Entropy Change in Isothermal Process

Q. 5 moles of an ideal gas expand reversibly from a volume of 8 $d{m}^3$ to 80 $d{m}^3$ at a temperature of ${27}^{\circ }C$. Calculate the change in entropy.

1. $70.26J{K}^{-1}$
2. $82.55J{K}^{-1}$
3. $95.73J{K}^{-1}$
4. $107.11J{K}^{-1}$

Q. Which is the correct expression that relates change in entropy with the change in pressure for an ideal gas at constant temperature?

1. $△S=nRTln\frac{P_1}{P_2}$
2. $△S=nRln\left(\frac{P_1}{P_2}\right)$
3. $△S=T(P_2-P_1)$
4. $△S=RTln\left(\frac{P_1}{P_2}\right)$

Q. 1 mole of an ideal gas at ${25}^{\circ }C$ is subjected to expand reversibly ten times of its initial volume. The change in entropy due to expansion is:

1. $19.15J{K}^{-1}{\text{mol}}^{-1}|$
2. $16.18J{K}^{-1}{\text{mol}}^{-1}|$
3. $22.15J{K}^{-1}{\text{mol}}^{-1}|$
4. $\text{none of these}$

Q. For the reaction, $2Cl\left(g\right)\to C{l}_2\left(g\right),$ the correct option is

1. ${\Delta }_{r}H>0$ and ${\Delta }_{r}S<0$
2. ${\Delta }_{r}H<0$ and ${\Delta }_{r}S>0$
3. ${\Delta }_{r}H<0$ and ${\Delta }_{r}S<0$
4. ${\Delta }_{r}H>0$ and ${\Delta }_{r}S>0$

Q. For a sample of perfect gas when its pressure is changed isothermally from $p_i$ to $p_f,$ the entropy change is given by

1. $\Delta S=nRTln\left(\frac{p_f}{p_i}\right)$
2. $\Delta S=RTln\left(\frac{p_i}{p_f}\right)$
3. $\Delta S=nRln\left(\frac{p_f}{p_i}\right)$
4. $\Delta S=nRln\left(\frac{p_i}{p_f}\right)$

Q. Calculate the entropy change when 2 mol of an ideal gas expands isothermally and reversibly from an initial volume of 10 $d{m}^3$ to 100 $d{m}^3$ at 300 K.

1. 45 J K^-1

2. 50 J K^-1

3. 28.294 J K^-1

4. 38.294 J K^-1

Q. What is the entropy change when 1 mole oxygen gas expands isothermally and reversibly from an initial volume of 10 L to 100 L at 300 K?

1. $19.14J{K}^{-1}$
2. $109.12J{K}^{-1}$
3. $29.12J{K}^{-1}$
4. $10J{K}^{-1}$

Q. Entropy change when 4 moles of an ideal gas expands reversibly from an initial volume of 1 $d{m}^3$ to a final volume of 10 $d{m}^3$ at a constant temperature of 298 K is

1. $5705.8J{K}^{-1}$
2. $-19.15J{K}^{-1}$
3. $76.58J{K}^{-1}$
4. $38.29J{K}^{-1}$

Q. Predict which of the following reaction (s) has a positive entropy change?
$I.A{g}^{+}\left(aq\right)+C{l}^{-}\left(aq\right)\to AgCl\left(s\right)$
$II.N{H}_{4}Cl\left(s\right)\to N{H}_3\left(g\right)+HCl\left(g\right)$
$III.2N{H}_3\left(g\right)\to N_2\left(g\right)+3H_2\left(g\right)$

1. I and II
2. III
3. II
4. II and III

Q. Oxygen gas weighing $64g$ is expanded from $1atm$ to $0.1atm$ at $30{}^{o}C.$ Calculate entropy change, assuming the gas to be ideal

1. $34.29J{K}^{-1}$
2. $38.29J{K}^{-1}$
3. $44.29J{K}^{-1}$
4. $48.29J{K}^{-1}$

Q. In a container 5 moles of $He$ gas are mixed with 4 moles of $H_2$ gas isothermally. Find out the entropy change in mixing for the system in $J{K}^{-1}$, given that $R=8.314Jmo{l}^{-1}{K}^{-1}$

1. 51.04
2. 98.88
3. 20.89
4. -66.89

Q. Entropy change when 4 moles of an ideal gas expands reversibly from an initial volume of 1 $d{m}^3$ to a final volume of 10 $d{m}^3$ at a constant temperature of 298 K is

1. $5705.8{\text{J K}}^{-1}$
2. $76.58{\text{J K}}^{-1}$
3. $\mathrm{38..29}{\text{J K}}^{-1}$
4. $-19.15{\text{J K}}^{-1}$

Q. Calculate the change in entropy of 2 moles of an ideal gas upon isothermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm.

1. $-4.5cal/K$
2. $-1.25cal/K$
3. $1.25cal/K$
4. $2.77cal/K$

Q. Calculate the entropy change ($inJ{K}^{-1}$) when $220g$ of Carbon dioxide expands reversibly and isothermally from an initial volume of $1litre$ to $100litre$ at $600K$.

1. $191.4J{K}^{-1}$
2. $280J{K}^{-1}$
3. $305.5J{K}^{-1}$
4. $168J{K}^{-1}$

Q. What is the entropy change involved in the isothermal expansion of 5 mol of ideal gas from a volume of 10L to 100L at 300 K?

1. $-95.7J{K}^{-1}$
2. $+95.7kJ{K}^{-1}$
3. $28.72kJ{K}^{-1}$
4. $-28.72kJ{K}^{-1}$

Q. Entropy change when $4$ moles of an ideal gas expands reversibly from an initial volume of $1{\text{dm}}^3$ to a final volume of $10{\text{dm}}^3$ at a constant temperature of $298\text{K}$ is:

1. $5705.8{\text{J K}}^{-1}$
2. $76.58{\text{J K}}^{-1}$
3. $\mathrm{38..29}{\text{J K}}^{-1}$
4. $-19.15{\text{J K}}^{-1}$

Q. In a container 5 moles of $He$ gas are mixed with 4 moles of $H_2$ gas isothermally. Find out the entropy change in mixing for the system in $J{K}^{-1}$, given that $R=8.314Jmo{l}^{-1}{K}^{-1}$

1. 20.89
2. 51.04
3. 98.88
4. -66.89

Q.

Paragraph for below question

नीचे दिये गये प्रश्न के लिए अनुच्छेद

The standard enthalpy change for the formation of one mole of a compound from its elements in their most stable states of aggregation (also known as reference states) is called standard molar enthalpy of formation (${\Delta }_f{H}^{\ominus }$). Enthalpy of reaction can be calculated in terms of enthalpy of formation of the reactants and the products of the reaction.

अपने समूहन की सर्वाधिक स्थायी अवस्थाओं (संदर्भ अवस्थाएं भी कहलाती हैं) में अपने तत्वों से एक मोल यौगिक के निर्माण के लिए मानक एन्थैल्पी परिवर्तन मानक मोलर संभवन एन्थैल्पी (${\Delta }_f{H}^{\ominus }$) कहलाती है। अभिक्रिया की एन्थैल्पी की गणना अभिक्रिया के अभिकारकों व उत्पादों की संभवन एन्थैल्पी के पदों में की जा सकती है।

Q. If heat of formation for CaCO₃(s), CaO(s) and CO₂(g) are –800 kJ mol^–1, –400 kJ mol^–1 and –250 kJ mol^–1 respectively then calculate enthalpy change of following reaction

CaCO₃(s) → CaO(s) + CO₂(g)

प्रश्न - यदि CaCO₃(s), CaO(s) तथा CO₂(g) की संभवन ऊष्मा क्रमशः –800 kJ mol^–1, –400 kJ mol^–1 तथा –250 kJ mol^–1 हैं; तो निम्नलिखित अभिक्रिया के एन्थैल्पी परिवर्तन की गणना कीजिए।

CaCO₃(s) → CaO(s) + CO₂(g)

1. –150 kJ mol^–1
2. +150 kJ mol^–1
3. –650 kJ mol^–1
4. +650 kJ mol^–1

Q. The change in entropy of 2 moles of an ideal gas upon isothermal expansion at 243.6 K from 20 L until the pressure becomes 1 atm is :

1. $-1.2cal/K$
2. $2.77cal/K$
3. $-1.2cal/K$
4. $1.385cal/K$

Q. Calculate the entropy change ($inJ{K}^{-1}$) when $220g$ of Carbon dioxide expands reversibly and isothermally from an initial volume of $1litre$ to $100litre$ at $600K$.

1. $191.4J{K}^{-1}$
2. $280J{K}^{-1}$
3. $305.5J{K}^{-1}$
4. $168J{K}^{-1}$

Q. Calculate $q$ (in kilo joules), for the reversible isothermal expansion of two mole of an ideal gas at ${27}^{o}C$ from a volume of $10d{m}^3$ to a volume of $30d{m}^3$.

1. $0.89kJ$
2. $3.4kJ$
3. $1.7kJ$
4. $5.4kJ$

Q. Calculate the change in entropy of 2 moles of an ideal gas upon isothermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm.

1. $-4.5cal/K$
2. $-1.25cal/K$
3. $1.25cal/K$
4. $2.77cal/K$

Q. What is the entropy change involved in the isothermal expansion of 5 mol of ideal gas from a volume of 10L to 100L at 300 K?

1. 
2. 
3. 
4. 

Q. Which one is correct about given P - V plot for 2 mole an ideal gas ?

1. $W_{AB}=-20L-atm$
2. $\Delta U$ for Cycle = 0
3. $\Delta S_{Cycle}=0$
4. $W_{CA}=+13.86Latm$

Q. One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to 2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surrounding $\left(\Delta S_{max}\right)$ in $J{K}^{-1}$ is ($1Latm=101.3J$)

1. 1.013
2. -1.013
3. -5.763
4. 5.763

Q. Six grams of hydrogen gas at a temperature of $273K$ was isothermally expanded to five times its initial volume and then isochorically heated so that the pressure in the final state becomes equal to that in the initial state. Find the total amount of heat absorbed by the gas during the entire process (in joules).

1. $78919.4$
2. $78990.2$
3. $80281.6$
4. $80110.8$

Q. When $10$ moles of an ideal gas expand from a pressure of $10$ atm pressure of $1$ atm reversibly and isothermally then entropy change is : [Take: ln $10=2.3$]

1. $-20cal$
2. $-46cal$
3. $-4.6cal$
4. $2cal$

Q. Calculate the free energy change at $298K$ for the reaction :

1. $1721.8J$
2. $1721.8kJ$
3. $17218J$
4. None of these

Q. During the derivation for the work done in isothermal reversible expansion of an ideal gas, the following expression appears.
$dW=(P-dP)dV=PdV+dP\cdot dV$

1. True
2. False

Q. The standard entropies of $C{O}_2\left(g\right),C\left(s\right)and{O}_2\left(g\right)$ are $213.50,5.74$ and $205J/K$ respectively. What will be the standard entropy of formation of $C{O}_2$:

1. $-2.76J/K$
2. $5.76J/K$
3. $2.76J/K$
4. $-5.76J/K$