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1

### AIPMT 2010 Prelims

Standard entropies of X2, Y2 and XY3 are 60, 40 and 50 J K$$-$$1 mol$$-$$1 respectively. For the reaction

1/2X2 + 3/2Y2 $$\rightleftharpoons$$ XY3, $$\Delta$$H = $$-$$ 30 kJ,

to be at equilibrium, the temperature should be
A
750 K
B
1000 K
C
1250 K
D
500 K

## Explanation

Given reaction is :

$${1 \over 2}$$X2 + $${3 \over 2}$$Y2 ⇌ XY3

We know,

$$\Delta$$So = $$\sum {S_{products}^o} - \sum {S_{reac\tan ts}^o}$$

= 50 - (30 + 60) = -40 J K-1 mol-1

At equilibrium $$\Delta$$Go = 0

$$\Delta$$Ho = T$$\Delta$$So

$$\therefore$$ $$T = {{\Delta {H^o}} \over {\Delta {S^o}}}$$ = $${{ - 30 \times {{10}^3}} \over { - 40}}$$ = 750 K
2

### AIPMT 2010 Prelims

For an endothermic reaction, energy of activation is Ea and enthalpy of reaction is $$\Delta$$H (both of these in kJ/mol). Minimum value of Ea will be
A
less than $$\Delta$$H
B
equal to $$\Delta$$H
C
more than $$\Delta$$H
D
equal to zero

## Explanation

Here,

Ea = activation energy of forward reaction

E’a = activation energy of backward reaction

$$\Delta$$H = enthalpy of the reaction From the given diagram it is clear that

Ea = E’a + $$\Delta$$H

$$\therefore$$ Ea > $$\Delta$$H
3

### AIPMT 2009

From the following bond energies :
H $$-$$ H bond energy   : 431.37 kJ mol$$-$$1
C $$=$$ C bond energy   : 606.10 kJ mol$$-$$1
C $$-$$ C bond energy   : 336.49 kJ mol$$-$$1
C $$-$$ H bond energy   : 410.50 kJ mol$$-$$1
Enthalpy for the reaction, will be
A
$$-$$ 243.6 kJ mol$$-$$1
B
$$-$$ 120.0 kJ mol$$-$$1
C
553.0 kJ mol$$-$$1
D
1523.6 kJ mol$$-$$1

## Explanation

$$\Delta$$Hreaction = Σ(Bond enthalpy)reactants

– Σ(Bond enthalpy)products

= [B.E(C-C) + B.E(H-H) + 4$$\times$$B.E(C-H)]

- [B.E(C-C) + 6$$\times$$B.E(C-H)]

= [606.10 + 4(410.50) + 431.37]

– [336.49 + 6(410.50)]

= 2679.47 – 2799.49

= – 120.02 kJ mol–1
4

### AIPMT 2009

The values of $$\Delta$$H and $$\Delta$$S for the reaction,

C(graphite) + CO2(g) $$\to$$  2CO(g)

are 170 kJ and 170 J K$$-$$1, respectively. This reaction will be spontaneous at
A
910 K
B
1110 K
C
510 K
D
710 K

## Explanation

We know, $$\Delta$$G = $$\Delta$$H – T$$\Delta$$S

For reaction to be spontaneous, $$\Delta$$G < 0

$$\Rightarrow$$ $$\Delta$$H – T$$\Delta$$S < 0

$$\Rightarrow$$ 170 $$\times$$ 103 - T(170) < 0

$$\Rightarrow$$ T > 1000 K

Among the given temperatures, only 1110 K is greater than 1000 K thus, at this temperate the reaction will be spontaneous.

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