Question

In an insulated container $1$ mole of a liquid. Molar volume $100$ ml at 1 bar. Liquid is steeply taken to $100$ bar, when volume of the liquid decreases by $1$ml. find $\Delta {\rm H}$ for the process.
A.$7900$ bar ml
B.$8900$ bar ml
C.$9900$ bar ml
D.$10900$ bar ml

Answer 1

Hint: Enthalpy of the chemical reaction is defined as the sum of the internal energy and the product of its pressure and volume which is expressed as $H = U + p\Delta V$. Change in the volume of the chemical reaction at constant pressure is referred to as pressure-volume work.

Complete answer:
From the first law of thermodynamics we know the relation between internal energy, heat and work of the system.
$\Delta U = q + w$
Since, an insulated chamber is used in the reaction which means the reaction is conducted under adiabatic conditions where heat change becomes zero $\left( {q = 0} \right)$.
$\Delta U = w$……….$\left( i \right)$
We know that work depend on the pressure and volume of reaction which is expressed as-
$w = - p\left( {{V_2} - {V_1}} \right)$
Where, is pressure of system which is $100$ in reaction
Is final volume of system which is $99$ ml
Is initial volume of system which is $100$ ml
$w = - 100\left( {99 - 100} \right)$
$w = - 100\left( { - 1} \right)$
After calculating this reaction, we get
$w = 100$
After putting the value of work in the equation $\left( i \right)$
$\Delta U = w$
$\Delta U = 100$ bar ml
From the equation of enthalpy as given above –
$H = U + \Delta pV$
$\Delta H = \Delta U + \left( {{p_2}{V_2} - {p_1}{V_1}} \right)$
Put all the obtained values in the above equation to obtain the value of $\Delta {\rm H}$.
$\Delta {\rm H} = 100 + \left( {100 \times 99 - 1 \times 100} \right)$
$\Delta {\rm H} = 100 + \left( {9900 - 100} \right)$
After solving the above equation, we get,
$\Delta {\rm H} = 100 + 9800$
Hence, $\Delta {\rm H} = 9900$ bar ml. Therefore option C is the correct option.

Note:
Amount of heat absorbed at constant volume is expressed as $\Delta U$ as while the amount of heat absorbed at constant pressure is expressed as $\Delta {\rm H}$.
Take the unit of pressure in the bar and volume of solution in ml.