Question

Calculate ΔS_sys, ΔS_surr, and ΔS_tot when 245 g of ice at 0 ^oC is added to 32 g of steam at 115 ^oC in a poorly insulated container. During this addition, 4530 J of heat energy is lost to the surroundings. The values of C_p,m for water, ice, and steam are 75.3 J/K mol, 37.7 J/K mol, and 35.5 J/K mol respectively. The ΔH_fus for water is 6.02 kJ/mol and the ΔH_vap for water is 40.656 kJ/mol.

Answer 1

Given data:

The mass of ice = 245 g = 245/18 = 13.61 mol, its temperature (T₁) = 0 ^oC = 273 K

The mass of steam = 32 g = 32/18 = 1.78 mol, its temperature (T₂) = 115 ^oC = 115 + 273 = 388 K

i.e. ΔT = 388 - 273 = 115 K

The molar specific heat capacity of water (C_p,m for water) = 75.3 J/K mol

The molar specific heat capacity of ice (C_p,m for ice) = 37.7 J/K mol

The molar specific heat capacity of steam (C_p,m for steam) = 35.5 J/K mol

ΔH_fus for water = 6.02 kJ/mol

ΔH_vap for water = 40.656 kJ/mol.

The heat released during the given addition process = 4530 J

ΔS_sys = Q_sys / ΔT

= 4530/115 K

= 39.4 J/K

ΔS_surr = Q_surr / ΔT

= -4530/115 K

= -39.4 J/K

ΔS_tot = ΔS_sys + ΔS_surr

= 39.4 - 39.4

= 0