Chemistry · Ch 10 — States of Matter

Boyle's Law

10.4.1

Boyle's Law

Robert Boyle, in 1662, carried out a large number of experiments on different gases and found that, at a fixed temperature, increasing the pressure on a fixed amount of gas reduced its volume, and vice versa. This is Boyle's law: for a fixed mass (number of moles $n$ ) of a gas at constant temperature, the pressure ( $P$ ) of the gas is inversely proportional to its volume ( $V$ ), i.e. $P \propto \frac{1}{V}$ (at constant $T$ and $n$ ), so $PV = k_1$ , a constant. Consequently, if a fixed amount of gas at constant temperature goes from an initial state ( $P_1, V_1$ ) to a final state ( $P_2, V_2$ ), then $P_1V_1 = P_2V_2$ . This can be pictured with a bicycle pump: pushing the piston down squeezes the same number of gas particles into a smaller volume, so they strike the pump walls more often and the pressure rises. Plotted graphically, $PV$ vs $P$ at fixed $T$ gives a straight horizontal line (since $PV$ is constant), while $P$ vs $V$ gives a curve called an isotherm, and $P$ vs $1/V$ gives a straight line through the origin. At very high pressure, real gases start to deviate from this ideal Boyle's-law behaviour. Because $V = k_1/P$ and density $d = m/V$ , …

Figure Fig 10.6Fig. 10.6: Schematic illustration of Boyle's law

What this figure shows. A simple diagram of a bicycle-pump-like piston/cylinder shown at two different pressures -- one panel labelled P = 1 atm with a larger gas volume, and a second panel labelled P = 2 atm with the piston pushed further in and a visibly smaller gas volume -- with captions noting that increasing the pressure decreases the volume and decreasing the pressure increases the volume, at constant t …

Figure Fig 10.7Fig. 10.7: Schematic of the Boyle's law experiment

What this figure shows. Two side-by-side cylinder/piston diagrams with graduated scales from 0 to 200 cm3. The left cylinder is labelled 'Low pressure, High volume' at 1 atm with the gas occupying about 200 cm3; the right cylinder is labelled 'High pressure, Low volume' at 2 atm with the gas compressed to about 100 cm3 -- a direct experimental illustration that doubling the applied pressure at constant temperature halves the gas volume, consistent w …

Figure Fig 10.8Fig. 10.8: Boyle's law -- graphical representations (a, b, c)

What this figure shows. Three related graphs, each drawn for several different constant temperatures T1, T2, T3. Panel (a) plots pressure P (y-axis) against volume V (x-axis): each temperature gives its own smooth downward-curving hyperbola-shaped curve (an isotherm), higher up for higher T. Panel (b) plots the product PV (y-axis) against pressure P (x-axis): for each fixed temperature this gives a straight horizontal line, parallel to the pressure axis, because PV is constant at constant T (a higher line for a higher T). Panel (c) plots pressure P (y-axis) against 1/V (x-axis): each temperature gives a straight line passing through the origin, since P is …

Misc Problem 10.1Problem 10.1: Volume change when pressure is increased (Boyle's law)

Worked out. A given mass of gas occupies 25 mL at 298 K and 1 atm pressure; find its volume when pressure is raised to 1.25 atm at the same temperature. By Boyle's law, P1V1 = P2V2, so V2 = P1V1/P2 = (1 atm x 25 mL)/1.25 atm = 20 mL. The gas is compressed from 25 mL down to 20 mL, consistent with pressure and volume varying inversely at constant temperature. …

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