Thermodynamics and Thermochemistry 1 Question 8
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8. For silver, $C_{p}\left(\mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)=23+0.01 \mathrm{~T}$. If the temperature $(T)$ of 3 moles of silver is raised from $300 \mathrm{~K}$ to $1000 \mathrm{~K}$ at $1 \mathrm{~atm}$ pressure, the value of $\Delta H$ will be close to
======= ####8. For silver, $C_{p}\left(\mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)=23+0.01 \mathrm{~T}$. If the temperature $(T)$ of 3 moles of silver is raised from $300 \mathrm{~K}$ to $1000 \mathrm{~K}$ at $1 \mathrm{~atm}$ pressure, the value of $\Delta H$ will be close to
3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed (a) $62 \mathrm{~kJ}$
(b) $16 \mathrm{~kJ}$
(c) $21 \mathrm{~kJ}$
(d) $13 \mathrm{~kJ}$
(2019 Main, 8 April I)
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Solution:
- According to Kirchoff’s relation,
$$ \Delta H=n \int_{T_{1}}^{T_{2}} C_{p} d T $$
where, $\Delta H=$ Change in enthalpy.
$C_{p}=$ Heat capacity at constant pressure.
Thermodynamics and Thermochemistry 113
Given, $n=3$ moles, $T_{1}=300 \mathrm{~K}, T_{2}=1000 \mathrm{~K}, C_{p}=23+0.01 \mathrm{~T}$ On substituting the given values in Eq. (i), we get
$$ \begin{aligned} \Delta H & =3 \int_{300}^{1000}(23+0.01 T) d T=3 \int_{300}^{1000} 23 d T+0.01 T d T \ & =3\left[23 T+\frac{0.01 T^{2}}{2}\right]_{300}^{1000} \ & =3\left[23(1000-300)+\frac{0.01}{2}\left(1000^{2}-300^{2}\right)\right] \ & =3[16100+4550]=61950 \mathrm{~J} \approx 62 \mathrm{~kJ} \end{aligned} $$
