Answer to Question #171923 in General Chemistry for Erin

Question

Calculate how much energy is required to heat 50 g of mercury from −50oC to 750oC.

Answer 1

n(Hg)=m/M=50/200=0.25(mol).

Mercury has a melting point of -38.9^oC, a boiling point of 356.7^oC, so in the given range solid mercury is 1)heated from -50°C to -38.9°C, 2)melts at -38.9°C, 3)then liquid mercury is heated from -38.9°C to 356.7°C, 4)vaporises at 356.7°C, 5)then mercury vapour is heated from 356.7°C to 750°C.

1) Heat capacity of solid mercury is 28.1 J/mol*K.

Q=C_p*n*∆T

∆T=50-38.9=11.1

Q=28.1*0.25*11.1=77.98(J).

2) Latent Heat of Fusion of Mercury is 2.295 kJ/mol.

Q=C_p*n

Q=2.295*0.25=0.57374(kJ)=573.74(J).

3) Specific heat of liquid mercury is 0.139 J/g*°C.

Q=C*m*∆T

∆T=|-38.9-356.7|=395.6

Q=0.139*50*395.6=2749.42(J).

4) Latent Heat of Vaporization of Mercury is 59.229 kJ/mol.

Q=C_p*n

Q=59.299*0.25=14.82475(kJ)=14824.75(J)

5) Heat capacity of gaseous mercury is 20.786 J/mol*K.

Q=C_p*n*∆T

∆T=750-356.7=393.3

Q=20.786*0.25*393.3=2043.78(J).

Q_total=77.98+573.74+2749.42+14824.75+2043.78=20269.67(J)=20.270(kJ).