When Robert Boyle conducted his experiments, he measured pressure in inches of mercury (in \(\mathrm{Hg}\) ). On a day when the atmospheric pressure was \(29.85 \mathrm{inHg}\), he trapped some air in the tip of a J-tube (1) and measured the difference in height of the mercury in the two arms of the tube \((b)\). When \(h=12.0\) inches, the height of the gas in the tip of the tube was \(32.0\) in. Boyle then added additional mercury and the level rose in both arms of the tube so that \(h=30.0\) inches \((2)\). (a) What was the height of the air space (in inches) in the tip of the tube in \((2)\) ? (b) What was the pressure of the gas in the tube in (1) and in (2) in inHg?

Gas laws explore the relationships between the pressure, volume, and temperature of a gas. Boyle's Law, specifically, delves into the pressure-volume relationship, holding temperature constant to comprehend how the two variables inversely affect one another.

In Boyle's Law, we observe that when a gas is compressed (decreasing volume), its pressure increases if the temperature remains unchanged. Conversely, if the pressure is decreased, the volume expands. This principle is fundamental in various scientific and real-world applications, such as when breathing – our lungs expand and contract changing volume and hence pressure to move air in and out.

Boyle’s Law provides a quantitative way to understand the pressure-volume relationship in gases. It is mathematically represented by the equation \( P_1V_1 = P_2V_2 \), where \( P \) is pressure, and \( V \) is volume, with subscripts 1 and 2 referring to the initial and final states of the gas.

This law implies two key ideas: when volume \( V \) increases, pressure \( P \) decreases, and vice versa, as long as temperature and amount of gas remain constant. It is a direct illustration of the inverse proportionality between pressure and volume.

The mercury barometer is an essential tool for measuring atmospheric pressure. Invented by Torricelli, it is composed of a tube filled with mercury inverted in a mercury-filled basin. The weight of the mercury column balances the atmospheric pressure, and the height of the mercury column provides a direct measurement of that pressure.

How Boyle Used Mercury

Robert Boyle utilized this technique to measure the pressure exerted on the gas. His use of a J-tube is similar to a barometer in that changes in mercury’s height reflect changes in pressure. By trapping air in the tube and altering the mercury levels, Boyle was able to study the pressure-volume relationship.

Chemical principles often revolve around understanding the behavior of particles. Boyle's Law illustrates how gas particles respond to changes in pressure and volume. When the volume in which these particles are contained becomes smaller (as mercury is added in the J-tube experiment), the particles collide more frequently with the walls, resulting in higher pressure.

Additionally, Boyle's experiments contribute to the foundations of stoichiometry in chemical reactions, where the relationships between reactants and products often involve considerations of gas volumes and pressures. Boyle's Law also finds practical applications in understanding the behavior of gases in chemical apparatus and the human body alike.