The authors definitions are for Kπν are : K = y1/x1 = mole fraction gas in gas phase ÷
mole fraction gas in liquid phase
π / atm = total pressure
ν = coefficient of fugacity
The function Kπν /atm, is equivalent to a Henry's constant in the form H1,2/atm = (1/atm)/x1 where 1 is the fugacity.