The P-V-T Relations of NH4Cl and NH4Br, and in Particular the Effect of Pressure on the Volume Anomalies

Measurements have been made of the volume as a function of pressure of N${\mathrm{H}}_4$Cl at 75°, 30°, and 0°C, and of N${\mathrm{H}}_4$Br at 75°, 0°, and -72°C. The pressure range was 12000 kg/${\mathrm{cm}}^2$, except at -72°, where it was 7500. There are discontinuities in the slope of the volume isotherm of N${\mathrm{H}}_4$Cl at 3370 kg at 0°, and at 9390 at 30°, and in the isotherm of N${\mathrm{H}}_4$Br at 1620 at -72°. The character of the discontinuity of N${\mathrm{H}}_4$Br is different from that of N${\mathrm{H}}_4$Cl, and is more like that of a polymorphic transition. These discontinuities correspond exactly to the discontinuities in the thermal expansion found by Simon and Ruhemann at atmospheric pressure. The displacement by pressure of the discontinuities to respectively higher and lower temperatures is that demanded by thermodynamics because of the opposite sign of the volume anomalies in the two cases. The thermodynamics of the effect of pressure and temperature on a discontinuity in a volume isotherm is discussed, and a generalized Clapeyron's equation shown to hold. By means of this equation the thermal effect accompanying the change can be calculated, and is found to be about 100 and 160 gm cal per mol for N${\mathrm{H}}_4$Cl and N${\mathrm{H}}_4$Br respectively. The thermal effect in N${\mathrm{H}}_4$Cl is approximately independent of pressure; the volume effect decreases rapidly with increasing pressure, being 0.0030 at 0° and 0.0015 at 30°. The volume effect in N${\mathrm{H}}_4$Br is approximately -0.017 at -72°. The explanation proposed by Pauling for the anomalies, namely passing from oscillational to rotational motion by the N${\mathrm{H}}_4$ radical, evidently must be supplemented by other considerations to account for the several marked differences between the behavior of the two substances. There are without doubt many other instances of such anomalies spread over a more or less localized range of pressure.