Entropy Change in Isothermal Process

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

Q. Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures $T_1$and $T_2$ ($T_1<T_2$). The correct graphical depiction of the dependence of work done (w) on the final volume (V) is:

1. 
   
   
2. 
   
   
3. 
   
   
4. 
   
   

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. 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 and III
4. II

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 and III
4. II

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

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. 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. $45J{K}^{-1}$
2. $50J{K}^{-1}$
3. $28.294J{K}^{-1}$
4. $38.294J{K}^{-1}$

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. $168J{K}^{-1}$