A gold coin whose mass is 7.06 g is heated to 137.6°C...

Question

A gold coin whose mass is 7.06 g is heated to 137.6^oC and then quickly dropped into an ice calorimeter. What mass of ice melts? (The amount of heat in an ice calorimeter is determined from the quantity of ice the melts, knowing that it takes 6.01 kJ of heat to melt exactly one mole of ice. Molar heat capacity of gold is 25.418 J/mol/K)

Answer 1

It takes 6.01 kJ of heat energy to melt 1 mole of ice at 0ºC (a phase change)

Find the kJ of energy (q) released by the hot gold: q = mC∆T = mass x specific heat x change in temp

q = ?

m = mass = 7.06 g x 1 mol / 197 g = 0.0354 moles

C = 25.418 J/molº

∆T = change in temperature = 137.6º (for gold to get to zero degrees C, the melting point of ice)

q = (0.0354 mols)(25.418 J/molº)(137.6º) = 125.3 J = 0.125 kJ

Mass of ice melted = 0.125 kJ x 1 mol ice / 6.01 kJ = 0.0208 mols of ice x 18 g/mol = 0.374 g of ice melted

Answer 2

Temp in Kelvin scale: 137.6+273.15

No. of moles of gold: 7.06g/197g/mol

Heat released from hot gold: 25.418 J/(mol.K) x (137.6+273.15)K x (7.06g/197g/mol)

Quantity of ice that melts (in moles):

[25.418 J/(mol.K) x (137.6+273.15)K x (7.06g/197g/mol)]/(6.01 kJ x1000)