{"id":188145,"date":"2025-02-06T12:14:23","date_gmt":"2025-02-06T12:14:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188145"},"modified":"2025-02-06T12:14:26","modified_gmt":"2025-02-06T12:14:26","slug":"mg-pb-phase-diagram","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/06\/mg-pb-phase-diagram\/","title":{"rendered":"Mg-Pb Phase diagram"},"content":{"rendered":"\n

Mg-Pb Phase diagram Composition (at% Pb) 5 10 20 1 L 0 30 40 70 100 700 L 1200 600 + a +L Mg,Pb M 1000 500 800 400 B Temperature (\u00b0C) L + Temperature (\u00b0F) L Mg2Pb 300 600 200 B 400 a + Mg Pb 100 B + Mg Pb 200 Mg Pb 20 40 60 80 100 (Mg) Composition (wt% Pb) (Pb) 19. Utilize the previously given sheet of the Mg-Pb phase diagram, and for the alloy with composition (60 wt.%Pb-40 wt.% Mg), at temperature 300 oC, write down the weight percentage of the alpha phase. (2 points) Enter your answer<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Utilize the previously given sheet of the Mg-Pb phase diagram, and for the alloy with composition (60 wt.%Pb-40 wt.% Mg), at temperature 300 oC, write down the weight percentage of the alpha phase.<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

o determine the weight percentage of the alpha (\u03b1) phase in a 60 wt.% Pb\u201340 wt.% Mg alloy at 300\u00b0C, we can utilize the lever rule, a fundamental principle in phase diagram analysis.
Understanding the Phase Diagram:<\/strong><\/p>\n\n\n\n

he Mg-Pb phase diagram illustrates the equilibrium phases present at various compositions and temperatures.t 300\u00b0C, the diagram indicates that the \u03b1 phase (a solid solution of Pb in Mg) and the liquid phase coexist for compositions between approximately 20 wt.% Pb and 80 wt.% Pb.or a 60 wt.% Pb alloy at 300\u00b0C, both \u03b1 and liquid phases are present.
Applying the Lever Rule:<\/strong><\/p>\n\n\n\n

he lever rule allows us to calculate the mass fraction of each phase in a two-phase region.t is expressed as:
[ W_{\\alpha} = \\frac{C_{\\text{L}} – C_0}{C_{\\text{L}} – C_{\\alpha}} ]
here:
( W_{\\alpha} ) = mass fraction of the \u03b1 phase- ( C_{\\text{L}} ) = composition of the liquid phase- ( C_{\\alpha} ) = composition of the \u03b1 phase- ( C_0 ) = overall composition of the alloy
Determining Phase Compositions at 300\u00b0C:<\/strong><\/p>\n\n\n\n

rom the phase diagram at 300\u00b0C:
The liquid phase composition (( C_{\\text{L}} )) is approximately 70 wt.% Pb. The \u03b1 phase composition (( C_{\\alpha} )) is approximately 10 wt.% Pb.
Calculating the Mass Fraction of the \u03b1 Phase:<\/strong><\/p>\n\n\n\n

ubstituting the known values into the lever rule equation:
[ W_{\\alpha} = \\frac{70\\% – 60\\%}{70\\% – 10\\%} = \\frac{10\\%}{60\\%} = 0.1667 ]
herefore, the mass fraction of the \u03b1 phase is approximately 16.67%.
Calculating the Weight Percentage of the \u03b1 Phase:<\/strong><\/p>\n\n\n\n

o find the weight percentage of the \u03b1 phase, multiply the mass fraction by 100:
[ \\text{Weight \\% of \u03b1 phase} = 0.1667 \\times 100 = 16.67\\% ]
Conclusion:<\/strong><\/p>\n\n\n\n

t 300\u00b0C, a 60 wt.% Pb\u201340 wt.% Mg alloy consists of approximately 16.67% \u03b1 phase and 83.33% liquid phase by weight.
For a visual explanation of identifying intermediate compounds in a phase diagram, you might find the following video helpful:<\/p>\n\n\n\n

\ue200video\ue202Identifying intermediate compounds in a phase diagram\ue202turn0search4\ue201<\/p>\n\n\n\n

    <\/ol>\n","protected":false},"excerpt":{"rendered":"

    Mg-Pb Phase diagram Composition (at% Pb) 5 10 20 1 L 0 30 40 70 100 700 L 1200 600 + a +L Mg,Pb M 1000 500 800 400 B Temperature (\u00b0C) L + Temperature (\u00b0F) L Mg2Pb 300 600 200 B 400 a + Mg Pb 100 B + Mg Pb 200 Mg Pb […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-188145","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188145","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=188145"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188145\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}