Question

For 11.20 kg of a magnesium-lead alloy of composition 30 wt% Pb-70 wt% Mg, is it possible, at equilibrium, to have α and Mg2Pb phases having respective masses of 7.39 kg and 3.81 kg? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.

Answer 1

Answer:

Maximum concentration for Pb is only 41%. we get 64.3% which exceeds the maximum concentration. Therefore it is not possible.

Explanation:

let's first determine the mass fraction of the phases as follows

$W_{a}=\frac{m_{a} }{m_{a}+m_{p_{g2}p_{b} } }$

Given that masses are $m_{a}=7.39kg$ and $m_{p_{g2}p_{b} }=3.81kg$

Thus, $W_{a} =\frac{7.39}{7.39+3.81}=0.659$

$W_{M_{g2Pb} } =1-W_{a}=1-0.659=0.341$

Now determine the concentration

$W_{a}=\frac{C_{0}-C_{a} }{C_{b}-C_{a} }$

At 81% PB and 70% Pb only point at which $M_{g2Pb}$ exists, we can solve

$0.659=\frac{70-81}{C_{b}-81 }$

$C_{b}=$64.3%

Refer text book page no. 326, figure 9.20, from figure we can say maximum concentration for Pb is only 41%. we get 64.3% which exceeds the maximum concentration.