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The Gas Laws
Scientists have been studying physical properties of gases for hundreds of years
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The observations of Boyle and others led to the development of the gas laws
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Boyle’s Law: Pressure-Volume Relationship
Robert Boyle discovered that doubling the pressure on a sample of gas at constant temperature reduces its volume by one-half
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As one variable increases, the other
decreases
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Suppose
the volume of a container is decreased but the same number of gas molecules is present at the same temperature
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The number of collisions with a given unit of wall area per unit time will increase as a result
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Plotting the values of volume versus pressure for a gas at constant temperature gives a curve such as: The general volumepressure relationship that is illustrated is called Boyle’s law
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Mathematically, Boy’s law can be expressed as follows:
PV = k
In the equation above, P is the pressure, V is the volume, and k is a constant
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Because two quantities that are equal to the same thing are equal to each other, the relationship between
changes of pressure and volume can be expressed as shown below
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P2and V2represent a different set of conditions
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Charles’s Law: Volume-Temperature Relationship
If pressure is constant, gases expand when heated
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At the higher temperature, the gas molecules move faster
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The volume of a flexible container must then
increase in order for the pressure to remain the same
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Charles’s experiments showed that all gases expand to the same extent when heated through the same temperature interval
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For example, raising the temperature to 1°C causes the gas volume to increase by 1/273 of the volume it
had at O°C
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The same regularity of volume change occurs if a gas is cooled at constant pressure,
The Kelvin temperature scale is a scale that starts at a temperature corresponding to -273
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That temperature is the lowest
one possible
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15°C is referred to as absolute zero and is given a value of zero in the Kelvin scale
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K = 273
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The relationship between Kelvin temperature and gas volume is known as Charles’s law
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Charles’s law may be expressed as
follows:
V = kT

or

V/T = k

The value of T is the Kelvin temperature, and k is a constant
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The form of Charles’s law that can be applied directly to most volume-temperature problems involving
gases is as follows:
V1/T2 = V2/T2
V1and T1 represents initial conditions
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When three of the four values T1, V1, T2,
and V2 are known, you can use this equation to calculate the fourth value for a system at constant pressure
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The energy and frequency of collisions depend
on the average kinetic energy of molecules
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Joseph Gay-Lussac is given credit for recognizing this in 1802
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P = kT or P/T = k
The value of T is the temperature in kelvins, and k is a constant that depends on the quantity of gas and the volume
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Unknown values can be
found using this form of Gay-Lussac’s law
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P2 and T2 represent a different set of conditions
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The Combined Gas Law
A gas sample often undergoes changes in temperature, pressure, and volume all at the same time
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Boyle’s law, Charles’s law, and Gay-Lussac’s law can be combined into a single
expression that is useful in such situations
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PV/T = k
In this equation, k is constant and depends on the amount of gas
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From this expression, any value can be calculated if the other five are known
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For example, Boyle’s law is obtained when the temperature is
constant
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P1V1 = P2V2



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