Laws of Gases: Boyle's Law

In studying the laws of gases there are different variables that we need to consider.  These are the volume, pressure, temperature, and the number of moles.  Volume is the amount of space occupied by a three-dimensional object as measured in cubic units (such as quarts and liter).  Pressure is the force applied in a given area, usually has the unit of atmosphere (atm), millimeter of  Mercury (mm Hg), torr, Pascal (Pa), kilopascal (kPa). Temperature is the degree of hotness and coldness measured on the definite scale such as Kelvin, ^oF and ^oC.  In solving problems related to gases, kelvin always is used.  Number of moles refer to the amount of substance, the unit is mol.

Boyle's Law

Robert Boyle is a British chemist who investigated the relationship between pressure and volume at constant temperature.  He used the J- shaped tube in studying the relationship between pressure and volume, he observed that adding pressure to the open end of the J-shaped tube at constant temperature will cause the decrease in the volume as shown in the figure below:

Boyle's law therefore can be stated as " if the volume of a fixed amount of gas is inversely proportional to volume at constant temperature." Inversely proportional mean that if you increase the pressure the volume will decrease or if the pressure is decreased the volume is increased.  If the relationship will be plotted in a graph, the graph will look like the figure below:

The mathematical equation that will express the inverse relationship between pressure and volume is

where ∝ is means proportional to.  We can change ∝ to an equal sign, 

where k₁ is the proportionality constant.   Arranging the equation:

This means that the product of pressure and volume at constants temperature is constant.

Using Boyle's Law we can predict the new pressure if there is a change in volume and at the same time volume can also be predicted if the pressure is also changed provided the temperature is not changed..  Since P₁V₁ = k, therefore P₂V₂ = k, combining both, the formula will be

P₁V₁ = P₂V₂

Using the above equation as the mother equation we can already formulate formulas for calculating P₁, V₁, P₂ and V₂.

These are the formulas:

Pressure of Gases

Pressure is defined as force that is applied in a given area,  P = F/A.  Gases exert pressure on the surface in which they are in contact because the molecules of gases are always moving.

For the unit of pressure, force has the SI unit of  newton (N), where

                             1 N = 1 kg.m/s²

and the area's unit is m² and therefore, the SI unit of pressure is Pa which is equivalent to

                            1 Pa = 1 N/m²

What is atmospheric pressure?

Atmospheric pressure is the pressure exerted by earth's atmosphere.  The value of atmospheric pressure  depends on location, temperature and weather condition.  The atmosphere is much denser  near the surface of earth  than at high altitudes,  The denser the air is, the greater the pressure exerted.

Barometer is an instrument  used for measuring atmospheric pressure.  It was invented in 1643 by an Italian scientist named Evangelista Torricelli (1608-1647), who had been a student of the famous astronomer Galileo.  Below is the Torricelli's Barometer:

Standard atmospheric pressure, corresponds to the typical pressure  at sea level, is the pressure sufficient  to support a column of mercury 760 mm high at 0^oC at sea level.  In SI unit this pressure is equal to 101,325 Pa.

Standard atmospheric pressure defines some common non-SI units used to express gas pressure, such as atmosphere (atm), millimeter of mercury (mm Hg), and torr.

1 atm  =  760 mm Hg = 760 torr = 101,325 Pa = 101.325 kPa = 1.01325 bar = 14.69 psi (pounds per square inch,

Manometer is a device used to measure the pressure of gases other than the atmosphere.  The principle of operation is similar to that of barometer.  There are two types of manometer, the closed-tube and the open-tube manometer.

-Open-tube manometer is suited for measuring pressures equal to or greater than atmospheric pressure.

-Closed-tube manometer is used to measure pressures below atmospheric pressure.

Below are the models of the two types of manometer:

a.  Closed-tube manometer
b.  Open-tube manometer

Pressure Conversion

Sample Problem:

1.  Convert a.  0.075 torr to kPa

                   b.  6.6 x 10^-2 torr to atm

                   c.  749 mm Hg

Solution:

a.

b.

c.