Which of the following are correct about the given changes shown below at 1 bar pressure and $25^{\circ} C$ ?
$a A + b B (T K) Δ H_{T K}^{\circ} - --- \to c C + d D (T K)$
$Δ C_{p_{1}} ↓ ↑ Δ C_{p_{2}}$
$a A + b B (298 K) - ---- \to Δ H_{298 K}^{\circ} c C + d D (298 K)$

Δ C_{p_{1}}^{\circ} = [a C_{p}^{\circ} (A) + b C_{p}^{\circ} (B)] \times (298 - T)

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Δ C_{p_{2}}^{\circ} = [c C_{p}^{\circ} (C) + d C_{p}^{\circ} (D)] \times (T - 298)

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Δ H_{T}^{\circ} = [a C_{p}^{\circ} (A) + b C_{p}^{\circ} (B)] \times (298 - T) + Δ H_{298}^{\circ} + [c C_{p}^{\circ} (C) + d C_{p}^{\circ} (D)] \times (T - 298)

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Δ H_{T}^{\circ} = Δ H_{298}^{\circ} + Δ C_{p}^{\circ} (T - 298)

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Solution

The correct options are
A $Δ C_{p_{2}}^{\circ} = [c C_{p}^{\circ} (C) + d C_{p}^{\circ} (D)] \times (T - 298)$
B $Δ C_{p_{1}}^{\circ} = [a C_{p}^{\circ} (A) + b C_{p}^{\circ} (B)] \times (298 - T)$
C $Δ H_{T}^{\circ} = [a C_{p}^{\circ} (A) + b C_{p}^{\circ} (B)] \times (298 - T) + Δ H_{298}^{\circ} + [c C_{p}^{\circ} (C) + d C_{p}^{\circ} (D)] \times (T - 298)$
D $Δ H_{T}^{\circ} = Δ H_{298}^{\circ} + Δ C_{p}^{\circ} (T - 298)$
(A) The expression for the heat capacity at constant pressure is $Δ C_{p_{1}}^{\circ} = [a C_{p}^{\circ} (A) + b C_{p}^{\circ} (B)] \times (298 - T)$
Thus, the option A is correct.
(B) The expression for the heat capacity at constant pressure is $Δ C_{p_{2}}^{\circ} = [c C_{p}^{\circ} (C) + d C_{p}^{\circ} (D)] \times (T - 298)$
Thus, the option B is correct.
(C) The expression for the enthalpy change is $Δ H_{T}^{\circ} = [a C_{p}^{\circ} (A) + b C_{p}^{\circ} (B)] \times (298 - T) + Δ H_{298}^{\circ} + [c C_{p}^{\circ} (C) + d C_{p}^{\circ} (D)] \times (T - 298)$
Thus, the option C is correct.
(D) The expression for the enthalpy change is $Δ H_{T}^{\circ} = Δ H_{298}^{\circ} + Δ C_{p}^{\circ} (T - 298)$
Thus, the option D is correct.

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Similar questions

Q. From the given table answer the following questions :

	CO(g)	$C O_{2} (g)$	$H_{2} O (g)$	$H_{2} (g)$
${(Δ H_{f}^{\circ})}_{298}$ ( -kCal / mole )	$-$ 26.42	$-$ 94.05	$-$ 57.8	0
${(Δ G^{\circ}_{f})}_{298}^{\circ}$ ( -kCal / mole )	$-$ 32.79	$-$ 94.24	$-$ 54.64	0
$S_{298}^{\circ}$ ( -Cal / Kmole )	47.3	51.1	?	31.2

Reaction :

H_{2} O (g) + C O (g) ⇌ H_{2} (g) + C O_{2} (g)

( i )

Δ_{r} H_{298}^{\circ}

( ii )

Δ_{r} G_{298}^{\circ}

( iii )

Δ_{r} S_{298}^{\circ}

( iv )

Δ_{r} E_{298}^{\circ}

( v )

S_{298}^{\circ} [H_{2} O (g)]

In the following diagram $P_{A}, P_{B}, P_{C}, P_{D} a n d P_{E}$ be the pressure exerted by the liquid in the vessels A, B, C, D and E respectively. Find the correct order of pressure exerted by each vessel.