In Hong Kong, I order an "Iceberg Coffee." I am served a
shot-jug of liquid and a glass of coffee sitting in a bowl of ice:
The liquid turns out to be sugar syrup, while the coffee is unsweetened. My course of action becomes clear; I
take the sugar syrup and pour a little into the bowl of ice. The waiter
probably thinks I’m stupid because the syrup was supposed to go into the
coffee, but the thing is:
0. After the ice leaves the freezer, it absorbs heat from the environment until it reaches 0 °C, the freezing point (T) of water. Any further heat goes into enthalpy of fusion (∆H) needed to melt the ice, so the temperature stays at 0 °C until all the ice is melted.
0. After the ice leaves the freezer, it absorbs heat from the environment until it reaches 0 °C, the freezing point (T) of water. Any further heat goes into enthalpy of fusion (∆H) needed to melt the ice, so the temperature stays at 0 °C until all the ice is melted.
1. Via Raoult’s
law, the freezing point of a solvent is changed by –RMT2/∆H per
molal of dissolved particles, so for water:
–8.31 J/(K
mol) × 0.0180 kg/mol × 2732 K2 ÷ 6010.0 J/mol = –1.86 °C
kg/mol
▪ For each 10 g of ice, each
gram of dissolved sucrose changes the freezing point by:
0.1 ×
–1.86 °C kg/mol ÷ 0.342 kg/mol = –0.543 °C
to a limit of –9.5 °C at the eutectic point.
to a limit of –9.5 °C at the eutectic point.
2.
The 0 °C ice is now hotter than its lowered freezing point so it melts. The
enthalpy of fusion (∆H = 334000 J/kg) needed is absorbed from any surrounding
heat; liquid water has a specific heat capacity of 4220 J/(kg K) at STP:
–334000 J/kg ÷ 4220 J/(kg K) = –79.1 °C
▪ Each 10 g of ice that melts from the sugar
removes enough heat to chill 100 mL of water by 7.91 °C until the new lowered
freezing point is reached.
I feel the spot where
I poured the sugar. It seems slightly colder, but sugar syrup isn’t going to cut it. I ask
the waiter for a salt shaker:
3. Salt dissolves more easily than sugar. It also dissociates into Na+ and Cl– so that’s double the molal.
▪ For 10 g of ice, each gram of dissolved NaCl changes the freezing point by:
3. Salt dissolves more easily than sugar. It also dissociates into Na+ and Cl– so that’s double the molal.
▪ For 10 g of ice, each gram of dissolved NaCl changes the freezing point by:
0.1 × –1.86 °C kg/mol
× 2 ÷ 0.0584 kg/mol = –6.36 °C
to a limit of –21.1 °C at the eutectic point
to a limit of –21.1 °C at the eutectic point
I pour in the salt. The outside of the bowl frosts over from the extra coldness. I like my iced coffee unsweetened and below freezing.
