the conversion of sugar to ethanol by the yeast. Water has a specific gravity of 1.000. Hydrometer readings are standardized to 59°F (15°C). Liquid gravity (density) is dependent on temperature and temperature correction tables are usually sold with the hydrometer or are available from chemistry handbooks.