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... le then existed he could not, and did not, determine the relationship between degree of hotness (temperature) and volume of a gas quantitatively. (Siebring, Richard, Page 32) Guillaume Amontons (d. 1705) developed the air thermometer, which uses the increase in the volume of a gas with temperature rather than the volume of a liquid. The air thermometer is an excellent demonstration of Charles' law because the atmosphere maintains a fixed downward pressure above a small mercury plug of constant mass. The volume of a trapped sample of air increases on heating until the pressure of the trapped air equals the pressure of the atmosphere plus the small pressure due to the plug. Nevertheless, Amontons failed to achieve formulation of Charles' law for the same reason as did Boyle: a quantitative scale of temperature was needed.
A quantitative scale of temperature could only be developed after it was realized that at a fixed pressure any pure substance undergoes a phase change at a single fixed temperature which is characteristic of that substance. The melting point of ice to water was taken as 0 oC and the boiling point of water was taken as 100 oC to give our common Celsius scale of temperature. The measurements of the French chemists used the very similar Reaumur scale (water freezes at 0 oRe and boils at 80 oRe) to establish the law of Charles. The study of the effect of temperature upon the properties of gases took considerably longer to achieve a simple quantitative relation than did study of the effect of pressure, primarily because the development of a quantitative scale of temperature was a difficult process. However, once such a scale was developed, the appropriate measurements were made, primarily by the French chemist Jacques Charles (1746 - 1823).
The experimental data were formulated into a general law which became known as the law of Charles or Charles' law: At any constant pressure, the volume of any sample of any gas is directly proportional to the temperature. Mathematically, the law of Charles can be expressed as where t represents the temperature on any convenient temperature scale and k' and k" are constants. However the volume extrapolates to zero at a temperature of - 273. 15 oC. If this temperature were taken as the zero of a temperature scale, the constant k" would be zero and it could be dropped from the equation. Such a temperature scale is now the fundamental scale of temperature in the SI. It is called the absolute scale, the thermodynamic scale, or the Kelvin scale.
Temperature on the Kelvin scale, and only on the Kelvin scale, is symbolized by T. The unit of temperature n the Kelvin scale is called the kelvin, and it has the same size as the degree Celsius. The symbol for the unit kelvin is K. (Metcafe H. Clark, Page 273 - 4) The law of Charles can be written more simply using the Kelvin scale of temperature as V = k'T, where T represents the absolute temperature. An alternative form, more useful when the volume of one particular sample of gas changes with temperature, is V 1 /T 1 = V 2 /T 2. Dalton's studies which led him to the atomic-molecular theory of matter included studies of the behavior of gases.
These led him to propose what is now called Dalton's law of partial pressures: For a mixture of gases in any container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone. This law can be expressed in equation form as: where p is the total or measured pressure are the partial pressures of the individual gases. For air, an appropriate form of Dalton's law would be: p (air) = p (N 2) + p (O 2) + p (CO 2) +... At temperatures near ordinary room temperature, the partial pressures of each of the components of air is directly proportional to the number of moles of that component in any volume of air.
When the total pressure of air is 100 kPa or one bar, the partial pressures of each of its components (in kPa) are numerically equal to the mole per cent of that component. Thus the partial pressures of the major components of dry air at 100 kPa are nitrogen, 78 kPa; oxygen, 21 kPa; argon, 0. 9 kPa; and carbon dioxide, 0. 03 kPa. (Metcafe H. Clark, Page 273 - 4) The same substance may be found in different physical states under different conditions. Water, for example, can exist as a solid phase (ice), a liquid phase (water), and a gas phase (steam or water vapor) at different temperatures. The processes by which a substance is converted from one phase to another are called by specific names.
The conversion from solid to liquid is melting or fusion and the reverse conversion from liquid to solid is freezing. The conversion from liquid to gas is called boiling or vaporization and the reverse conversion from gas to liquid is called condensation. The conversion from solid to gas, when it occurs directly without going through a liquid state as in the case of iodine and carbon dioxide, is called sublimation; the reverse conversion from gas to solid shares the name of condensation. The Ideal Gas Law was first written in 1834 by Emil Clapeyron. This is just one way to derive the Ideal Gas Law: For a static sample of gas, we can write each of the six gas laws as follows: Note that the last law is written in reciprocal form. The subscripts on k indicate that six different values would be obtained.
When you multiply them all together, you get: Let the cube root obe called R. (Wilbraham, Antony C. , page 234) Each unit occurs three times and the cube root yields L-atm / mol-K, the classic units for R when used in a gas law context. (Dickson, T. R. , Page 78 - 9) PV / nT = R PV = nRT R is called the gas constant. Sometimes it is referred to as the universal gas constant. If you wind up taking enough chemistry, you will see it showing up over and over and over. R's value can be determined many ways.
This is just one way: Assume we have 1. 000 mol of a gas at STP. The volume of this amount of gas under the conditions of STP is known to a high degree of precision. We will use the value of 22. 414 L. By the way, 22. 414 L at STP has a name. It is called "molar volume. " It is the volume of ANY ideal gas at standard temperature and pressure. (Siebring, Richard, Page 54) Let's plug our numbers into the equation: (1. 000 atm) (22. 414 L) = (1. 000 mol) (R) (273. 15 K) Notice how atmospheres were used as well as the exact value for standard temperature. Solving for R gives 0. 08206 L atm / mol K, when rounded to four significant figures.
This is usually enough. Remember the value. You " ll need it for problem solving. Notice the weird unit on R: say out loud "liter atmospheres per mole Kelvin. " This is not the only value of R that can exist.
It depends on which units you select. Those of you that take more chemistry than high school level will meet up with 8. 3145 Joules per mole Kelvin, but that's for another time. Bibliography:
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