Answer : The value of q, w and ΔE in kilojoule are -67.7 kJ, 27.05 kJ and -40.65 kJ respectively.
Explanation :
Formula used :
![\Delta H=\Delta q\\\\\Delta q=nC_p\Delta T\\\\Q=nC_p\Delta T](https://tex.z-dn.net/?f=%5CDelta%20H%3D%5CDelta%20q%5C%5C%5C%5C%5CDelta%20q%3DnC_p%5CDelta%20T%5C%5C%5C%5CQ%3DnC_p%5CDelta%20T)
where,
Q = heat at constant pressure = ?
= change in enthalpy energy
n = number of moles of helium gas = 78.25 mol
![\text{Moles of }He=\frac{\text{Mass of }He}{\text{Molar mass of }He}](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DHe%3D%5Cfrac%7B%5Ctext%7BMass%20of%20%7DHe%7D%7B%5Ctext%7BMolar%20mass%20of%20%7DHe%7D)
Molar mass of He = 4 g/mole
![\text{Moles of }He=\frac{313g}{4g/mole}=78.25mole](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DHe%3D%5Cfrac%7B313g%7D%7B4g%2Fmole%7D%3D78.25mole)
= heat capacity at constant pressure = ![20.8J/mol.^oC](https://tex.z-dn.net/?f=20.8J%2Fmol.%5EoC)
= change in temperature = ![-41.6^oC](https://tex.z-dn.net/?f=-41.6%5EoC)
Now put all the given values in the above formula, we get:
![Q=nC_p\Delta T](https://tex.z-dn.net/?f=Q%3DnC_p%5CDelta%20T)
![Q=(78.25mol)\times (20.8J/mol.^oC)\times (-41.6)^oC](https://tex.z-dn.net/?f=Q%3D%2878.25mol%29%5Ctimes%20%2820.8J%2Fmol.%5EoC%29%5Ctimes%20%28-41.6%29%5EoC)
![Q=-67708.16J=-67.7kJ](https://tex.z-dn.net/?f=Q%3D-67708.16J%3D-67.7kJ)
Now we have to calculate the work done.
Formula used :
![w=-p\Delta V\\\\w=-p(V_2-V_1)](https://tex.z-dn.net/?f=w%3D-p%5CDelta%20V%5C%5C%5C%5Cw%3D-p%28V_2-V_1%29)
where,
w = work done
p = pressure of the gas = 1 atm
= initial volume = 1910 L
= final volume = 1643 L
Now put all the given values in the above formula, we get:
![w=-p(V_2-V_1)](https://tex.z-dn.net/?f=w%3D-p%28V_2-V_1%29)
![w=-(1atm)\times (1643-1910)L](https://tex.z-dn.net/?f=w%3D-%281atm%29%5Ctimes%20%281643-1910%29L)
![w=267L.artm=267\times 101.3J=27047.1J=27.05kJ](https://tex.z-dn.net/?f=w%3D267L.artm%3D267%5Ctimes%20101.3J%3D27047.1J%3D27.05kJ)
conversion used : (1 L.atm = 101.3 J)
Now we have to calculate the value of
of the gas.
![\Delta E=q+w](https://tex.z-dn.net/?f=%5CDelta%20E%3Dq%2Bw)
![\Delta E=(-67.7kJ)+27.05kJ](https://tex.z-dn.net/?f=%5CDelta%20E%3D%28-67.7kJ%29%2B27.05kJ)
![\Delta E=-40.65kJ](https://tex.z-dn.net/?f=%5CDelta%20E%3D-40.65kJ)
Therefore, the value of
of the gas is -40.65 kJ.