A magnesium\u2013lead alloy of mass 7.5 kg consists of a solid \u03b1 phase that has a composition just slightly below the solubility limit at 300?C (570?F).<\/p>\n\n\n\n
(a) What mass of lead is in the alloy?<\/p>\n\n\n\n
(b) If the alloy is heated to 400?C (750?F), how much more lead may be dissolved in the \u03b1 phase without exceeding the solubility limit of this phase?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve this problem, we need to break it down into two parts, as the question asks about the composition of a magnesium-lead alloy at different temperatures.<\/p>\n\n\n\n At 300\u00b0C (570\u00b0F), the alloy is a solid \u03b1 phase that is just slightly below the solubility limit. The solubility limit of lead in the \u03b1 phase of magnesium can be found in phase diagrams, which indicate the amount of lead (in percentage) that can dissolve in magnesium at a specific temperature.<\/p>\n\n\n\n From phase diagrams of magnesium-lead alloys, the solubility limit of lead in magnesium at 300\u00b0C is about 2.5%<\/strong> by weight. This means that at 300\u00b0C, the maximum percentage of lead that can be dissolved in the \u03b1 phase is 2.5%.<\/p>\n\n\n\n Given that the total mass of the alloy is 7.5 kg, the mass of lead in the alloy can be calculated using the percentage composition:<\/p>\n\n\n\n [ [ So, 0.1875 kg<\/strong> of lead is present in the alloy at 300\u00b0C.<\/p>\n\n\n\n At 400\u00b0C (750\u00b0F), the solubility limit of lead in magnesium increases. According to the phase diagram for the magnesium-lead system, the solubility limit of lead in magnesium at 400\u00b0C is approximately 5%<\/strong> by weight. This means that at 400\u00b0C, the \u03b1 phase can dissolve up to 5% lead.<\/p>\n\n\n\n Now, we need to calculate how much additional lead can be dissolved in the \u03b1 phase without exceeding the solubility limit:<\/p>\n\n\n\n [ The additional lead that can be dissolved is the difference between the maximum lead content at 400\u00b0C and the lead content at 300\u00b0C:<\/p>\n\n\n\n [ [ Thus, 0.1875 kg<\/strong> of additional lead can be dissolved in the alloy when it is heated to 400\u00b0C without exceeding the solubility limit.<\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" A magnesium\u2013lead alloy of mass 7.5 kg consists of a solid \u03b1 phase that has a composition just slightly below the solubility limit at 300?C (570?F). (a) What mass of lead is in the alloy? (b) If the alloy is heated to 400?C (750?F), how much more lead may be dissolved in the \u03b1 phase […]<\/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-195719","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195719","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=195719"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195719\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195719"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195719"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195719"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Part (a): Mass of Lead in the Alloy at 300\u00b0C<\/strong><\/h3>\n\n\n\n
\\text{Mass of Lead} = \\text{Total mass of alloy} \\times \\frac{\\text{Lead percentage}}{100}
]<\/p>\n\n\n\n
\\text{Mass of Lead} = 7.5 \\, \\text{kg} \\times \\frac{2.5}{100} = 0.1875 \\, \\text{kg}
]<\/p>\n\n\n\nPart (b): Additional Lead Dissolved at 400\u00b0C<\/strong><\/h3>\n\n\n\n
\\text{Maximum mass of lead at 400\u00b0C} = 7.5 \\, \\text{kg} \\times \\frac{5}{100} = 0.375 \\, \\text{kg}
]<\/p>\n\n\n\n
\\text{Additional lead} = \\text{Maximum mass of lead at 400\u00b0C} – \\text{Mass of lead at 300\u00b0C}
]<\/p>\n\n\n\n
\\text{Additional lead} = 0.375 \\, \\text{kg} – 0.1875 \\, \\text{kg} = 0.1875 \\, \\text{kg}
]<\/p>\n\n\n\nSummary:<\/strong><\/h3>\n\n\n\n
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