Chapter 4: Free Energy and Chemical Equilibria Flashcards

1
Q

What is Gibbs free energy?

A

Gibbs Free Energy (G): It tells you whether a chemical reaction is likely to occur or not. If G is negative, the reaction is spontaneous and will proceed and head towards equilibrium. If G is positive, the reaction is not spontaneous and will not occur without an external energy source. ΔG = 0: The system is at equilibrium, and there is no net change.

In even simpler terms, you can think of Gibbs free energy as the “energy currency” of chemical reactions. If a reaction has a negative Gibbs free energy, it has enough energy “money” to happen on its own. If it has a positive Gibbs free energy, it doesn’t have enough energy “money” and won’t occur without a push (like adding heat or energy from another source).

measures the energy available to do work in a system AT CONSTANT TEMPERATURE AND PRESSURE.

G = H - TS

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2
Q

What does equilibrium mean? come back to this

A

Equilibrium: When a reaction is at equilibrium, it means that the forward and reverse reactions are happening at the same rate, and there is no net change in the concentrations of reactants and products over time. At equilibrium, the Gibbs free energy change is zero. This implies that the system has reached a stable state, and no more work can be done.

When a reaction reaches equilibrium, it means that the system has the composition that minimizes Gibbs free energy, indicating that it’s stable.

At equilibrium: rate forward = rate reverse

When a chemical reaction reaches equilibrium at a constant temperature and pressure, the system has found a balance between the reactants and products.

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3
Q

What is Gibbs free energy?

A

Gibbs Free Energy (G): It tells you whether a chemical reaction is likely to occur or not. If G is negative, the reaction is spontaneous and will proceed and head towards equilibrium. If G is positive, the reaction is not spontaneous and will not occur without an external energy source. ΔG = 0: The system is at equilibrium, and there is no net change.

In even simpler terms, you can think of Gibbs free energy as the “energy currency” of chemical reactions. If a reaction has a negative Gibbs free energy, it has enough energy “money” to happen on its own. If it has a positive Gibbs free energy, it doesn’t have enough energy “money” and won’t occur without a push (like adding heat or energy from another source).

measures the energy available to do work in a system at constant temperature and pressure.

G = H - TS

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4
Q

What is Partial Molar Gibbs Free Energy?

A

a concept used in thermodynamics and chemistry to understand how the Gibbs free energy of a substance changes when a small amount of that substance is added to a system. The term “partial” is used because it focuses on the change in Gibbs free energy for a specific component or substance within a mixture, rather than the entire system.

chemical systems consist of multiple substances interacting with each other. When we’re interested in how one particular substance’s presence affects the overall Gibbs free energy of the system, we use the concept of partial molar quantities. Instead of looking at the entire system’s Gibbs free energy change, we isolate our analysis to a specific substance’s contribution.

Can only add a very small amount to barely change the rest of the system.

In summary, “partial” in partial molar Gibbs free energy indicates that we are focusing on the change in Gibbs free energy for a specific component within a mixture.

Has an Equation***

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5
Q

Why is Gibbs free energy important

A

Gibbs free energy (G) is a fundamental concept in thermodynamics because of its prevelance in chemical reactions. Chemical reactions in cells are driven by changes in Gibbs free energy. When the reaction ends in a decrease of G, the reaction can occur. (lower G in end products than starting). Change in G is the driving force behind chemical reactions. Chemical reactions need to have a decrease in G to occur spontaneously. All processes depends on if they are energetically favorable or not. (-) G means it is.
Gibbs free energy is a type of energy available to do work (perform tasks or drive processes in a system)

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6
Q

The partial molar Gibbs free energy of a species is often referred to as?

A

Its chemical potential (μ)

The chemical potential
is defined as the partial molar Gibbs free energy for reactions occurring at the common
biological conditions of constant temperature and pressure

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7
Q

What is chemical potential?

A

-Think of chemical potential as a measure of how much a substance “wants” to undergo a chemical change or reaction.

-If a substance has a higher chemical potential compared to others in the system, it means that it has a stronger “desire” to react or change. This suggests that, under the right conditions, it will tend to participate in a chemical reaction.

-Chemical potential provides insight into what drives chemical reactions. Substances with higher chemical potentials are like the eager participants in a reaction, and they will tend to react with other substances to lower their chemical potential and move toward a more stable state.

  • chemical potential helps us understand which chemical reactions are likely to occur in a given set of conditions.

-Chemical potential (μ) is a way to quantify the “desire” of a substance to undergo a chemical reaction. Just like the ball on the hill wants to roll down, a substance with a higher chemical potential “wants” to undergo a chemical change or reaction.

-Chemical potential becomes more meaningful when we compare it to other substances in the same system. If Substance A has a higher chemical potential than Substance B, it means Substance A has a stronger “desire” or tendency to react or change compared to Substance B.
Driving Force for Reactions: In a chemical reaction, substances will tend to change in a way that reduces their chemical potential. It’s like the ball rolling down the hill to reduce its potential energy. Similarly, in chemistry, substances react to lower their chemical potential. This drive to lower chemical potential is what makes chemical reactions happen spontaneously.
Equilibrium: At equilibrium, the chemical potentials of all substances involved are equal. This means there’s no net “desire” for any substance to change further

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8
Q

If the reactants are at a higher overall chemical potential than the products, then
how will the reaction proceed?

A

The reaction will proceed spontaneously in the forward direction.

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9
Q

The chemical potential is invariably measured relative to what? How?

A
  1. to the standard chemical potential of the same substance under a chosen set of conditions, its standard
    state.
    (its regularly compared to the standard chemical potential)(μ°)

Standard chemical potential is the chemical potential of a substance in its standard state. It represents the chemical potential of a substance under the conditions of the standard state.

the standard chemical potential is the chemical potential of a substance when it is in its standard state.

  1. By comparing the actual behavior of the substance (μ) to how it behaves in its standard chemical potential (μ°), we can see if it’s more or less eager to react or change in the current conditions.
    Variables: We can express this difference (μ - μ°) in terms of variables we understand, like temperature, pressure (if it’s a gas), or concentration (if it’s a solute).
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10
Q

To understand the chemical potential (μ) of a substance, what do we do?

A

We compare it to it’s standard chemical potential (μ°). This reference state is like a baseline or a standard condition that we use for comparison.

  1. By comparing the actual behavior of the substance (μ) to how it behaves in its standard chemical potential (μ°), we can see if it’s more or less eager to react or change in the current conditions.
    Variables: We can express this difference (μ - μ°) in terms of variables we understand, like temperature, pressure (if it’s a gas), or concentration (if it’s a solute).

represents the difference between the actual chemical potential (μ) of a substance under specific conditions and its standard state chemical potential (μ°)

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11
Q

What is a standard state?

A

The standard state refers to a specific set of conditions under which the thermodynamic properties of a substance are defined. These conditions are chosen as a reference point for comparing and understanding chemical reactions. For gases, the standard state is often 1 bar (standard atmospheric pressure) pressure. For solutes in solutions, it’s often 1 molar concentration. Standard state conditions also specify a particular temperature, which is typically 25°C (298.15 K)

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12
Q

How is the composition of a reaction at equilibrium determined ?

A

the specific composition at equilibrium is determined by the standard chemical potentials of the substances involved. In simpler terms, the balance between reactants and products at equilibrium is guided by the inherent tendencies of these substances to react, as indicated by their standard chemical potentials.

-The equilibrium composition of a chemical reaction is determined by the standard chemical potentials of the substances involved in the reaction. In other words, the conditions at which the Gibbs free energy is minimized, as indicated by these standard chemical potentials, define the composition of a reaction at equilibrium.

-Understanding the standard chemical potentials of substances involved in a reaction helps us determine the equilibrium composition of that reaction.

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13
Q

What is Le Châtelier’s Principle?

A

-This principle describes how a system at equilibrium responds to external changes, such as changes in temperature, pressure, or concentration. Understanding how these changes affect the chemical potentials of species helps in predicting the direction in which the equilibrium will shift.

-how perturbations (changes) to a chemical system affect the chemical potentials of the species

the specific composition at equilibrium is determined by the standard chemical potentials of the substances involved. In simpler terms, the balance between reactants and products at equilibrium is guided by the inherent tendencies of these substances to react, as indicated by their standard chemical potentials.

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14
Q

What are some practical applications of thermodynamic analysis discussed in the chapter?

A

(1) metabolic reactions in which chemical bonds are broken and new ones formed,
( 2 ) d i s s o c i a t i o n o f H
+
from acidic compounds and binding of H
+
t o b a s e s , ( 3 ) o x i d a t i o n –
reduction reactions in which electron transfer occurs, (4) interactions involving the aqueous
medium in which metabolites and ionic species occur in the cytoplasm or other biological
fluids, and (5) the assembly and disassembly of membranes and other multicomponent
cellular structures.

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15
Q

What are partial derivatives ?

A

describe
changes in thermodynamic
quantities when one system
parameter is altered.

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16
Q

Chemical potential describes how much the free energy of a system changes when what changes?

A

When the number of moles of that substance (A) changes

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17
Q

Explain the chemical potential fo a substance A equation.

μ A =( ∂G / ∂nA) T,P,nj=/nA

A

The chemical potential of a substance (such as A) is defined as the partial molar Gibbs free energy of that substance under constant temperature (T) and pressure (p), when the quantities of all other chemicals (B, C, D, etc.) in the system remain constant. here the notation nj nA specifies that the molar quantities of all other chemicals
present in the system is also constant

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18
Q

the chemical potential of A depends on what?

A

Depends on what else is present. (composition of the system, represented by nj).

The presence of other substances influences this attractiveness

Understanding how the attractiveness (chemical potential) changes when you add or remove molecules (change the number of moles)

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19
Q

chemical potential vs chemical potential of pure A

A

For chemical potential, A is in a mixture with other substances.

For pureA, G m,A specifically applies to a scenario where only pure A is present in the system.

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20
Q

In an open system, the Gibbs free energy (G) is a function of?

A

temperature, pressure, and the number of moles of different chemical species (nA, nB, nC, nD).

***Equation

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21
Q

What is total differential (dG)

A

It considers how Gibbs free energy changes concerning multiple variables simultaneously, such as temperature (
T
T), pressure (
P
P), and the number of moles of various substances (
It provides a complete picture of how Gibbs free energy is affected by changes in all these variables at once.

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22
Q

What is the sum rule/equation for for partial molar quantities?

A

The equation states that the total Gibbs free energy (G) of the system is equal to the sum of the products of the number of moles of each component (nA, nB, nC, and nD) and their respective chemical potentials (μA, μB, nC, and μD). This equation holds under constant temperature and pressure conditions.

G= nAμA, nBμB, nCμC, and nDμD

EXPLANATION: Starting with a System: Imagine a system containing small amounts of substances A, B, C, and D. You’re gradually adding infinitesimal amounts of these substances to the system, always in proportion to their existing amounts in the mixture. This ensures that the composition of the system remains the same as the quantities of A, B, C, and D increase.
Keeping Chemical Potentials Constant: During these additions, the chemical potentials of the components (mA, mB, mC, and mD) are kept constant. This means the system is being modified without changing the chemical potential of any component.
Integration of Gibbs Free Energy: By integrating the infinitesimal changes in Gibbs free energy (dG) with respect to the infinitesimal changes in the number of moles of each component (dnA, dnB, dnC, and dnD), the equation (4.4) is derived.

**Equation

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23
Q
A

The total volume V of a system containing components A, B, C,
and D, for example, is equal to nAyA+nByB+nCyC+nDyD, where yA, yB, yC, and yD
are the partial molal volumes of the components.

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24
Q

dξ is what? Positive and negative dξ mean the reaction heads in which direction?

A

a measure of the extent of the reaction.
It’s a measure of how far the reaction has progressed from its initial state to its current state.

Positive dξ means dnA and dnB are negative and dnC and dnD are positive: the amounts of A and B are decreasing, and those of C and D are increasing and the reaction is proceeding from left to right.
Conversely, a
negative dξ means the reaction is proceeding from right to left.

As the reaction proceeds, the values of
dξ change, indicating the progress of the reaction. When
dξ is positive, it signifies that the reaction has proceeded in the forward direction (from left to right in the reaction equation), and when it’s negative, it means the reaction has proceeded in the reverse direction (from right to left in the reaction equation).

For a chemical reaction of the form

aA+bB⇌cC+dD, the extent of the reaction dξ could represent, for instance, the number of moles of A that have reacted (or products formed) up to a certain point in time.

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25
Q

The value (dG) is crucial because?

A

It determines the directionality of the reaction. If dG is negative, the reaction is spontaneous in the given direction.

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26
Q

the Gibbs free energy change (dG) for an ideal gas at constant temperature ?

A

dG=Vdp,

btw Ideal gases are a theoretical concept in thermodynamics. These gases follow specific rules, making them simpler to study.

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27
Q

When the pressure of the gas changes from p1 to p2
the change in Gibbs free energy (G) is given by ?

A

G(p 2) −G(p 1) =nRTln(p2/p1)

We will now designate p1 =1 bar as the standard state and denote G(p1 =1 bar) as G °
G-G ° =nRT ln(p/1 bar)

Dividing both sides by n and remembering that the chemical potential of a pure substance
is its molar free energy, we obtain
μ=μ°+RT ln a (p/1 bar)

28
Q

If gas A is part of a mixture with a partial pressure (pA)the chemical potential of gas A (μA) in the mixture is given by?

This equation applies to individual gases within a mixture, allowing the calculation of their chemical potentials based on their partial pressures.

A

μA=μ°A+RT lm(pA/1 bar)

29
Q

Difference between μ=μ°+RT ln a (p/1 bar) and μA=μ°A+RT lm(pA/1 bar) equations?

A
  1. This equation represents the chemical potential μ of a substance (not necessarily a gas, it could be any substance) at a given pressure (p) relative to its chemical potential at the standard state μ° when the pressure is 1 bar. This equation is a general form and can apply to any substance, not just gases. It describes how the chemical potential changes with pressure for a specific substance.

2.This equation specifically applies to an ideal gas component A within a gas mixture. It represents the chemical potential (μA ) of this particular gas component at a partial pressure (pA ) within the mixture, relative to its chemical potential at the standard state (μ°A)
when the partial pressure is 1 bar. This equation focuses on a specific gas component within a mixture and describes how its chemical potential changes concerning its partial pressure.

In summary, the first equation is a general expression for the chemical potential of any substance concerning its pressure, while the second equation is specific to a particular gas component (A) within a gas mixture, describing its chemical potential concerning its partial pressure.

30
Q

What is Q?

A

Definition:
Q
Q is a measure of the relative amounts of products and reactants in a chemical reaction at any given moment. It is calculated using the same formula as the equilibrium constant (K)but with partial pressures of substances at non-equilibrium conditions.

31
Q

What occurs if Q>K or Q<K?

A

Q tells us about the current state of the reaction, whether it’s closer to equilibrium or favoring reactants/products. If
Q
<
K
Q<K, the reaction will proceed in the forward direction (towards products) to reach equilibrium. If
Q
>
K
Q>K, the reaction will proceed in the reverse direction (towards reactants) to reach equilibrium.

32
Q

What is K? Difference betweenQ and K?

A

Equilibrium Constant (
K
K): This represents the ratio of product concentrations to reactant concentrations at equilibrium for a chemical reaction. If
K>1 products are favored at equilibrium. If K<1, reactants are favored at equilibrium
tells you about the balance between reactants and products once a reaction has reached equilibrium.

Q represents the same ratio but at any point during the reaction, not just at equilibrium. It helps us understand whether the reaction has reached equilibrium yet.
It helps you understand which direction the reaction is currently favoring

33
Q

How is dG related to K and Q?

A

its related to Q and K through the equation dG=RTln(Q/K)

34
Q
A

pg 107 for equations

35
Q

What does activities mean?

A

Activities, denoted as aA, are unitless numbers that describe how a substance behaves compared to an idealized standard state.

activity, which accounts for non-ideal behavior in solutions

For any substance A, its activity is defined by the equation:

The activity of a substance A is related to its chemical potential (μA) by the equation:
μA=μA0+RTlnaA

μA represents the chemical potential of A.μ A0 is the chemical potential of A at the standard state, R is the gas constant, andT is the temperature.

Activity is introduced to handle non-ideal systems, including real gases, liquids, solids, and solutions besides ideal gases.

36
Q

μA=μA0+RTlnaA describe this equation

A

uses (μA−μ°A)​ to calculate the chemical potential in a non-standard state based on the substance’s activity.

37
Q

Which equation represents the difference in chemical potential between the substance A in its actual state and its standard state. What is the significance of this equation?

A

the difference in chemical potential
(μA−μ°A)​between the actual state and the standard state.

This difference is divided by RT to obtain the activity. If a substance is in its standard state, its activity (aA) is 1

It is often used to calculate the change in chemical potential (Δμ) for a substance when it transitions from the standard state to a non-standard state.

Significance: If this difference is known, it can be used to calculate the activity (aA) using this equation: μA=μA0+RTlnaA This equation helps to determine the deviation of a real substance from an idealized standard state.

38
Q

The concept of activity is applied to chemical reactions how?

A

ΔG=ΔG °+RTlnQ
Here, Q is the reaction quotient based on activities (aA ), and ΔG °represents the standard Gibbs free energy change. At equilibrium, ΔG=0, and Q equals the equilibrium constant (K)

39
Q

Standard State and Activity: If a substance is in its standard state, its activity must be?

A

1 (ideal behavior)

40
Q

For gases, the standard state is often defined as a pressure of ? For solutions, it’s often defined as a concentration of ?
For ideal gases they have a partial pressure of?

A

1 bar.

1 molar (1 M).

1 bar

41
Q

why are standard states important

A

The choice of standard states is crucial because it defines the reference point for ideal behavior.

Different standard states are chosen for different forms of matter (gases, liquids, solids, solutions)

a consistent reference point

42
Q

What is the standard state for an ideal gas?

A

The standard state for an ideal gas is when the gas has a partial pressure of 1 bar (a unit of pressure).

The
notation for the standard pressure is pA° =1 bar representing the standard pressure for the gas component A.

43
Q

What is the activity for ideal gases?

A

The activity of an ideal gas is defined as
its actual partial pressure divided by its standard pressure
aA=pA/p°A=pA/1 bar

44
Q

In the standard state, the partial pressure and the activity are ?

A

numerically equal because the standard state is defined as having a partial pressure of 1 bar.

45
Q

What is the the activity coefficient (γA)?

A

In the context of real gases, the activity coefficient (γA) accounts for the deviation of a real gas from ideal behavior. Ideal gases follow the ideal gas law perfectly, but real gases deviate from this behavior under certain conditions, especially at high pressures. The activity coefficient adjusts the partial pressure of a real gas to account for these deviations and ensures that the chemical potential is accurate.

The activity coefficient is a correction factor used to adjust the partial pressure of a real gas to make it comparable to an ideal gas under the same conditions. It accounts for nonideal behavior and varies with pressure and temperature.

how a real gas deviates from ideal behavior at different pressures

46
Q

When γA is 1, how does the gas behave?

A

the gas behaves ideally.

47
Q

What does (μA−μ°A)​ mean?

A

the chemical potential of the gas matches its standard state, meaning it behaves ideally at that pressure.

48
Q

when do real gases behave more like ideal gases, at low or high pressures?

A

low pressures

49
Q

The standard state for a pure solid or liquid ?

the activity of the pure solid or liquid substance is ?

A

The standard state for a pure solid or liquid is when the substance exists in its natural state as a solid or liquid at a pressure of 1 bar (or 1 atmosphere) and a specific temperature.
Activity Value: In this standard state, the activity of the pure solid or liquid substance is defined to be 1. This means that the substance in its natural state at 1 bar has an activity of 1.

50
Q

Why is the activity of a pure solid or liquid is considered to be 1 at any pressure.

A

The Gibbs free energy of a pure solid or liquid changes only slightly with pressure. Therefore, in practical terms, the activity of a pure solid or liquid is considered to be 1 at any pressure. This simplifies calculations and allows for consistent comparisons of thermodynamic properties.

51
Q

what is a solution?

A

a homogeneous mixture composed of two or more substances.

a homogeneous mixture is like a uniform blend, where everything is so evenly mixed that you can’t distinguish the individual components, even with a microscope

52
Q

In the context of solutions, the activity of a substance is influenced by?

A

the activity of a substance is influenced by its concentration as well as the concentrations of all other substances present in the mixture.

The relationship between activity and concentration in solutions is described by the equation:

Activity= (Activity Coefficient)×
(Concentration Value/Standard Concentration Value)

Key points to note about this equation:

Activity Coefficient (
γ
γ): The activity coefficient is a measure of how the activity of a substance in a solution deviates from ideal behavior. It incorporates the complex influence of the concentrations of all components in the solution on the activity of the substance of interest. The activity coefficient is not a constant and varies depending on the specific solution conditions.
Concentration Value: This represents the actual concentration of the substance in the solution. It could be expressed in various units such as molarity (moles per liter), molality (moles per kilogram of solvent), or mole fraction (moles of the solute divided by total moles of all components in the solution).
Standard Concentration Value
∘[A] : The standard concentration value is a reference concentration used to define the standard state for the substance in the solution. The choice of standard concentration depends on the context and can vary based on the units used.
Units: It’s important to note that different concentration units can be used in the equation, such as molarity, molality, or mole fraction. The appropriate unit depends on the specific situation and the properties being studied.

53
Q

describe mole fraction use:

A

Mole fraction (x)is a way to express the concentration of a component in a solution. For a component A in a solution containing multiple components, the mole fraction (xA) of A is calculated by dividing the number of moles of A (nA) by the total number of moles of all components in the solution (nT) It’s represented as:

xA=nA/nT

54
Q

meaning of solvent standard state?

A

In many solutions, especially those involving water (H2O) as a solvent, it’s common to designate one component as the solvent. The solvent standard state is a way to define the standard state for this solvent in terms of its mole fraction (x).

For the solvent, the standard state mole fraction (x°A) is defined as 1 because it represents the pure component.

55
Q

How is The activity (a) of the solvent in the solution expressed?

A

The activity (a) of the solvent in the solution can then be expressed using its mole fraction (xA) and an activity coefficient (γA):
aA=γAxA

56
Q

In the case of very dilute solutions, where the solvent is essentially pure, the activity of the solvent is?

In dilute solutions or ideal solutions, the activity of the solvent is ?

In real solutions, where interactions between components affect the behavior, the activity of the solvent is?

A

1 (asolv=1)

equal to its mole fraction (asolv=xsolv)

it is given by the product of its mole fraction and an activity coefficient
(asolv=γsolvxsolv)

57
Q

What was made for components(solutes) that are typically found in very low concentrations in solutions.

A

For these kinds of solutions, scientists define a solute standard state.This standard state is a hypothetical state where the concentration of the solute is precisely 1 molar (M) or 1 molal (m), but the properties are extrapolated from very dilute solutions. In other words, it represents the behavior of a solute in an ideal solution where its concentration is exactly 1 M or 1 m.

58
Q

Concentrations are commonly measured in ?

A

molarity, with units of mol L-1=M

(We
use the symbol c for molarities.)

Molarity is a measure of the concentration of a solute in a solution.

59
Q

What is molarity?

A

Molarity is a measure of the concentration of a solute in a solution. It represents the number of moles of solute per liter of solution. The symbol used for molarity is c. So, if you have 1 mole of solute in 1 liter of solution, the molarity is 1 M.

60
Q

What is the activity (a) of a solute?

what is the activity coefficient (γ) ?

A

The activity represents its effective concentration in a non-ideal solution. It takes into account deviations from ideal behavior due to interactions between solute molecules.

The activity coefficient (γ) is a measure of how the activity deviates from the ideal behavior.

61
Q

What is the standard State for Molarity?

A

The standard state in the context of molarity is a reference state used to calculate activities of solutes in solutions. For a solute in a solution, we want its activity (
a
a) to be equal to its concentration (
c
c) as the concentration approaches zero (
c

0
c→0). In other words, we want the activity to be equal to the concentration in very dilute solutions. However, in real solutions, especially at higher concentrations, the activity is not equal to the concentration due to non-ideal behavior, which is represented by the activity coefficient (
γ
γ).

62
Q

what is molality?(m)

A

Molality (m) is a concentration unit used in chemistry, representing the number of moles of solute dissolved in 1 kilogram of solvent. Unlike molarity, which is based on volume and can vary with temperature, molality is defined by weight and is temperature-independent. Molality is particularly useful in thermodynamic measurements because it provides accurate and consistent results regardless of temperature changes.

63
Q

Activity in Terms of Molality:

A

The activity of a solute in a solution can be expressed in terms of molality (mB) and the activity coefficient (γB ) as
aB=γBmB
This equation indicates that the activity (aB) of the solute B is equal to its molality (mB) multiplied by the activity coefficient (γB).

64
Q

Standard State and Extrapolation:

A
65
Q
A