Show how the parameters in the two equations are related.

Question

Liquid/vapor saturation pressure is often represented as a function of temperature by the Antoine equation,

which can be written in the form:







Here, parameters a, b, and c are substance-specific constants. Suppose this equation is to be rewritten in the equivalent form:

Answer 1

We must convert both the units and the logarithm (between base 10 and natural logarithm). We know that t in degrees Celsius is equal to T in Kelvins minus 273.15. Also 1 kPa is equal to 7.50 torr (we might have to look up this conversion factor). So, we have







Next, we might recognize that 10 can be written as exp(ln(10)) or exp(2.303). That is how we convert from base 10 log to natural log in general. So,







Here, I have also substituted T - 273.15 for t. Taking the natural log of both sides gives







For the two functions to be equal for all values of T, each part of the functions must be the same, so we must have

A = 2.303a -ln(7.5) or A = ln(10)*a - ln(7.5)

B = 2.303b or B = ln(10)*b

C = c - 273.15