On the assumption that copper– nickel alloys are random mixtures of copper and nickel atoms, calculate the mass of copper which,

Question

2 months ago

13

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.

1 answer:

inna [3.1K] · Answer 1 · 2026-03-11T14:02:17+03:00

Response:

65.14 g

Clarification:

The entropy change resulting from mixing two metals is

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

Here, R is the real gas constant, n_{cu} denotes the moles of copper, while n_{Ni} signifies the moles of nickel.

Therefore, determining the moles of Nickel yields

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

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

Then substituting n_{Ni} = 1.7 into the equation produces ΔS= 15,

with R= 8.314, and solving gives

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

Upon resolving, the quantity of moles of copper in the mixture equals

n_cu= 1.025

Thus, the copper mass is calculated as n_cu×M_cu = 1.025×63.55 = 65.14 g

Consequently, the required mass is found to be = 65.14 g