5g of LiCl is dissolved in 40 ml of water at 17°C. When the temperature of a solution rises to 40.3°C, the molar heat of a LiCl solution is 32.7 kJ/mol.
The molar heat of a solution(ΔH) is calculated by the formula
ΔH=q/n
Where, n-Number of moles
q- Energy of the system
q is calculated by the formula
q=m×c×ΔT
Where ΔT=(T_f-T_i)
T_f=40.3°C, T_i=17°C
ΔT=(40.3-17)°C=23.3°C
c=4.18 J/g°C
The mass of water is
m=40 ml×(1 g/1 ml)=40 g
Plug all values in the formula
q=40g×(4.18 J/g°C)×23.3°C
q=3895.76 J
The molar mass of LiCl is 42g/mol. Therefore, the moles of LiCl is
moles=5g×(1 mol/42 g)
moles=0.11905 mol
Hence, the molar heat of a solution is
ΔH=3895.76 J/0.11905 mol
ΔH=32723.7295 J/mol
Convert the value in kJ
ΔH=32723.7295 J/mol×(1 kJ/1000 J)
ΔH=32.7 kJ/mol
Therefore, the molar heat of a solution is 32.7 kJ/mol.
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