Question

78.
If 7 cal heat is required to raise the temperature
of 2g hydrogen gas by 1°C at constant volume.
Then enthalpy change for heating of 10 g
hydrogen gas from 10°C to 20°C will be :-
(1) 450 cal
(2) 250 cal
(3) 50 cal
(4) 650 cal​

Answer 1

The enthalpy change is, (1) 450 cal

Explanation :

Heat released at constant pressure is known as enthalpy.

Heat released at constant volume is known as internal energy.

First we have to calculate the value of $C_p$.

As are given that, heat at constant volume is, 7 cal for 1 mole of gas.

$C_p-C_v=R\\\\C_p=R+C_v\\\\C_p=2+7=9cal$

Now we have to caculate the change in enthalpy.

The formula used for change in enthalpy of the gas is:

$\Delta Q_p=\Delta H\\\\\Delta H=nC_p\Delta T\\\\\Delta H=nC_p(T_2-T_1)$

where,

$\Delta Q_p$ = heat at constant pressure

$\Delta H$ = change in enthalpy energy  = ?

n = number of moles of hydrogen gas = $\frac{10g}{2g/mol}=5mol$

$C_p$ = heat at constant pressure = 9 cal

$T_1$ = initial temperature = $10^oC$

$T_2$ = final temperature = $20^oC$

Now put all the given values in the above formula, we get:

$\Delta H=nC_p(T_2-T_1)$

$\Delta H=(5moles)\times (9cal/^oC.mol)\times (20-10)^oC$

$\Delta H=450cal$

Thus, the enthalpy change is, 450 cal

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