MPBSE Class 11 Chemistry Notes For Entropy

Entropy Class 11 Chemistry Notes

MPBSE Class 11 Chemistry Notes For  Concept Of Entropy

We have already seen that enthalpy is not the ultimate criterion of spontaneity. Another factor such as the randomness of the constituting particles (molecules, atoms, or ions) of the system may also be responsible for determining the spontaneity of a process.

Rudolf Clausius introduced a new thermodynamic property or state function known as entropy, from the Greek word ‘trope’ meaning transformation. It is denoted by the letter ‘S’. The entropy of a system is a measure of the randomness or disorderliness of its constituent particles.

The more disordered or random state of a system, the higher the entropy it has. Thus, from the molecular point of view, the entropy of a system can be defined below.

Entropy In Thermodynamics Class 11

The entropy of the system is a thermodynamic property that measures the randomness or disorderliness of the constituent particles making up the system.

According to the above definition, it may seem that entropy is related to the individual constituent particle of the system. However, thermodynamics, whose framework is based on a macroscopic approach, is not concerned with the existence and the nature of the constituent particles of the system.

Entropy, which is a macroscopic property, is in no way related to the behavior of the individual atoms or molecules of a system, instead, it reflects the average behavior of a large collection of atoms or molecules by which a system usually consists.

MPBSE Class 11 Chemistry Notes For  Mathematical interpretation of entropy

Since heat (q) is not a state function, the exchange of heat (5q) i.e., the amount of heat absorbed or rejected by a system during a process is not an exact differential.

But in a reversible process, the ratio of the heat exchanged between the system and surroundings \(\frac{\delta q_{r e v}}{T}\) to an absolute temperature at which the heat exchanger takes place is an exact differential. Hence, the quantity indicates the change ofa state function. This function is called entropy (S). Therefore, the change in entropy,

⇒ \(d S=\frac{\delta q_{r e v}}{T}=\frac{\begin{array}{c}
\text { Reversible heat transfer between } \\
\text { system and its surroundings }
\end{array}}{\begin{array}{c}
\text { Temperature (K) at which } \\
\text { heat is transferred }
\end{array}}\) …………………………….(1)

a reversible process, the state of a system changes from state 1 (initial state) to state 2 (final state), then the change in entropy (AS) in the process can be determined by integrating the equation

⇒ \(\int_1^2 d S=\int_1^2 \frac{\delta q_{r e v}}{T} \text { or, } S_2-S_1=\int_1^2 \frac{\delta q_{r e v}}{T} \text { or, } \Delta S=\int_1^2 \frac{\delta \tilde{q} q_{r e t}}{T}\)

For the process occurring at a constant temperature, the change in entropy, \([\Delta S=\frac{1}{T} \int_1^2 \delta q_{r e v}=\frac{q_{r e v}}{T}.\)

Entropy In Thermodynamics Class 11

It is not possible to define entropy; however, we can define the change in entropy of a system ( dS or AS) undergoing a reversible process. It is defined as the ratio of reversible heat exchange between the system and its surroundings to the temperature at which the heat exchange takes place.

The relation tells us for a given input of heat into a system, the entropy of the system increases more at a lower temperature than at a higher temperature.

The randomness in a system is a measure of its entropy. The more randomness the more entropy. Therefore, for a given input of heat into a system, the randomness of the system increases more when heat is added to the system at a lower temperature than at a higher temperature.

MPBSE Class 11 Chemistry Notes For  Characteristics of entropy

The entropy of a system quantifies the unpredictability of its constituent particles. Entropy is a state function as its value for a system relies solely on the current state of the system, and its change (ΔS) during a process is determined exclusively by the beginning and final states of the system, independent of the pathway taken to execute the process.

• Being a state function, it is a quantity that is independent of the path taken. Entropy is an extended property, as its value for a system is contingent upon the quantity of matter within the system.
• The entropy of the cosmos grows in a spontaneous process (ΔSuniv > 0) and decreases in a non-spontaneous process (ΔSuniv < 0). At equilibrium, the change in entropy of the system is zero. At absolute zero, the entropy of a pure, perfect crystalline solid is zero.

MPBSE Class 11 Chemistry Notes For Physical significance of entropy

There exists a relationship between the entropy of the system and the randomness of its constituent particles (atoms, ions, or molecules).

The entropy of a system increases or decreases with the increase or decrease in randomness of the particles constituting the system. Therefore, entropy is the measure of the randomness of the constituent particles in a system. this is the physical significance of entropy.

Mpbse Class 11 Chemistry Notes Pdf

The change in entropy is defined in terms of a reversible process, for which it is defined as

⇒ \(d S=\frac{\delta q_{r e v}}{T}\) where 8qrev) Is the reversible exchange of heat between a system and its surroundings at 7’K. in case of an irreversible process, the change in entropy

⇒ \(d S \neq \frac{\delta q_{i r r}}{T}\) where 5<](rr represents irreversible exchange of heat between a system and its surroundings at 7’K.

As entropy is a state function, its change in a particular process does not depend on the nature of the process. Thus, the change in entropy in a process carried out reversibly is the same as the change in entropy that occurs if the same process is carried out irreversibly.

MPBSE Class 11 Chemistry Notes For  Unit of Entropy

In the CGS system, the unit of entropy = cal.deg-1, while the unit of entropy in SI = J. K^-1

Change In Entropy Of The System In Some Processes

When a system undergoes a process, its change in entropy in the process is ΔS = S₂ – S₁; where S₁ and S₂ are the entropies of the initial and final states of the system respectively, in a process.

In a process, if S₂ > S₁, then ΔS is positive. This means that the entropy of a system increases in the process. For example, the melting of ice or vaporization of water is associated with an increase in the entropy of the system, so AS is involved in these processes.

If S₂ < S₁, then ΔS is negative, indicating that the entropy of the system decreases in the process. For example, when ice is formed from liquid water or water is formed from water vapor, the entropy of the system decreases i.e., ΔS =-ve.

MPBSE Class 11 Chemistry Notes For  Change in entropy in a chemical reaction

In any chemical reaction, the initial entropy (S₁) of the system means the total entropy of the reactants, and the final entropy of the system (S₂) means the total entropy of the products.

Hence, the change in entropy in a chemical reaction, ΔS = \(S_2-S_1^{3 i}=\sum S_{\text {products }}-\sum S_{\text {reactants }} \text {, where, } \sum S_{\text {reactants }}\text { and } \sum S_{\text {products }}\)

Change in entropy of the system in a cyclic process:

The change in entropy of the system in any process, ΔS = S₂– S₁ where S₁ and S₂ are the initial and final entropies of the system, respectively. Because entropy is a state function, and in a cyclic process the initial and the final states of a system are the same, = S₂, and the change in entropy ofthe system, ΔS = 0.

MPBSE Class 11 Chemistry Notes For  Change in entropy of the system in a reversible adiabatic process

In an adiabatic process, heat exchange does not occur between a system and its surroundings. Therefore, in a reversible adiabatic process, q_rev = 0 and the change in entropy ofthe system in this process.

⇒ \(d S=\frac{\delta q_{r e v}}{T}=\frac{0}{T}=\mathbf{0} \text { or, } d s=0 \text { or, } \Delta S=0\)

Therefore, the change in entropy of a system undergoing a reversible adiabatic process is zero, i.e., the entropy of a system remains the same in an adiabatic reversible change. Owing to this a reversible adiabatic process is sometimes called an isentropic process.

Entropy Chemistry Class 11 Ncert Notes

Change in entropy of the system in an irreversible adiabatic process: Like reversible adiabatic process, heat exchange does not also occur in an irreversible adiabatic process. However, it can be shown that in an irreversible adiabatic process, the entropy change of a system is always positive, i.e., ΔS > 0.

MPBSE Class 11 Chemistry Notes For  Change in entropy of the system in an isothermal reversible process

Let us consider, a system change from state 1 to state 2 in an isothermal reversible process. Therefore, in this process, the change in entropy of the system.

⇒ \(\int_1^2 d S=\int_1^2 \frac{\delta q_{r e v}}{T} \text { or, } S_2-S_1=\frac{1}{T} \int_1^2 \delta q_{r e v} \text { or, } \Delta S=\frac{q_{r e v}}{T}\)

Since T= constant as the process is isothermal]

MPBSE Class 11 Chemistry Notes For  Change in entropy during a phase transition

Melting of a solid, vaporization of a liquid, solidification of a liquid, condensation of vapor, etc. are some examples of phase transition.

At a particular temperature, a phase transition occurs at a constant pressure. The temperature remains unaltered during the transition although heat is exchanged between the system and the surroundings.

Entropy Chemistry Class 11 Ncert Notes

The phase transition can be considered as a reversible process. If qrev of heat is absorbed during a phase transition at constant pressure and 7’K, then the change in entropy, of the system. As the process is occurring at constant pressure

⇒ \(q_{\text {re }}=q_p=\Delta H.\).

hence \(\Delta s=\frac{\Delta n}{r}\) \(\Delta s=\frac{\Delta n}{r}\) ……………………….(1)

MPBSE Class 11 Chemistry Notes For  The entropy of fusion

It In defined as the change in entropy associated with the transformation of one mole of a solid substance into its liquid phase at its melting point

According to equation (1) \(\Delta S_{f u s}=\frac{\Delta H_{f u s}}{T_f}\)

where ΔH_vap= the enthalpy of fusion = die heat required for the transformation of 1 mol of a solid at its melting point into 1 ml of liquid and T1= melting point (K) of the given solid As the fusion of a solid substance is an endothermic process (Le, A> 0 ), the change in entropy due to fusion (ΔS_vap) is always positive.

Entropy Definition Class 11

In the solid phase of a substance, the constituent particles are held in an ordered state. The degree of orderliness is less in the liquid phase as the particles in the liquid have freedom of motion. This is why, when a solid melts, the randomness within the system increases, causing an increase in the entropy of the system.

Example: The enthalpy of fusion of ice at 0°C and 1 atm. Therefore, the change in entropy during the transformation of 1 mol of ice into 1 mol of water at 0°C and 1 atm is-

MPBSE Class 11 Chemistry Notes For  Entropy of vaporization

It is defined as the change in entropy when one mole of a liquid at its boiling point changes to its vapor phase.

Where ΔH = the enthalpy of vaporization = the heat required for the transformation of 1 mol of liquid at its boiling point into 1 mol of vapor and Tb = boiling point ofthe liquid (K).

As the vaporization of a liquid is an endothermic process [i.e., \(\Delta H_{v a p}>0\)), the change in entropy in a vaporization process (ΔS_vap) is always positive. When a liquid vaporizes, the molecular randomness in the system increases as the molecules in the vapor phase have more freedom of motion thus they have in the liquid phase. As a result, the vaporization of a liquid always leads increase in the entropy ofthe system.

Example: The enthalpy of vaporization of water at 100°C and 1 atm (ΔHvap) = 40.4 kj .mol^-1

. Thus, the change in entropy due to the transformation of 1 mol of water into 1 mol of water vapor at 0°C temperature and 1 atm pressure is

⇒ \(\Delta S_{\text {vap }}=\frac{\Delta H_{\text {vap }}}{T_b}=\frac{40.4 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}}{373 \mathrm{~K}}=108.3 \mathrm{~J} \cdot \mathrm{K}^{-1} \cdot \mathrm{mol}^{-1}\)

Entropy Definition Class 11

Entropy change in an isothermal reversible expansion or compression of an ideal gas

Let, n mol of an ideal gas undergoes an isothermal reversible expansion from its initial state (P1 V1 to the final state (P₂, V₂). The equation showing the change in entropy of the gas in the process can be derived.

The result of this derivation gives the relation—

⇒ \(\Delta S=n R \ln \frac{V_2}{V_1}=2.303 n R \log \frac{V_2}{V_1}=2.303 n R \log \frac{P_1}{P_2}\)

As the gas expands, V₂ > V₂ (or, P₁> P₂ ), so according to the equation [1], the change in entropy (AS) of the gas due to its expansion is positive i.e., the entropy of the system increases.

If the isothermal reversible compression of the same amount of gas causes a change in the state of the gas form (P₁ V₁ to (P₂, V₂), then the change in entropy of the gas is given by

⇒ \(\Delta S=n R \ln \frac{V_2}{V_1}=2.303 n R \log \frac{V_2}{V_1}=2.303 n R \log \frac{P_1}{P_2}\)

As the gas is compressed, V₂ < V₁ (or P₂> P₁ ), According to equation [2], the change in entropy (AS) of the gas due to its compression is negative, i.e., the entropy of the system decreases.

Entropy Class 11 Chemistry Notes

If the volume of a gas is increased, the gas molecules will get more space for their movement i.e., the gas molecules will move in greater volume. As a result, the randomness of the gas molecules as well as the entropy ofthe system (gas) will increase.

Thus, the entropy of a gas increases with the increase of its volume. On the other hand, the entropy of a gas decreases with the decrease of its volume.

MPBSE Class 11 Chemistry Notes For  Change in entropy of the surroundings

When a system exchanges heat with its surroundings, the entropy of the system as well as its surroundings changes.

To calculate the change in entropy of the surroundings, the given points are to be considered:

Surroundings are so large compared to one system that they serve as a heat reservoir without undergoing any temperature change.

Surroundings absorb or release heat reversibly, and during these processes, the temperature and pressure of the surroundings remain almost the same In a process at TK, if the amount of heat released by the system to the surroundings is sys, then the amount of heat absorbed by tire surroundings = -guys (the sign of q is -ve).

Therefore, in this process, the change in entropy of the surroundings \(\Delta S_{s u r r}=-\frac{q_{s y s}}{T}\)

Entropy Class 11 Chemistry Notes

Hence, the entropy of the surroundings increases if heat is released by the system to the surroundings.

In a process at T K, if the amount of heat absorbed by the system from the surroundings is q, then the amount of heat released by the surroundings will be -qsys (the sign of qsys is +ve ). So, in this process, the change in entropy of the surroundings, \(\Delta S_{\text {surr }}=-\frac{q_{s y s}}{T}.\)

Hence, the entropy of the surroundings decreases if heat is absorbed by the system from the surroundings

MPBSE Class 11 Chemistry Notes For  Standard entropy change in a chemical reaction

Standard molar entropy of a substance:

Entropy of 1 mol of a pure substance at a given temperature (usually 25°C) &1 atm pressure is termed as the standard molar entropy of that substance.

It is denoted by S° and its unit is J. K-1.mol^-1.

Standard entropy change in a chemical reaction (ΔS°):

In a chemical reaction, the change in standard entropy, ΔS° = total standard entropies of the products – total standard entropies of the reactants i.e.,

⇒  \(\Delta s^0=\sum n_i s_i^0-\sum n_j s_j^0\)

Where S^o_i and S^o_j are the standard entropy of the i -tit product and j -th reactant, respectively. n₁ and n₂ are the number of moles of the Mil product and i-th reactant, respectively In the balanced equation.

Entropy Chemistry Class 11 Ncert Notes

In the case of the reaction.

⇒  \(a A+b B \rightarrow c C+a D\Delta S^0=\left(c S_C^0+d S_b^0\right)-\left(a S_A^0+b S_B^0\right)\)

MPBSE Class 11 Chemistry Notes For  Change in entropy of the surroundings in a chemical reaction

The change In entropy of the surroundings in a given process,

⇒ \(\Delta S_{s t u r}=\frac{-q_{s y s}}{T},\) where qÿ is the heat absorbed by the system at 7’K.

In case of chemical reactions occurring at constant pressure \(q_{s y s}=q_P=\) change in enthalpy of the reaction system

⇒\(=\Delta H . \mathrm{So}_1, \Delta \mathrm{S}_{\text {surr }}=-\frac{\Delta H}{T}\)

For exothermic reactions,

⇒ \(\Delta H<0. \text { So, } \Delta S_{\text {surr }}=+v e \text {. }\) I-Ience, the entropy of the surroundings increases In an exothermic reaction.

For endothermic reaction

⇒ \(\Delta H>0 \text {. So, } \Delta S_{\text {surr }}=-v e \text {. }\) Hence, the entropy of the surroundings decreases in an endothermic reaction.