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Chemical Equilibrium
Equilibrium is a state of a system where the entropy is at its maximum and
the free energy is at its minimum
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In chemical reactions, equilibrium is reached
when all the measurable properties such as moles, pressure, and
concentration become constant
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Graphical Overview of Equilibrium
Let's understand equilibrium with the help of a graph
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Initially,
at time t = 0, we have 10 moles of reactant A
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Eventually,
there will be a point where the rate of the forward reaction is equal to the
rate of the backward reaction, and this is called the equilibrium state
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At equilibrium, the
concentration of reactants and products becomes constant
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The number of moles of
reactants and products does not change at equilibrium
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The concentration of reactants and products can be
represented graphically over time
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These different scenarios can be
represented by different graphs
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At
this point, the system is most stable
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The concentration of reactants
decreases with time and then becomes constant, while the concentration

of products increases with time and then becomes constant
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The concentration
of reactants can be greater than, equal to, or less than the concentration
of products at equilibrium
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For substances in
pure liquid state, the active mass is typically taken as unity
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Gaseous substances can be represented by either concentration or
pressure
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The equilibrium constant expression is written by placing the active mass
of products in the numerator and the active mass of reactants in the
denominator
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Kc
is used when the active masses are replaced by concentrations, while Kp is
used when the active masses are replaced by partial pressures
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In a reaction involving gaseous reactants, we can write the Kc
expression as the concentration of H2 multiplied by the concentration of
I2, divided by the concentration of HI
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For reactions involving aqueous substances, the active mass is represented
by concentration
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However, for reactions
involving solids and gases, the expression for Kp cannot be written
because the active mass of solids is unity
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Gaseous Reactants

When calculating Δng for a reaction, you only need to consider the
reactants and products that are in the gaseous state
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

Δng for the first reaction is 0



Δng for the second reaction is 1

To write the Kp expression, start with the product and divide it by the
concentration of the reactant raised to the stoichiometric coefficient
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There is a relation between Kp and Kc: Kp = Kc * (RT)^(Δng)
For the first reaction, Kp = Kc
For the second reaction, Kp = Kc * RT
For the third reaction, Kp = Kc * (RT)^(-2)
Units of Kp and Kc are calculated as moles per liter raised to the power of
Δng
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These constants provide information
about the concentrations of reactants and products in a reaction mixture
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Characteristics of Equilibrium Constants


If a reaction is multiplied by a number, the equilibrium constant is
raised to the power of that number
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

When two reactions are added, the equilibrium constants are
multiplied
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The equilibrium
constant (K) for this reaction is given as 49
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Solution

To calculate the equilibrium constant for the given reaction, we need to
reverse the original reaction and then multiply it by a factor of 1/2
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Relation between Equilibrium Constants

Consider two reactions with equilibrium constants K1 and K2
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If the first
reaction is multiplied by a number n, the equilibrium constant becomes
K1^n
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K Dash Relation and Equilibrium
Constants
In this passage, we will discuss the K Dash relation and how it relates to
the equilibrium constant
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K Dash Relation
The K Dash relation is a mathematical equation that relates the equilibrium
constant (K) to its square root (K Dash)
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This relationship can be derived by multiplying the
balanced equation by a factor of 1/2, which results in the exponent of 1/2
in the equilibrium constant
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Kp is
the equilibrium constant expressed in terms of partial pressures, while Kc
is expressed in terms of concentrations
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If Δng is zero, then Kp and Kc will be equal
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Calculating Kp and Kc using the Mole Method
There are two methods to calculate Kp and Kc for a reaction: the mole
method and the degree of dissociation method
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The mole method involves determining the number of moles of reactants
and products at equilibrium and using these values to calculate the
concentrations of the species
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Let's consider a generic reaction:
aA (g) ⇌ bB (g) + cC (g)
To calculate the values of Kp and Kc, we need to know the number of
moles of reactants and products at equilibrium
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The concentrations of A, B, and C at equilibrium can be calculated using
the formula:
[A] = (a - x) / V
[B] = x / V
[C] = x / V
Where [A], [B], and [C] represent the concentrations of A, B, and C at
equilibrium, and V represents the total volume of the container
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Partial Pressure and Equilibrium
The total pressure of a mixture is the sum of the partial pressures of each
component
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Calculating Kp
To calculate the equilibrium constant Kp, we need the partial pressure of
each reactant and product at equilibrium
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At equilibrium, the concentration of
C is 0
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We need to calculate Kc
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We can assume that x moles of A react with B
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The concentrations can be calculated by
dividing the moles by the volume:


Concentration of A at equilibrium: (2 - x)/10



Concentration of B at equilibrium: (1 - x)/10



Concentration of C at equilibrium: x/10

Given that the concentration of C at equilibrium is 0
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5
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Finally, we
can write the Kc expression using the concentrations and stoichio metric
coefficients
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5 moles of Y, and 0
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At equilibrium, the concentration of Z is 1
M
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Using similar steps as in Example 1, we can calculate the concentrations of
X, Y, and Z at equilibrium
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Substituting these values back into the
expressions, we can calculate the concentrations of X and Y at equilibri um
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Calculating the Value of x
In this problem, we are given the reaction n2 gas + 3 times h2 gas → 2
times nh3 gas
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To solve this, we assume that at equilibrium, x moles of the reactant have
reacted with y moles of another reactant
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One mole of the first reactant reacts with one mole of
the second reactant, so x moles of the first reactant gives 2x moles of the
product
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5 moles of another
reactant present in the container
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We then
solve the equation to find the value of x
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We
substitute the given values and solve the equation to find the value of x
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If the reaction is taking place at constant volume and
temperature, we know that pressure is directly proportional to moles
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As the moles of b and c increase with time, the pressure due to b and c
will also increase, causing the pressure due to a to decrease
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So, the same
treatments applied to the moles can be directly applied to the pressure
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At equilibrium, the pressure due to a
will be p0-x, where x is the number of moles of a that have reacted
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The equilibrium constant (Kp) expression can be written as the partial
pressure of b at equilibrium (x^1) divided by the partial pressure of a at
equilibrium (p0-x), raised to the stoichiometric coefficient (1/1), multiplied
by the partial pressure of c at equilibrium (x^1) divided by the partial
pressure of a at equilibrium (p0-x), raised to the stoichiometric coefficient
(1/1)
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For
example, if the reaction is a gas in equilibrium with 2 times b gas plus 3
times c gas, the equilibrium pressures can be calculated using the same
approach
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This can be used to determine the moles of
reactants and products at equilibrium

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