Table of Contents

• Overview
• Conversion Equation
• Example 1: No Water
• Example 2: With Water
• Example 3: With a Solid
• Example 4: With a Vapor
• Finding Equilibrium Constants in OLI
  • Sample Chemistry
  • OLI Studio: Stream Analyzer input grid
  • OLI Flowsheet: ESP input grid
  • Calculation Results
    • OLI Studio: Stream Analyzer Results
    • OLI Flowsheet: ESP Results

Overview

OLI software internally uses the mole-fraction-based concentration system for its thermodynamic calculations. This system yields an equilibrium constant value different from that of the molal-based system. 

For example, for the dissociation constant of pure water at 25 °C and 1 atmosphere:

K(m) = 1.0E-14 (approximate)

while 

K(x) = 3.8E-10 (approximate)

This introduction of the mole-fraction basis was primarily done to support the Mixed-Solvent Electrolyte (MSE) thermodynamic package. The change-of-basis transformation was also applied to the Aqueous Electrolyte (AQ) model.

Frequently, a user needs to compare an equilibrium constant reported by OLI with literature values. Often, the literature reports equilibrium constants on the molal basis rather than the mole-fraction basis. Fortunately, there is an easy conversion.

Conversion Equation

Let’s define two equilibrium constants: K(m) and K(x). K(m) is the molal-based equilibrium constant, and K(x) is the mole fraction-based equilibrium constant.

The conversion is:

K(m) = K(x) * 55.5091^Δn

Where Δn = the changes in moles across the equation, excluding H₂O

Δn = moles_product - moles_reactant 

Example 1: No Water

Let’s consider this equilibrium reaction:

NaHCO₃⁰ = Na⁺ + HCO₃^-

The software calculates an equilibrium constant, K(x) = 8.43828E-13 with Δn = (2 moles product – 1 mole reactant) = 1. Thus, the conversion is:

K(m)=K(x) * 55.50911 = 8.43828E-13 * 55.5091 = 4.68401E-11

Example 2: With Water

Now, let’s consider a conversion in which water is present.

H₂PO₄^- + H₂O = H₃O⁺ + HPO₄^2-

The software calculates an equilibrium constant, K(x) = 1.1224E-09, and Δn = (2 moles of product - 1 mole of reactant) = 1. Thus, our conversion equation is:

K(m) = K(x) x 55.50911 = 1.1224E-09 * 55.5091= 6.23033E-08

Why was there only 1 mole of reactant? In our conversion, we ignore the moles of H2O (on a molality basis, the activity of water is unity for the conversion)

Example 3: With a Solid

Now let’s consider a conversion where a solid is dissolving:

CaCO₃(s) = Ca²⁺ + CO₃^2-

The software calculates an equilibrium constant, K(x) = 9.66059E-13, (Δn= is 2 moles of product - 0 moles of reactant) = 2. Thus our conversion equation is:

K(m) = K(x) x 55.50912 = 9.66059E-13* 3081.26 = 2.97668E-09

Why were there 0 moles of reactant? In our conversion, we ignore the moles of a solid (on a molality basis, the activity of a solid is unity for the conversion)

Example 4: With a Vapor

Now let’s consider vapor–liquid equilibrium. We will use methane as an example:

CH4(vap) = CH4(aq)

The software calculates an equilibrium constant, K(x) = 2.46184E-05 (Δn = 1 mole of product - 0 moles of reactant) = 1.

Although the vapor can be a solution of species, we treat it as a single phase. Thus, the vapor-phase components are set to zero for this conversion.

Thus, our conversion equation is:

K(m) = K(x) x 55.50911 = 2.46184E-05* 55.5091 = 1.36655E-03

Finding Equilibrium Constants in OLI

Sample Chemistry

We will create a stream with the following inflows in both OLI Studio: Stream Analyzer and OLI Flowsheet: ESP. We will keep the temperature and pressure at ambient conditions, and keep the inflows at low concentrations. 

H₂O
NaHCO₃
H₃PO₄
CaCO₃
CH₄

OLI Studio: Stream Analyzer input grid

OLI Flowsheet: ESP input grid

Calculation Results

For both OLI Studio and OLI Flowsheet: ESP, the equilibrium constants are reported in the calculation output.

OLI Studio: Stream Analyzer Results

The default report does not include the equilibrium constants. To enable them, please click the Customize button:

Scroll down to find Species K-Values. Check the box.

Click ok to return to the report.

Please scroll to find the equilibrium constant section ("Species K(eq)-Values"), or use the Jump to: drop-down menu as shown above. 

This displays the entire list of equilibrium constants for all equilibrium reactions in this case. We have highlighted the CaCO3(s) equation. The variable for the solid is always written in the OLI TAG format, with the letter "K" as a prefix. The mole fraction-based and the molal-based values of the equilibrium constant are displayed.

OLI Flowsheet: ESP Results

The equilibrium constants are always enabled in OLI Flowsheet: ESP. On a stream report, scroll down to find the section named K-values

The mole fraction-based equilibrium constant value is the same as in the OLI Studio report. OLI Flowsheet: ESP only reports mole fraction-based values.