Chemistry · Ch 6 — Gaseous State

Gay-Lussac's Law (Pressure-temperature relationship)

6.2.3

Gay-Lussac's Law (Pressure-temperature relationship)

Joseph Gay-Lussac established the third pairwise gas law: at constant volume, the pressure of a fixed mass of gas is directly proportional to its Kelvin temperature.

P\propto T\qquad\text{or}\qquad\frac{P}{T}=\text{constant}\ k

Comparing two states of the same fixed-volume system,

\frac{P_1}{T_1}=\frac{P_2}{T_2}

Lines on a pressure-vs-temperature graph, each drawn for a different fixed volume, are called isochores. Activity 1 works through this directly: for 1 mole of an ideal gas held first in a 50 L container and then in a 75 L container, pressure is recorded at six different temperatures (32 to 191 $^\circ$ C); plotting either data set gives a straight line through (extrapolated) absolute zero, confirming that P rises in direct proportion to T at each fixed volume -- and that the 75 L data sits b …

Table 6.2-activity1Activity 1: pressure of 1 mole of an ideal gas at different temperatures, in two container sizes

Temperature ( $^\circ$ C)	32	69	94	130	154	191
Pressure in 50 L container (atm)	0.51	0.56	0.60	0.66	0.70	0.76

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