Question

A chemistry student needs to calculate the new value of the ionization constant (Ka) of a weak acid when the temperature is raised from 25°C to 45°C, given that the initial value of Ka is 1.8 x 10^-5 at 25°C and the enthalpy of ionization (ΔHion) is 50.2 kJ/mol.

Answer 1

To calculate the new value of the ionization constant  Ka  at the higher temperature, we can use the van't Hoff equation:ln Ka2/Ka1  = -Hion/R *  1/T2 - 1/T1 where:- Ka1 is the initial ionization constant at 25C  1.8 x 10^-5 - Ka2 is the ionization constant at 45C  which we want to find - Hion is the enthalpy of ionization  50.2 kJ/mol - R is the gas constant  8.314 J/molK - T1 is the initial temperature in Kelvin  25C + 273.15 = 298.15 K - T2 is the final temperature in Kelvin  45C + 273.15 = 318.15 K First, we need to convert Hion from kJ/mol to J/mol:Hion = 50.2 kJ/mol * 1000 J/kJ = 50200 J/molNow, we can plug the values into the van't Hoff equation:ln Ka2/1.8 x 10^-5  = - 50200 J/mol  /  8.314 J/molK  *  1/318.15 K - 1/298.15 K Solve for Ka2:ln Ka2/1.8 x 10^-5  = -9.244Ka2/1.8 x 10^-5 = e^-9.244 Ka2 = 1.8 x 10^-5 * e^-9.244 Ka2  2.97 x 10^-6So, the new value of the ionization constant  Ka  at 45C is approximately 2.97 x 10^-6.