Answer to Question #60845 in General Chemistry for MJ

Question

Gallium, Ga: 69.723 g/mole

Solid specific heat, Csolid 0.371 J/g C

Enthalpy of Fusion, 80.2 J/g

melting point temperature, Tmelt 29.76 C

Liquid specific heat, Cliquid 0.371 J/g C

Suppose you cast 20.0 g spoon out of pure Gallium, cool it to an initial temperature of 0.00 C and use it to stir a 250 mL cup of coffee that starts at a temperature of 95.00 C. Assume that the coffee has a heat capacity identical to water (4.184 J/g C) and a density of 1.00 g/mL

a) Assuming that the entire spoon is heated uniformly, how much energy is required to warm the Gallium to its melting point?

b) what is the temperature of the coffee after the Gallium has been warmed to its melting point?

c) how much energy is required to melt the Gallium after it has reached its melting point?

d) what is the temperature of the coffee after this energy transfer?

Answer 1

a) According to Q = c(Ga)·m·(t1 – t2) = 20.0 g · 0.371 J/g·°C · 29.76 °C = 221 J. Thus, it needs 221 Joule to be heated to 29.76 degrees from 0.
b) The coffee liquid loose same quantity of heat as gallium obtained within the stirring process. Thus, Q = c(H2O)·m Δt and Δt = Q/c(H2O)·m = 221 J/4.184 J/g·°C 250 g = 0.21 °C. Spoon will be cooled down to 95.00 – 0.21 = 94.79 °C.
c) The required heat is Q1 = λ·m(Ga) = 80.2 J/g · 20.0 g = 1604 J.
d) Again, the coffee loose same quantity of heat as gallium required for the melting process: Q1 = c(H2O)·m·Δt and Δt = Q1/c(H2O)·m = 1604 J/4.184 J/g·°C·250 g = 1.53 °C. Thus, the temperature of coffee liquid will be 94.79 – 1.53 = 93.26 °C.