Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 1: Exercise 1

One mole of ${\mathrm{O}}_2\left(\mathrm{g}\right)$, initially at a temperature of $120 \mathrm{K}$ and under a pressure of $4 \mathrm{atm}$ is expanded adiabatically to $1 \mathrm{atm}$ in such a way that the temperature of the gas falls to $90 \mathrm{K}$ (just above its normal boiling point). ${\mathrm{C}}_{\mathrm{p}}$ of ${\mathrm{O}}_2\left(\mathrm{g}\right)$ is $28.2{\mathrm{JK}}^{-1}{ \mathrm{mol}}^{-1}$ and is constant over the required temperature range. ${\mathrm{O}}_2\left(\mathrm{g}\right)$ is supposed to behave ideally. Choose the correct options : $\left(\log 2=0.3010, \log 3=0.4771\right)$

An ideal gas in thermally insulated container, at internal pressure $P_1$, volume $V_1$ and absolute temperature $T_1$ expands irreversibly against zero external pressure so that the pressure of gas becomes $P_2$, volume $V_2$ and temperature $T_2$. Which of the following statement(s) is/are correct ?

A normal boiling point of a liquid is $350\mathrm{K}$ and ${\mathrm{\Delta H}}_{\mathrm{vap}}$ is $35\mathrm{kJ} {\mathrm{mol}}^{-1}.$ Assume that ${\mathrm{\Delta H}}_{\mathrm{vap}}$ is independent from temperature and pressure. The correct statement (s) is/are

Read the following statements carefully and pick the correct statements:

A reaction attain equilibrium state under standard condition, then

One mole of a gas changed from its initial state $\left(15\mathrm{L},2 \mathrm{atm}\right)$ to final state $\left(4\mathrm{L},10\mathrm{atm}\right)$ reversibly. If this change can be represented by a straight line in $\mathrm{P}-\mathrm{V}$ curve maximum temperature (approximate), the gas attained is '$\mathrm{x}$' $\mathrm{K}$. Then find the value of '$\mathrm{x}$'. ('$\mathrm{x}$'value is in hundreds)

The enthalpy of tetramerization of $\mathrm{X}$ in gas phase $\left(4\mathrm{X}\left(\mathrm{g}\right)\to {\mathrm{X}}_4\left(\mathrm{g}\right)\right)$ is $-100 \mathrm{kJ}/\mathrm{mol}$ at $300 \mathrm{K}$. The enthalpy of vaporisation for liquid $\mathrm{X}$ and ${\mathrm{X}}_4$ are respectively $30 \mathrm{kJ}/\mathrm{mol}$ and $72 \mathrm{kJ}/\mathrm{mol}$ respectively. $\mathrm{\Delta S}$ for tetramerization of $\mathrm{X}$ in liquid phase is $-125 \mathrm{J}/\mathrm{K}$ $\mathrm{mol}$ at $300 \mathrm{K}$. What is the $\left|\mathrm{\Delta G}\right|$ at $300 \mathrm{K}$ for tetramerization reaction of $\mathrm{X}$ in liquid phase $\left(4\mathrm{X}\left(\mathrm{\ell }\right)⟶{\mathrm{X}}_4\left(\mathrm{\ell }\right)\right)$ in $(\mathrm{kJ}/\mathrm{mol})$ ?

Report the value of $\left|\mathrm{\Delta G}\right|$ by rounding off to two significant figures.

In a constant volume calorimeter, $3.5 \mathrm{g}$ of a gas(hydrocarbon) with molecular weight $28$ was burnt in excess oxygen at $298.0 \mathrm{K}$. The temperature of the calorimeter was found to increase from $298.0 \mathrm{K}$ to $298.45 \mathrm{K}$ due to the combustion process. Given that the heat capacity of the calorimeter is $2.5 \mathrm{kJ}{ \mathrm{K}}^{-1}$, If the value for the enthalpy of combustion of the gas is $-\mathrm{A}$ ${\mathrm{kJmol}}^{-1}$, Report the value of $\mathrm{A}$ by rounding off to two significant figures,  $(\mathrm{R}=8.314 \mathrm{J}/\mathrm{K}/\mathrm{mol})$