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 need to use the concept of the enthalpy of mixing and the given value of delta w (-4250 J/mol).
Enthalpy of mixing (delta H_mix) is the change in enthalpy when two or more substances mix to form a solution. It is related to the change in Gibbs free energy (delta G_mix) by the equation:
delta G_mix = delta H_mix - T * delta S_mix
where T is the temperature and delta S_mix is the change in entropy of mixing.
In this case, we are given the value of delta w (in J/mol), which is the change in enthalpy for the mixing of 1 mole of the components. To find the enthalpy of mixing for a solution with 10% platinum and 90% gold, we can use the equation:
delta H_mix = (percentage of platinum/100) * delta w
In this case, the percentage of platinum is 10% (0.1) and the percentage of gold is 90% (0.9). Thus, we have:
delta H_mix = (0.1) * (-4250 J/mol)
To express the answer in kJ/mol, we need to convert J to kJ by dividing by 1000. Therefore, the enthalpy of mixing for a solution of 10% platinum and 90% gold is:
delta H_mix = (-4250 J/mol) / 1000 = -4.25 kJ/mol
So, the enthalpy of mixing for this solution is -4.25 kJ/mol.