Chemical Thermodynamics

Which of the following relation is not correct ?

Among the following the number of state variables is ______.

Internal energy (U)

Volume (V)

Heat (q)

Enthalpy (H)

When 600 mL of 0.2 M HNO$_3$ is mixed with 400 mL of 0.1 M NaOH solution in a flask, the rise in temperature of the flask is _______ $\times10^{-2}$ °C.

(Enthalpy of neutralisation = 57 kJ mol$^{-1}$ and Specific heat of water = 4.2 J K$^{-1}$ g$^{-1}$)

(Neglect heat capacity of flask)

$\mathrm{C(s)+O_2(g)\to CO_2(g)}$ + 400 kJ
$\mathrm{C(s)+\frac12O_2(g)\to CO(g)}$ + 100 kJ

When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is converted into 'CO' and the remaining is converted into 'CO$_2$'. The heat generated when 0.6 kg of coal is burnt is _______.

Which of the following is the plot of Gibb's free energy (G) vs temperature (T), at constant pressure, for a pure substance?

The value of standard enthalpy, $\Delta H^\ominus$ (in kJ mol$^{-1}$) for the given reaction is ____.

The value of $\Delta S^\ominus$ (in J K$^{-1}$ mol$^{-1}$) for the given reaction, at 1000 K is ____.

An ideal gas undergoes a reversible isothermal expansion from state I to state II followed by a reversible adiabatic expansion from state II to state III. The correct plot(s) representing the changes from state I to state III is(are)

($p$: pressure, $V$: volume, $T$: temperature, $H$: enthalpy, $S$: entropy)

Correct match of the C-H bonds (shown in bold) in Column J with their BDE in Column K is

Column J: Molecule	Column K: BDE (kcal mol$^{-1}$)
(P) $\mathbf{H{-}C}\mathrm{H(CH_3)_2}$	(i) 132
(Q) $\mathbf{H{-}C}\mathrm{H_2Ph}$	(ii) 110
(R) $\mathbf{H{-}C}\mathrm{H{=}CH_2}$	(iii) 95
(S) $\mathbf{H{-}C}{\equiv}\mathrm{CH}$	(iv) 88

For the following reaction
$$\ce{CH4(g) + Cl2(g) ->[light] CH3Cl(g) + HCl(g)}$$
the correct statement is

One mole of an ideal gas at 900 K, undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of $\ln\dfrac{V_3}{V_2}$ is ____.

($U$: internal energy, $S$: entropy, $p$: pressure, $V$: volume, $R$: gas constant)

(Given: molar heat capacity at constant volume, $C_{V,m}$ of the gas is $\frac52R$)

In thermodynamics, the $P-V$ work done is given by

$$w = -\int dV\,P_{\text{ext}}.$$

For a system undergoing a particular process, the work done is,

$$w = -\int dV\left(\frac{RT}{V-b} - \frac{a}{V^2}\right).$$

This equation is applicable to a

Consider a 70% efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and 298 K. Its cell reaction is

$$\ce{H2(g) + 1/2 O2(g) -> H2O(l)}.$$

The work derived from the cell on the consumption of $1.0\times10^{-3}$ mol of $\ce{H2(g)}$ is used to compress 1.00 mol of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in K) of the ideal gas?

The standard reduction potentials for the two half-cells are given below.

$$\ce{O2(g) + 4H+(aq) + 4e- -> 2H2O(l)},\quad E^0 = 1.23\ \text{V},$$

$$\ce{2H+(aq) + 2e- -> H2(g)},\quad E^0 = 0.00\ \text{V}.$$

Use $F = 96500\ \mathrm{C\,mol^{-1}}$, $R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}$.

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K) at which the reduction of cassiterite by coke would take place.

At 298 K: $\Delta_fH^0(\ce{SnO2}(s)) = -581.0\ \mathrm{kJ\,mol^{-1}}$, $\Delta_fH^0(\ce{CO2}(g)) = -394.0\ \mathrm{kJ\,mol^{-1}}$,

$S^0(\ce{SnO2}(s)) = 56.0\ \mathrm{J\,K^{-1}mol^{-1}}$, $S^0(\ce{Sn}(s)) = 52.0\ \mathrm{J\,K^{-1}mol^{-1}}$,

$S^0(\ce{C}(s)) = 6.0\ \mathrm{J\,K^{-1}mol^{-1}}$, $S^0(\ce{CO2}(g)) = 210.0\ \mathrm{J\,K^{-1}mol^{-1}}$.

Assume that the enthalpies and the entropies are temperature independent.

Choose the reaction(s) from the following options, for which the standard enthalpy of reaction is equal to the standard enthalpy of formation.

A reversible cyclic process for an ideal gas is shown below. Here, $P$, $V$, and $T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q$, $w$, $H$ and $U$ are heat, work, enthalpy and internal energy, respectively.

The correct option(s) is (are)

For a reaction, A ⇌ P, the plots of [A] and [P] with time at temperatures $T_1$ and $T_2$ are given below.

If $T_2 > T_1$, the correct statement(s) is (are)

(Assume $\Delta H^\ominus$ and $\Delta S^\ominus$ are independent of temperature and ratio of $\ln K$ at $T_1$ to $\ln K$ at $T_2$ is greater than $T_2/T_1$. Here $H$, $S$, $G$ and $K$ are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)

The surface of copper gets tarnished by the formation of copper oxide. $\mathrm{N_2}$ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the $\mathrm{N_2}$ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below:

$$\mathrm{2Cu(s) + H_2O(g) \rightarrow Cu_2O(s) + H_2(g)}$$

$p_{\mathrm{H_2}}$ is the minimum partial pressure of $\mathrm{H_2}$ (in bar) needed to prevent the oxidation at 1250 K. The value of $\ln(p_{\mathrm{H_2}})$ is ____.

(Given: total pressure = 1 bar, $R$ (universal gas constant) = 8 J K$^{-1}$ mol$^{-1}$, ln(10) = 2.3. Cu(s) and Cu$_2$O(s) are mutually immiscible.

At 1250 K: $\mathrm{2Cu(s) + \tfrac{1}{2}O_2(g) \rightarrow Cu_2O(s)}$; $\Delta G^\ominus = -78{,}000$ J mol$^{-1}$

$\mathrm{H_2(g) + \tfrac{1}{2}O_2(g) \rightarrow H_2O(g)}$; $\Delta G^\ominus = -1{,}78{,}000$ J mol$^{-1}$; $G$ is the Gibbs energy)

Consider an electrochemical cell: $\mathrm{A(s)\,|\,A^{n+}(aq,\ 2\ M)\,||\,B^{2n+}(aq,\ 1\ M)\,|\,B(s)}$. The value of $\Delta H^\ominus$ for the cell reaction is twice that of $\Delta G^\ominus$ at 300 K. If the emf of the cell is zero, the $\Delta S^\ominus$ (in J K$^{-1}$ mol$^{-1}$) of the cell reaction per mole of B formed at 300 K is ____.

(Given: ln(2) = 0.7, $R$ (universal gas constant) = 8.3 J K$^{-1}$ mol$^{-1}$. $H$, $S$ and $G$ are enthalpy, entropy and Gibbs energy, respectively.)

An ideal gas is expanded from $(\mathrm{p_1, V_1, T_1})$ to $(\mathrm{p_2, V_2, T_2})$ under different conditions. The correct statement(s) among the following is(are)