Boyle's Law

Concepts

Some of the earliest quantitative measurements were performed on gases. The first of these studies was conducted by Robert Boyle in 1662.

Robert Boyle employed a J-shaped piece of glass tubing that was sealed on one end. A gas (air) was trapped in the sealed end of the tube and varying amounts of mercury were added to the J-shaped tube to vary the pressure of the system. Boyle systematically varied the pressure and measured the volume of the gas. These measurements were performed using a fixed amount of gas and a constant temperature. In this way Boyle was able to examine the pressure-volume relationship without complications from other factors such as changes in temperature or amount of gas.

The manometer that was employed in the previous experiment can also be used to perform Boyle's experiment. A small amount of air is trapped in the sealed end of the manometer. The scale that is used to read the height of a column of mercury can also be used to read the height of the column of air. (You will need to estimate the position of the top of the tube, which is curved.) The inside diameter of the tube, 4.286 cm, and the height of the column of air can be used to calculated the volume of air.

The pressure of the gas will be varied in exactly the same manner as Robert Boyle varied the pressure: mercury will be added or removed from the open end of the manometer. After changing the pressure (by changing the amount of mercury in the manometer), the pressure and volume are recorded.

Once the volume-pressure data has been obtained, the next challenge is to determine the mathematical relationship between the two properties. Although an enormous number of relationships are possible, one likely possibility is that the volume will be directly related to the pressure raised to some power:

The exponent a is expected to be independent of the mass of gas and temperature; the goal is to determine the value of a from the "experimental" data. The constant C_BL is expected to vary with the mass of gas and the temperature; at this point, this constant is not of interest.

A simple way to determine the value of a is to prepare a plot of ln V vs ln P. If the proposed relationship is valid (and it might not be valid), this plot should yield a straight line of slope a. Thus the linearity of the plot serves as a test of our original hypothesis (that the volume-pressure relation may be described by the equation shown above).

For more information, please click here