Question

Calculate the heat required to form a liquid solution at 1356 k starting with 1 mole of cu and 1 mole of ag at 298 k. at 1356 k the molar heat of mixing of liquid cu and liquid ag is given δhm = 20,590xcuxag .

Answer 1

Answer:

$Q=87924J$

Explanation:

Hello,

At first, we must consider that at the beginning, both copper and silver are solid, so we must melt both of them, thus, the following enthalpic routes are proposed in order to know each heat because coppers melting points as a value of 1356K and silver's melting point 1235K:

$H_{Cu}=n_{Cu}*(Cp_{solid,Cu}(T_2-T_1)+H_{melt})\\H_{Cu}=1mol*(0.3768J/gK*63.546g/mol*(1356-298)K+13590J/mol) \\H_{Cu}=38922.89J$

$H_{Ag}=n_{Ag}*(Cp_{solid,Ag}(T_m-T_1)+H_{melt}+Cp_{liquid,Ag}(T_2-T_m))\\H_{Ag}=1mol*(0.235J/gK*107.868g/mol*(1235-298)K+11300J/mol+0.28J/gK*107.868g/mol*(1356-1235)K) \\H_{Ag}=38706.56J$

Now, the released heat due to the mixing process turns out into:

$H_{mix}=2mol*(20590x_{Cu}x_{Ag}J/mol)\\H_{mix}=2mol*20590(0.5)(0.5)J/mol\\H_{mix}=10295J$

Finally, the total heat required is found by:

$Q=H_{Cu}+H_{Ag}+H_{mix}\\Q=38922.89J+38706.56J+10295J\\Q=87924J$

Best regards.