Basic concepts Questions in English

(A) For an exothermic reaction,heat is released to the surroundings.
Therefore,the enthalpy of the products $(H_{product})$ is less than the enthalpy of the reactants $(H_{reactant})$,which results in a negative change in enthalpy $(\Delta H < 0)$.
Thus,the correct option is $(A)$.

(C) The heat of reaction $(q_p)$ at constant pressure is defined as the change in enthalpy $(\Delta H)$ of the system.
$\Delta H = H_P - H_R$,where $H_P$ is the enthalpy of the products and $H_R$ is the enthalpy of the reactants.

(B) In an endothermic reaction,heat is absorbed from the surroundings.
Therefore,the enthalpy change $\Delta H$ is always positive $(+ve)$.

(C) Enthalpy change $(\Delta H)$ is a state function,which means it depends only on the initial and final states of the system.
It does not depend on the path taken or the intermediate steps involved in the reaction.
Therefore,it is independent of the different intermediate reaction paths.

(D) Internal energy $(U)$ is a state function,which means its value depends only on the state of the system and not on the path taken.
For a cyclic process where the system returns to its initial state,the total change in internal energy is zero.
Given the process $A \rightarrow B$ with change $E_1$ and $B \rightarrow A$ with change $E_2$,the total change is $E_1 + E_2 = \Delta U_{total} = 0$.

(C) For an ideal gas,the enthalpy change $\Delta H$ is given by the formula $\Delta H = n C_p \Delta T$.
Since the process is isothermal,the change in temperature $\Delta T = 0$.
Therefore,$\Delta H = n C_p \times 0 = 0 \ kJ$.

(D) The heat content of a system at constant pressure is defined as its enthalpy $(H)$.
Mathematically,the change in enthalpy $(\Delta H)$ is equal to the heat exchanged at constant pressure $(q_p)$,
i.e.,$\Delta H = q_p$.
Therefore,the correct option is $D$.

(D) The work done in a reversible isothermal expansion is given by the formula $w = -2.303 \, nRT \, \log \frac{V_2}{V_1}$.
Since the expression involves the ratio of two volumes $\frac{V_2}{V_1}$,the units of volume cancel out.
Therefore,the volume can be expressed in any unit as long as both $V_1$ and $V_2$ are in the same unit.
Thus,the correct option is $D$.

(A) The correct option is $A$.
In an endothermic reaction,heat is absorbed from the surroundings.
Therefore,the enthalpy of the products $(H_P)$ is greater than the enthalpy of the reactants $(H_R)$.
Mathematically,the change in enthalpy is given by $\Delta H = H_P - H_R$.
Since $H_P > H_R$,the value of $\Delta H$ is positive.

(A) The heat of reaction at constant volume $(q_v)$ is measured using a $Bomb \ calorimeter$.
Since the volume is kept constant,the work done $(w = -P \Delta V)$ is zero,and the heat measured corresponds to the change in internal energy $(\Delta U)$.

(C) bomb calorimeter is a constant-volume calorimeter used to measure the heat of combustion of a substance.
Since the volume is kept constant $(dV = 0)$,the work done is zero $(w = -P_{ext} \Delta V = 0)$.
According to the first law of thermodynamics,$\Delta U = q + w$.
Since $w = 0$,the heat measured $(q_v)$ is equal to the change in internal energy,$\Delta U$ (or $\Delta E$).

(C) The relationship between enthalpy change $(\Delta H)$ and internal energy change $(\Delta E)$ is given by the equation: $\Delta H = \Delta E + \Delta n_g RT$,where $\Delta n_g$ is the change in the number of moles of gaseous species.
$\Delta H$ is not equal to $\Delta E$ when $\Delta n_g \neq 0$.
For option $A$: $\Delta n_g = 2 - (1 + 1) = 0$.
For option $B$: $\Delta n_g = 1 - 1 = 0$.
For option $C$: $\Delta n_g = 2 - (1 + 3) = -2 \neq 0$.
For option $D$: $\Delta n_g = 0$ (as there are no gaseous species).
Therefore,for the reaction in option $C$,$\Delta H \neq \Delta E$.

(C) process is defined as reversible in thermodynamics if the system and surroundings are always in equilibrium with each other throughout the entire process. This implies that the driving force is infinitesimally small,allowing the process to be reversed at any stage.

(C) The process is the sublimation of dry ice: $CO_{2(s)} \rightarrow CO_{2(g)}$.
$1$. Sublimation is an endothermic process,meaning heat is absorbed from the surroundings,so $\Delta H > 0$ (positive).
$2$. The transition from solid to gas represents a significant increase in the randomness or disorder of the system,so $\Delta S > 0$ (positive).
Therefore,both $\Delta H$ and $\Delta S$ are positive.

(C) Extensive properties are those properties whose values depend on the quantity or size of matter present in the system.
$1$. $Molar \ volume$,$Molarity$,and $Mole \ fraction$ are intensive properties because they are independent of the amount of substance.
$2$. The $Number \ of \ moles$ $(n)$ is an extensive property because it is directly proportional to the amount of matter present in the system.

(A) In a vacuum,the external pressure is zero $(P_{ext} = 0)$.
According to the formula for work done in expansion: $W = -P_{ext} \times \Delta V$.
Since $P_{ext} = 0$,the work done $W = 0 \ J$.

(B) An extensive property is a property whose value depends on the quantity or size of matter present in the system.
Examples of extensive properties include mass,volume,internal energy,enthalpy,and entropy.
Temperature,viscosity,and refractive index are intensive properties because their values are independent of the amount of matter present in the system.
Therefore,$Volume$ is an extensive property.

(B) In an endothermic process,heat is absorbed from the surroundings by the system.
According to the first law of thermodynamics,the change in enthalpy $\Delta H$ is defined as the heat exchanged at constant pressure.
Since heat is absorbed,the enthalpy of the products is greater than the enthalpy of the reactants $(H_{products} > H_{reactants})$.
Therefore,$\Delta H = H_{products} - H_{reactants} > 0$.
Thus,for an endothermic process,$\Delta H$ is positive.

(A) The process $CO_2(s) \rightarrow CO_2(g)$ represents sublimation.
Since the substance changes from a solid state to a gaseous state,the disorder increases,therefore $\Delta S > 0$.
Sublimation is an endothermic process,meaning the system absorbs heat from the surroundings,therefore $\Delta H > 0$.

(B) Thermodynamics deals with the energy changes associated with physical and chemical processes in a system.

(B) In thermodynamics,a process in which there is no exchange of heat between the system and the surroundings $(q = 0)$ is known as an adiabatic process.

(C) An adiabatic process is defined as a process in which there is no exchange of heat between the system and its surroundings $(q = 0)$.
This condition is characteristic of an isolated system,where neither matter nor energy (heat) can be exchanged with the surroundings.

(D) state function is a property of a system whose value depends only on the current state of the system and not on the path taken to reach that state.
Internal energy $(U)$,Gibbs free energy $(G)$,and Enthalpy $(H)$ are all state functions because they depend only on the state variables of the system.
Work $(W)$ and Heat $(q)$ are path functions,meaning their values depend on the process or path taken to change the state of the system.
Therefore,Work $(W)$ is not a state function.

(C) An exothermic reaction is a process that releases energy in the form of heat to the surroundings.
In such reactions,the enthalpy of the products $(H_p)$ is less than the enthalpy of the reactants $(H_r)$.
Therefore,the change in enthalpy $(\Delta H = H_p - H_r)$ is negative.
Since $H_p < H_r$,it implies that the reactants have more energy than the products.

(D) The molar heat capacity at constant pressure $(C_P)$ is defined as the rate of change of enthalpy $(H)$ with respect to temperature $(T)$ at constant pressure $(P)$.
Mathematically,it is expressed as: $C_P = (\frac{\partial H}{\partial T})_P$.

(A) The process $CO_{2(s)} \rightarrow CO_{2(g)}$ represents sublimation,which is an endothermic process.
Therefore,the enthalpy change $\Delta H$ is positive $(> 0)$.
Since the substance is changing from a solid state (ordered) to a gaseous state (disordered),the entropy increases.
Therefore,the entropy change $\Delta S$ is positive $(> 0)$.

(C) An ideal thermos flask is designed to prevent the exchange of both matter and energy (heat) with the surroundings.
Since neither matter nor energy can be exchanged,it represents an $Isolated$ system.

(C) An isolated system is one in which there is no exchange of energy or matter with the surroundings. $A$ thermos flask is designed to prevent heat transfer (energy) and matter exchange with the surroundings. Therefore,it is an example of an isolated system.

(C) The enthalpy change is given by the formula: $\Delta H = \Delta U + \Delta (PV)$
Substituting $\Delta (PV) = P_2 V_2 - P_1 V_1$:
$\Delta H = \Delta U + (P_2 V_2 - P_1 V_1)$
Given $\Delta U = 30.0 \, \text{L} \cdot \text{atm}$,$P_1 = 2.0 \, \text{atm}$,$V_1 = 3.0 \, \text{L}$,$P_2 = 4.0 \, \text{atm}$,and $V_2 = 5.0 \, \text{L}$:
$\Delta H = 30.0 + (4.0 \times 5.0 - 2.0 \times 3.0)$
$\Delta H = 30.0 + (20.0 - 6.0) = 30.0 + 14.0 = 44.0 \, \text{L} \cdot \text{atm}$.

(A) The work done during expansion against a constant external pressure is given by the formula: $W = -P_{ext} \Delta V$.
Given:
$P_{ext} = 1 \, atm$
$V_1 = 1 \, L$
$V_2 = 5 \, L$
$\Delta V = V_2 - V_1 = 5 \, L - 1 \, L = 4 \, L$.
Substituting the values:
$W = -(1 \, atm) \times (4 \, L) = -4 \, L \cdot atm$.
Converting to Joules:
$W = -4 \times 101.3 \, J = -405.2 \, J$.
The negative sign indicates that work is done by the system on the surroundings.

(C) In an adiabatic process,there is no exchange of heat between the system and the surroundings.
Therefore,the heat exchange $q = 0$.

(A) According to Kirchhoff's law,the variation of enthalpy of reaction with temperature is given by: $\Delta H_2 - \Delta H_1 = \int_{T_1}^{T_2} \Delta C_p \, dT$.
Given that $\Delta C_p = 0$,the equation becomes $\Delta H_2 - \Delta H_1 = 0$,which implies $\Delta H_2 = \Delta H_1$.
Therefore,the enthalpy of the reaction remains constant at all temperatures when $\Delta C_p = 0$.
Thus,the enthalpy at $373 \, K$ is the same as at $273 \, K$,which is $-3.57 \, kJ$.

(D) The heat of solution is defined as the enthalpy change when one mole of a solute is dissolved in a specified amount of solvent.
As more solvent is added to a solution,the process approaches infinite dilution.
The heat of solution changes with the concentration of the solution until it reaches a constant value at infinite dilution.
Therefore,the heat of solution depends on the amount of solvent added and can either increase or decrease depending on the nature of the solute-solvent interaction.

(C) Solution: For free expansion of a gas in a vacuum,the external pressure $P_{ext} = 0$.
The formula for work done is $W = -P_{ext} \Delta V$.
Since $P_{ext} = 0$,$W = -0 \times \Delta V = 0 \ J$.

(D) Extensive properties are those properties of a system whose values depend on the quantity or size of matter present in the system.
Mass,enthalpy,and energy are all dependent on the amount of substance present in the system.
Therefore,all of these are extensive properties.

(C) state function is a property of a system whose value depends only on the current state of the system,not on the path taken to reach that state.
Examples include pressure $(P)$,volume $(V)$,temperature $(T)$,internal energy $(U)$,enthalpy $(H)$,entropy $(S)$,and Gibbs free energy $(G)$.

(B) state function is a property whose value depends only on the current state of the system and not on the path taken to reach that state.
$I. \, q + W = \Delta U$ (Internal energy change),which is a state function.
$II. \, q$ (Heat) is a path function.
$III. \, W$ (Work) is a path function.
$IV. \, H - TS = G$ (Gibbs free energy),which is a state function.
Therefore,$q$ and $W$ are not state functions. The correct option is $B$.

(B) In a cyclic process,the system returns to its initial state after a series of changes.
Since internal energy $(U)$ is a state function,its value depends only on the initial and final states.
For a cyclic process,the initial state and final state are the same.
Therefore,the change in internal energy is $\Delta U = U_{final} - U_{initial} = 0$.

(A) In a closed vessel,the volume of the system remains constant,so $\Delta V = 0$.
Since the work done $W = -P_{ext} \times \Delta V$,and $\Delta V = 0$,the work done $W = 0$.

(A) The internal energy $U$ of a substance is a state function that depends on the temperature of the system.
For an ideal gas,the internal energy is directly proportional to the absolute temperature $(U \propto T)$.
Therefore,as the temperature increases,the kinetic energy of the molecules increases,leading to an increase in the internal energy of the substance.
Thus,both options $A$ and $B$ describe the relationship correctly,but in the context of standard multiple-choice questions,$A$ is the most common representation of this dependence.

(A) The enthalpy change is defined as $\Delta H = \Delta U + \Delta(PV)$.
For a system where pressure $(P)$ is constant,the expression becomes $\Delta H = \Delta U + P \Delta V$.
Therefore,the given relation is valid under the condition of constant pressure.

(A) For an ideal gas,the internal energy $U$ is a function of temperature only.
According to the kinetic theory of gases,the average kinetic energy of an ideal gas is directly proportional to its absolute temperature $(U \propto T)$.
Therefore,the change in internal energy $\Delta U$ increases as the temperature increases.

(B) For an ideal gas,the internal energy $(U)$ is a function of temperature only,i.e.,$U = f(T)$.
Since the process is isothermal,the temperature remains constant $(T_2 = T_1 = 300 \text{ K})$.
Therefore,the change in internal energy $\Delta U = nC_v \Delta T = 0$.

(C) The relationship between enthalpy change $(\Delta H)$ and internal energy change $(\Delta U)$ is given by the equation: $\Delta H = \Delta U + \Delta n_g RT$.
For $\Delta H = \Delta U$ to hold true,the term $\Delta n_g$ must be equal to $0$.
$\Delta n_g$ is defined as the difference between the number of moles of gaseous products and gaseous reactants.
For the reaction $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$:
$\Delta n_g = (2) - (1 + 1) = 0$.
Therefore,for this reaction,$\Delta H = \Delta U$.

(D) state function is a property whose value depends only on the current state of the system and not on the path taken to reach that state.
$(i)$ The height of a hill is a fixed property of the location,independent of the path taken to reach the top,so it is a state function.
$(ii)$ The distance covered depends on the path taken,so it is a path function.
$(iii)$ The change in energy (internal energy) is a state function because it depends only on the initial and final states of the system.
Therefore,both $(i)$ and $(iii)$ are state functions.

(B) Internal energy $(U)$ is a state function.
$A$ state function depends only on the initial and final states of the system,not on the path taken.
Since the system starts at state $A$ and eventually returns to state $A$ after completing the cycle,the final state is the same as the initial state.
Therefore,the net change in internal energy $(\Delta U)$ for any cyclic process is zero.

(C) An isolated system is a system that cannot exchange either energy or matter with its surroundings.
$A$ human being is an open system as it exchanges both matter and energy.
An ice cube tray is an open system.
Coffee in a thermos flask is an example of an isolated system because the insulated walls prevent the exchange of heat (energy) and matter with the surroundings.
$A$ satellite in orbit is not considered an isolated system in this context.