In this lesson, we're going to cover more details about Gibbs free energy. Now, before we get to the other forms of the Gibbs free energy equations, let's first recall the standard Gibbs free energy equation, which relates the changes in free energy to the changes in enthalpy, temperature, and the changes in entropy. And recall that Gibbs free energy is the energy that's available to perform work. Work is done in a reaction when the concentrations of that reaction or system change. And so, recall that at equilibrium, the concentrations of reactants and products do not change. They are constant. And so, there's no work done at equilibrium, and the delta G is going to be equal to 0 at equilibrium. This goes to show that the concentrations within a system influence the direction of a reaction. And so, we're going to talk about the reaction direction in our next video. So I'll see you guys in that video.
Gibbs Free Energy: Study with Video Lessons, Practice Problems & Examples
Created using AIGibbs free energy (ΔG) indicates the energy available for work in a reaction, with ΔG = 0 at equilibrium. Cellular reactions rarely reach equilibrium, necessitating the use of the reaction quotient (Q) to predict reaction direction. When Q < K (equilibrium constant), the reaction proceeds forward; when Q > K, it shifts backward. Under standard conditions (25°C, 1 atm, 1 M), ΔG can be calculated using ΔG° = -RT ln(K). Physiological conditions often differ, affecting ΔG, which can be calculated as ΔG = ΔG° + RT ln(Q), determining spontaneity in biological systems.
Gibbs Free Energy Equation
Video transcript
Reaction Direction
Video transcript
So in our previous video, we talked about how the concentrations of a reaction impact the direction of that reaction. And what's interesting to note is that cellular reactions are almost never at equilibrium. This is due to several different factors such as the conditions of the reactions changing, products being siphoned away into different reactions, and reactants being constantly added. When a reaction is not at equilibrium, we need to make the appropriate adjustments. One of those adjustments is to replace the equilibrium constant with the reaction quotient, which can be symbolized by the letter q. Notice that the reaction quotient expression is the same as the expression of the equilibrium constant. So it's the concentrations of products over the concentrations of reactants.
The difference between the reaction quotient and the equilibrium constant is that the equilibrium constant is specifically at equilibrium, whereas the reaction quotient is not at equilibrium. Recall from your previous chemistry courses that Le Chatelier's principles state that when an equilibrium is disturbed or when a reaction is not at equilibrium, such as cellular reactions, the reaction direction is going to proceed towards a direction to restore equilibrium. It will proceed to restore equilibrium.
In the example below, we're going to consider the reaction and then we're also going to complete the chart. In this reaction, we have carbon monoxide gas interacting with hydrogen gas to produce methanol. Recall that the reaction quotient expression is the concentration of products over the concentration of reactants. We only have one product here and that's methanol, so up here we can put methanol, CH3OH. Now for the reactants, we have two reactants, carbon monoxide, which we can put over here, and hydrogen gas, or H2. The coefficients are expressed as exponents. So we can go ahead and put this 2, as an exponent here.
The reaction quotient expression is pretty much exactly the same as the equilibrium constant expression. The only difference is that the equilibrium constant's expression specifically has the concentrations of these substances at equilibrium, whereas the reaction quotient is not at equilibrium. Over here in this chart, what we're going to do is compare the reaction quotient with the equilibrium constant. Because if we know the equilibrium constant and we also know the concentrations of the substances at any particular moment in the reaction, we can predict the direction of that reaction.
When the reaction quotient is smaller than the equilibrium constant, what that means is that the products are going to be very small in their amounts, and the reactants are going to be very large in their amounts. We'll have a whole bunch of reactant that's going to react and produce more product. So the reaction is going to proceed in a forward direction. When the reaction quotient is larger than the equilibrium constant, that means there's a whole bunch of product and only a little bit of reactant. We have a whole bunch of the product and that's going to go backwards and react to produce more of the reactants. When the reaction quotient is larger than the equilibrium constant, the reaction proceeds from right to left in a reverse direction or a backwards direction. Of course, when the reaction quotient is equal to the equilibrium constant, that means that we are at equilibrium. At equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction. Here, we can put two arrows, showing that at equilibrium, the reaction rates are the same going in both directions.
What you're able to see is that the reactants and the concentrations of the reactants and products impact the direction, and that is very apparent here. What's really important to note is that the concentrations are a part of the conditions of the reaction. In our next video, we're going to talk about how standard conditions impact the Gibbs free energy equation. I'll see you guys in that video.
Gibbs Free Energy (Standard Conditions)
Video transcript
So from our previous video, we know that we can predict the direction of a reaction just by having the equilibrium constant and the concentrations of reaction components. And so the concentrations are part of the conditions, and scientists use standard conditions to allow them to compare different reactions under the same conditions since the conditions have a big impact on the reaction. And this little symbol here is used to represent standard conditions. Now recall from your previous chemistry courses that the equilibrium constant can be used to calculate the change in free energy under standard conditions. And so, recall that the little symbol here delta, which is this triangle here, represents change. G represents the free energy. And again, this little symbol here, °, represents standard conditions. So this is the change in free energy under standard conditions. Now, the \( \Delta G \) without the NOT symbol represents the actual change in free energy under any conditions, and we'll talk about that one in our next video.
So recall that standard conditions include, having a temperature at 25 degrees Celsius, which is equivalent to 298 Kelvin. It also includes having a gas constant or \( R \) here, which is equal to 8.315 joules per mole kelvin. And so the gas constant, magnitude here, the value of this number, can actually change depending on the units. And so you might be familiar with a number \( 1.98 \times 10^{-3} \), and this is when the units are in kilocalories per mole kelvin. And so it's good to be able to recognize that the gas constant can change depending on the units. And so, the pressure, the atmospheric pressure under standard conditions is 1 atmosphere and the concentrations of reactants and products, the initial concentrations, are 1 molar. And so you can see over here on the left that the Gibbs free energy under standard conditions is specifically shown as the following equation, where the change in free energy under standard conditions is equal to negative \( R \) or negative gas constant times the temperature in units of Kelvin, times the natural log of the equilibrium constant under standard conditions.
And so we'll be able to apply this equation in some of our practice problems. Now, in our next video, we're going to talk about the Gibbs free energy under physiological conditions, which vary from standard conditions. So I'll see you guys in that video.
Gibbs Free Energy (Physiological Conditions)
Video transcript
So in our previous video, we talked about how scientists use standard conditions to compare different reactions under the same conditions. Standard conditions occur in a very controlled environment within a test tube inside a lab. However, physiological conditions within biological systems or living things can vary greatly from standard conditions. It’s important to note that by studying a particular reaction within a test tube in a lab under standard conditions, we're able to determine the change in free energy under standard conditions. We can use this change in free energy under standard conditions to calculate the actual change in free energy under any condition, or delta G without the knot. As shown in the Gibbs free energy equation under any condition, this equation is used to calculate the change in free energy under physiological conditions. The change in free energy under any condition is equal to the change in free energy under standard conditions plus the gas constant times the temperature in Kelvin times the natural log of the reaction quotient.
In this example, we are going to calculate the change in free energy under standard conditions and the actual change in free energy. We consider a specific reaction that occurs in glycolysis. Recall from your previous biology courses that glycolysis is the process of taking a glucose molecule and breaking it down into two pyruvates. Here's a specific reaction that occurs within glycolysis: it takes a reactant known as dihydroxyacetone phosphate or DHAP, and converts this reactant into the product of Glyceraldehyde 3-phosphate or G3P. The equilibrium expression, under standard conditions, is simply the concentrations of products at equilibrium over the concentrations of reactants at equilibrium. The equilibrium constant under standard conditions is given to us as 0.0475. Recall that delta G under standard conditions is equal to negative R times the temperature times the natural log of the equilibrium constant under standard conditions. We plug in our values here to calculate the change in free energy under standard conditions. R here is equal to 8.315 Joules per mole Kelvin, the temperature under standard conditions is 298 Kelvin. The calculation yields a delta G under standard conditions of 7550 Joules per mole. This positive delta G indicates that the reaction under standard conditions is an endergonic or non-spontaneous reaction. However, since glycolysis occurs regularly in our cells, we need to determine the actual delta G under physiological conditions to determine the spontaneity of the reaction within a cell.
The concentration of DHAP under physiological conditions is 2 x 10-4 molar and the concentration of Glyceraldehyde 3-phosphate is 3 x 10-6 molar. The quotient Q is the concentration of our product, G3P at 3 x 10-6 M, over the concentration of reactant, DHAP at 2 x 10-4 M. After calculation, the resultant delta G under physiological conditions is -2856.32 Joules per mole. The negative value indicates that the reaction is a spontaneous exergonic reaction under physiological conditions, which aligns with the fact that glycolysis is an ongoing process in our cells.
This summary explains the Gibbs free energy under physiological conditions well, and I'll see you guys in our practice videos.
Consider a reaction where Keq=1.6 but Q = 3.19. What direction will the reaction proceed?
At equilibrium, the reaction A ⇌ B + C has the following reactant concentrations: [A] = 3 mM, [B] = 4 mM, and [C] = 10 mM. What is the standard free energy change for the reaction & is it endergonic or exergonic?
ΔG˚=141.7 kJ for the following reaction. Calculate ΔG: T=10˚C, [SO 3] = 25mM, [SO2] = 50mM, & [O2] = 75 mM.
2 SO3(g) ⇌ 2 SO2(g) + O2(g)
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What is Gibbs free energy and why is it important in chemical reactions?
Gibbs free energy (ΔG) is a thermodynamic quantity that represents the amount of energy available to do work in a chemical reaction. It is crucial because it helps predict whether a reaction will occur spontaneously. The equation for Gibbs free energy is:
where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous reaction, while a positive ΔG means the reaction is non-spontaneous.
Created using AIHow do you calculate Gibbs free energy under standard conditions?
To calculate Gibbs free energy under standard conditions (ΔG°), you can use the following equation:
where R is the gas constant (8.315 J/mol·K), T is the temperature in Kelvin (usually 298 K), and K is the equilibrium constant. This equation helps determine the spontaneity of a reaction under standard conditions, which include 25°C, 1 atm pressure, and 1 M concentration of reactants and products.
Created using AIWhat is the difference between the reaction quotient (Q) and the equilibrium constant (K)?
The reaction quotient (Q) and the equilibrium constant (K) are both ratios of the concentrations of products to reactants, but they differ in their application. Q is used to describe the state of a reaction at any point in time, while K specifically describes the state at equilibrium. The expressions for Q and K are:
If Q < K, the reaction proceeds forward; if Q > K, it proceeds backward; if Q = K, the reaction is at equilibrium.
Created using AIHow do physiological conditions affect Gibbs free energy calculations?
Physiological conditions often differ from standard conditions, affecting Gibbs free energy (ΔG). Under physiological conditions, ΔG can be calculated using:
where ΔG° is the Gibbs free energy under standard conditions, R is the gas constant, T is the temperature in Kelvin, and Q is the reaction quotient. This equation accounts for the actual concentrations of reactants and products in a biological system, providing a more accurate measure of reaction spontaneity in living organisms.
Created using AIWhat is the significance of ΔG being zero at equilibrium?
When ΔG is zero at equilibrium, it indicates that the system is in a state of balance, with no net change in the concentrations of reactants and products. This means that the forward and reverse reactions occur at the same rate, and no work can be done by the system. The equation for this state is:
At equilibrium, the system has reached its lowest possible free energy state, and any deviation from this state will result in a shift to restore equilibrium, as described by Le Chatelier's principle.
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