Question

On the assumption that copper– nickel alloys are random mixtures of copper and nickel atoms, calculate the mass of copper which, when mixed with 100 g of nickel, causes an increase in entropy of 15 J/K. The gram atomic weights of Cu and Ni are, respectively, 63.55 and 58.69.

Answer 1

Answer:

65.14 g

Explanation:

The change in the entropy of two ,metals on mixing is

$\delta S= R[(n_{cu}+n_{Ni})ln(n_{cu}+n_{Ni})-n_{cu}lnn_{cu}-n_{Ni}lnn_{Ni}]$

Here, R is real gas constant, n_{cu} is the number of moles of the copper, and n_{Ni} is the number of moles of nickel

Thus the number of moles of Nickel is

$n_{Ni}=\frac{m_{Ni}}{M_{Ni}}$

$n_{Ni}=\frac{100}{58.69}$ =1.7 moles

now put n_{Ni} = 1.7  ΔS= 15,

R= 8.314 and solve

$15= R[(n_{cu}+1.7)ln(n_{cu}+1.7)-n_{cu}lnn_{cu}-1.7ln1.7]$

On solving the number of moles of copper in the mixture

n_cu= 1.025

Thus the mass of copper is = n_cu×M_cu = 1.025×63.55 =  65.14 g

Therefore the required mass is =  65.14 g