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.
Well, let's take a moment to appreciate the combo of gold and platinum - it's like a luxurious match made in chemical heaven! Now, to calculate the enthalpy of mixing, you need to take into account the value of delta w, which is -4250 J/mol.
To express our answer in kJ/mol, we divide this value by 1000, since there are 1000 J in a kJ. So, delta w is equal to -4.25 kJ/mol.
Now, since we have a solution with 90% gold and 10% platinum, we can say that the enthalpy of mixing for this solution is 90% of gold's enthalpy plus 10% of platinum's enthalpy.
Since we don't have the individual enthalpies for gold and platinum, let's just pretend they're at a comedy show - they both bring a lot of heat to the stage! So, we can assume the enthalpies are 0 for gold and 0 for platinum.
Therefore, the enthalpy of mixing for the 10% platinum and 90% gold solution would be:
(90% × 0) + (10% × 0) = 0 kJ/mol
So, the enthalpy of mixing for this solution is zero, my friend! It's like there's no heatwave in the solution - it's all cool as a cucumber.
To calculate the enthalpy of mixing for a solution of 10% platinum and 90% gold, we can use the equation:
ΔH_mix = x_A * x_B * Δw
where
ΔH_mix is the enthalpy of mixing
x_A and x_B are the mole fractions of the components
Δw is the change in molar Gibbs energy of mixing per mole of solute
Given that Δw = -4250 J/mol and the solution contains 10% platinum (0.1 mole fraction) and 90% gold (0.9 mole fraction), we can substitute these values into the equation:
ΔH_mix = (0.1) * (0.9) * (-4250 J/mol)
Now, let's calculate the enthalpy of mixing:
ΔH_mix = -0.1 * 0.9 * 4250 J/mol
To express the answer in kJ/mole, we divide the result by 1000 (since 1 kJ = 1000 J):
ΔH_mix = (-0.1 * 0.9 * 4250 J/mol) / 1000 kJ/J
ΔH_mix = -38.25 kJ/mol
Therefore, the enthalpy of mixing for a solution of 10% platinum and 90% gold is -38.25 kJ/mol.
To calculate the enthalpy of mixing for a solution of 10% platinum and 90% gold, we need to use the energy of mixing, also known as the enthalpy of mixing, which is denoted as ΔH_mix.
Given that the value of Δw is -4250 J/mole, we need to convert it to kJ/mole since the question asks for the answer in those units.
1 kJ = 1000 J
So, -4250 J/mole = -4.25 kJ/mole
Now, let's calculate the enthalpy of mixing.
ΔH_mix = (moles of gold * ΔH_gold) + (moles of platinum * ΔH_platinum)
Since the solution contains 10% platinum and 90% gold, we can assume that we have 10 moles of platinum and 90 moles of gold in a 100-mole solution.
ΔH_mix = (90 moles * 0 J/mole) + (10 moles * -4.25 kJ/mole)
The reason we assume ΔH_gold is 0 J/mole is that we take pure gold as the reference state with no mixing enthalpy.
Simplifying the equation:
ΔH_mix = 0 kJ/mole + (-42.5 kJ/mole)
ΔH_mix = -42.5 kJ/mole
Therefore, the enthalpy of mixing for a solution of 10% platinum and 90% gold is -42.5 kJ/mole.