- #1

ArtZ

- 48

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- TL;DR Summary
- Using rate kinetics to calculate the time to reach final CF of alcohol knowing starting C0 and heating T

Hi,

This is my first post on PF. I am engaged in a project seeking to find a simple way to reduce ethanol content in wine for those wishing to minimize alcohol intake for health or personal reasons. The alcohol-reduced wine will be used for cooking. Seems heating would do the trick however, the temperature must be kept as low as reasonable to minimize degradation to the wine flavor.

Keep in mind that my field is EE not CE so I am feeling this out as I go.

So as I understand it, the rate of alcohol removal in wine is dependent on several factors, including temperature, time, and alcohol concentration. One common model used to describe the kinetics of alcohol removal is the first-order reaction model, which assumes that the rate of reaction is proportional to the concentration of alcohol remaining in the wine.

The general equation for the first-order reaction model is:

dC/dt = -kC

where:

- dC/dt is the rate of change of alcohol concentration with time

- k is the reaction rate constant

- C is the concentration of alcohol in the wine at any given time

Assuming that the reaction follows first-order kinetics, seems that we can use the following equation to calculate the concentration of alcohol remaining in the wine after a given time:

C/C0 = exp(-kt)

where:

- C0 is the initial concentration of alcohol in the wine

- t is the time (in minutes)

- exp is the exponential function

I've defined the reaction rate constant, k, using the following:

k = A * exp(-Ea/RT)

where:

A is the pre-exponential factor or frequency factor, A = 10^13 s^-1

Ea is the activation energy, Ea = 65 kJ/mol = 65000 J/mol

R is the gas constant, R = 8.314 J/(mol*K)

T is the absolute temperature used in heating, T = 356.45 K

Substituting the values of A, Ea, R, and T into the equation, we get:

k = (10^13 s^-1) * exp(-65000 J/mol / (8.314 J/(mol*K) * 356.45 K))

k = 2.982 x 10^3 s^-1

When I solved for t using the above:

t = -ln(C/C0)/k

I found that the time, t, value returned, was too short given the Cf desired and the C0 of the unheated wine. The first-order reaction model does not account for the energy needed to overcome the heat of evaporation making this an incomplete solution to dC/dt.

As I understand it, the heat of vaporization or heat of evaporation, is the amount of energy that must be added to a liquid substance, to transform a quantity of that substance into a gas.

The heat of vaporization of ethanol (hfg) is (0.826 kJ/g). To incorporate we'll convert the heat of vaporization from kJ/g to J/mol. The molar mass of ethanol is 46.07 g/mol, so: hfg = 0.826 kJ/g * 1000 J/kJ * 1 mol/46.07 g = 17930 J/mol

In both equations below, C0 represents the starting alcohol concentration, Cf represents the desired final alcohol concentration, k is the rate constant for ethanol at the given temperature (in units of s^-1), hfg is the heat of vaporization for ethanol (in J/mol), and R is the gas constant (8.314 J/mol*K).

With some algebraic manipulation I arrived at these canonical forms of the t, and T equations, where t represents time (in seconds) and T represents temperature (in Kelvin):

To solve for time (given T):t = -ln(Cf/C0) / (k*(1 + (hfg/R*T)*k))

To solve for temperature (given t):T = hfg/(Rk) * (1/t - 1/(kln(Cf/C0)))

In both equations below, C0 represents the starting alcohol concentration, Cf represents the desired final alcohol concentration, k is the rate constant for ethanol at the given temperature (in units of s^-1), hfg is the heat of vaporization for ethanol (in J/mol), and R is the gas constant (8.314 J/mol*K).

Hopefully this makes sense so far. Like I said, am an EE not a CE. The first example that I'd like to solve for is using the expression for t above given T:

Given:

• Heating temperature of wine = 83.3C • Initial alcohol concentration, C0= = 0.15 (15%) • Final concentration desired, Cf = 0.04 (4%) • Reaction rate constant = 2.982 x 10^3 s^-1 • Heat of evaporization for ethanol = 17930 J/mol • Boiling point of ethanol =78.5C

An answer that I arrived at that seemed reasonable = 51 minutes to reduce the alcohol concentration from 15% to 4%. Everything I've presented seems reasonable, however, I don't get agreement between Excel and Mathcad which I use for units consistency checking.

Maybe my approach is way off base or just needs some fine tuning. Is there someone in the Forum with a better background in this area who could point me in the right direction?

Any help is greatly appreciated.

Thanks,

Art

This is my first post on PF. I am engaged in a project seeking to find a simple way to reduce ethanol content in wine for those wishing to minimize alcohol intake for health or personal reasons. The alcohol-reduced wine will be used for cooking. Seems heating would do the trick however, the temperature must be kept as low as reasonable to minimize degradation to the wine flavor.

Keep in mind that my field is EE not CE so I am feeling this out as I go.

So as I understand it, the rate of alcohol removal in wine is dependent on several factors, including temperature, time, and alcohol concentration. One common model used to describe the kinetics of alcohol removal is the first-order reaction model, which assumes that the rate of reaction is proportional to the concentration of alcohol remaining in the wine.

The general equation for the first-order reaction model is:

dC/dt = -kC

where:

- dC/dt is the rate of change of alcohol concentration with time

- k is the reaction rate constant

- C is the concentration of alcohol in the wine at any given time

Assuming that the reaction follows first-order kinetics, seems that we can use the following equation to calculate the concentration of alcohol remaining in the wine after a given time:

C/C0 = exp(-kt)

where:

- C0 is the initial concentration of alcohol in the wine

- t is the time (in minutes)

- exp is the exponential function

I've defined the reaction rate constant, k, using the following:

k = A * exp(-Ea/RT)

where:

A is the pre-exponential factor or frequency factor, A = 10^13 s^-1

Ea is the activation energy, Ea = 65 kJ/mol = 65000 J/mol

R is the gas constant, R = 8.314 J/(mol*K)

T is the absolute temperature used in heating, T = 356.45 K

Substituting the values of A, Ea, R, and T into the equation, we get:

k = (10^13 s^-1) * exp(-65000 J/mol / (8.314 J/(mol*K) * 356.45 K))

k = 2.982 x 10^3 s^-1

When I solved for t using the above:

t = -ln(C/C0)/k

I found that the time, t, value returned, was too short given the Cf desired and the C0 of the unheated wine. The first-order reaction model does not account for the energy needed to overcome the heat of evaporation making this an incomplete solution to dC/dt.

As I understand it, the heat of vaporization or heat of evaporation, is the amount of energy that must be added to a liquid substance, to transform a quantity of that substance into a gas.

The heat of vaporization of ethanol (hfg) is (0.826 kJ/g). To incorporate we'll convert the heat of vaporization from kJ/g to J/mol. The molar mass of ethanol is 46.07 g/mol, so: hfg = 0.826 kJ/g * 1000 J/kJ * 1 mol/46.07 g = 17930 J/mol

In both equations below, C0 represents the starting alcohol concentration, Cf represents the desired final alcohol concentration, k is the rate constant for ethanol at the given temperature (in units of s^-1), hfg is the heat of vaporization for ethanol (in J/mol), and R is the gas constant (8.314 J/mol*K).

With some algebraic manipulation I arrived at these canonical forms of the t, and T equations, where t represents time (in seconds) and T represents temperature (in Kelvin):

To solve for time (given T):t = -ln(Cf/C0) / (k*(1 + (hfg/R*T)*k))

To solve for temperature (given t):T = hfg/(Rk) * (1/t - 1/(kln(Cf/C0)))

In both equations below, C0 represents the starting alcohol concentration, Cf represents the desired final alcohol concentration, k is the rate constant for ethanol at the given temperature (in units of s^-1), hfg is the heat of vaporization for ethanol (in J/mol), and R is the gas constant (8.314 J/mol*K).

Hopefully this makes sense so far. Like I said, am an EE not a CE. The first example that I'd like to solve for is using the expression for t above given T:

Given:

• Heating temperature of wine = 83.3C • Initial alcohol concentration, C0= = 0.15 (15%) • Final concentration desired, Cf = 0.04 (4%) • Reaction rate constant = 2.982 x 10^3 s^-1 • Heat of evaporization for ethanol = 17930 J/mol • Boiling point of ethanol =78.5C

An answer that I arrived at that seemed reasonable = 51 minutes to reduce the alcohol concentration from 15% to 4%. Everything I've presented seems reasonable, however, I don't get agreement between Excel and Mathcad which I use for units consistency checking.

Maybe my approach is way off base or just needs some fine tuning. Is there someone in the Forum with a better background in this area who could point me in the right direction?

Any help is greatly appreciated.

Thanks,

Art