Question

Calculate the activity at 25 degrees Celsius of NACl(s) at 1, 10, 100, and 1000 bar. The density of NaCl at 25 degrees Celsius and 1 bar is 2.16 (g/cm3).

Answer 1

The density is determined by utilizing a variation of the ideal gas law where density and molar mass replace moles and volume.

The original ideal gas law uses the formula PV = nRT, the density version of the ideal gas law is PM = dRT, where P is pressure measured in atmospheres (atm), T is temperature measured in kelvin (K), R is the ideal gas law constant 0.0821 atm(L)mol(K)just as in the original formula, but M is now the molar mass (gmol) and d is the density (gL).

By rearranging the formula to PM / RT=d the units of atm, mol and K will cancel and the value will be left with the gL units for density.

So the formula is PM = dRT

=> M = dRT / P

So applying the same formula fopr all the conditions

For 1 bar M = 2.16 * 81.34 * 298 / 1 = 5.23 * 10⁴

81.34 is the value of R in bar cm³

For 10 bar M = 5.23 * 10³ moles / cm³

For 100 bar M = 5.23 * 10² moles / cm

for 1000 bar M = 52.3 moles / cm