Consider the gold-platinum system which has a value of delta w of -4250 J/mole;
(a) Calculate the enthalpy of mixing for a solution of 10% platinum and 90% gold. Express your answer in units of kJ/mole.
To calculate the enthalpy of mixing for a solution of 10% platinum and 90% gold, we can use the formula:
ΔH_mix = (n₁ * ΔH₁ + n₂ * ΔH₂) / (n₁ + n₂)
Where:
ΔH_mix is the enthalpy of mixing,
n₁ and n₂ are the number of moles of the components,
ΔH₁ and ΔH₂ are the enthalpy values for each component.
In this case, since we have 10% platinum and 90% gold, we can assume a 100-mole sample of the solution. Therefore, we have:
n₁ = 10 moles of platinum
n₂ = 90 moles of gold
Now, we need to determine the enthalpy values of platinum (ΔH₁) and gold (ΔH₂). Given that the value of Δw is -4250 J/mole, we can use the following formula to convert it to enthalpy:
ΔH = Δw + RT
Where:
ΔH is the enthalpy change,
Δw is the work done,
R is the gas constant, and
T is the temperature.
Assuming that the temperature is constant at room temperature (298 K) and R is 8.314 J/(mol K), we can calculate ΔH for platinum:
ΔH₁ = -4250 J/mole + (8.314 J/(mol K) * 298 K)
= -4250 J/mole + 2466.372 J/mole
= -1783.628 J/mole
Now, let's calculate ΔH for gold:
ΔH₂ = -4250 J/mole + (8.314 J/(mol K) * 298 K)
= -4250 J/mole + 2466.372 J/mole
= -1783.628 J/mole
Finally, we can substitute the values into the formula to find the enthalpy of mixing:
ΔH_mix = (10 moles * -1783.628 J/mole + 90 moles * -1783.628 J/mole) / (10 moles + 90 moles)
= -16052.652 J/mole
Converting the result to kJ/mole:
ΔH_mix = -16052.652 J/mole / 1000 J/kJ
= -16.05 kJ/mole
Therefore, the enthalpy of mixing for a solution of 10% platinum and 90% gold is -16.05 kJ/mole.