Question

The heat of combustion of $H_{2}(g)$ at constant pressure and 300 K is – 280 kJ $mol^{-1}$. What will be heat of combustion at constant volume and at 300 K ?

Answer 1

"At constant pressure heat of combustion denotes "change in enthalpy" and it is indicated by the \Delta H.

At constant volume heat of combustion denotes change in internal energy and it is indicated by \Delta U.

The relation between two quantities are as follows.

$\Delta H\quad =\quad \Delta U\quad +\quad \Delta nRT$

Here, $\Delta n =$ Change in number of moles of gases during the reaction

The combustion reaction of hydrogen is as follows.

${ H }_{ 2 }(g)\quad \quad +\quad \frac { 1 }{ 2 } { O }_{ 2 }(g)\quad \quad\rightarrow\quad { H }_{ 2 }O\quad (l)$

$\Delta n\quad =\quad 0\quad -1.5\quad =\quad 1.5$

From the given

Heat of combustion = -280 KJ

Temperature = 300K

Substituting the given values

$-280000\quad =\quad \Delta U\quad +\quad (-1.5)\quad \times \quad 0.0821\quad \times \quad 300$

$\Delta U\quad =\quad -279963\quad J\quad =\quad -279.96\quad kJ$"

Answer 2

Answer:

ANSWER

The combustion reaction is as shown below.

H

2

(g)+

2

1

O

2

(g)⟶H

2

O(l)

The heat of combustion at constant pressure is ΔH=−280 kJ mol

−1

ΔH=ΔU+ΔnRT ,

Δn=0−

2

3

Δn=−

2

3

,

Here ΔU is the heat of combustion at constant volume.

Substitute values in the above expression.

ΔH=ΔU−

2

3

×8.314×300

−280kJ=ΔU−

20

74826

×

1000

1

kJ

⇒ΔU=−276.2587 kJ

Hence, the correct option is A