{"id":37315,"date":"2025-06-25T15:33:16","date_gmt":"2025-06-25T15:33:16","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=37315"},"modified":"2025-06-26T07:57:10","modified_gmt":"2025-06-26T07:57:10","slug":"the-equation-for-a-semi-circle-centered-at-the-origin-with-radius","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-equation-for-a-semi-circle-centered-at-the-origin-with-radius\/","title":{"rendered":"The equation for a semi-circle centered at the origin with radius\u00a0"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

\u2705 Percent Recovery Calculation<\/strong><\/h3>\n\n\n\n

Given:<\/p>\n\n\n\n

    \n
  • Average caffeine per tea bag = 55.0 mg<\/strong><\/li>\n\n\n\n
  • Crude caffeine isolated = 25.0 mg<\/strong><\/li>\n<\/ul>\n\n\n\n

    Percent Recovery = (actual yield \/ theoretical yield) \u00d7 100<\/strong>Percent Recovery=(25.0 mg55.0 mg)\u00d7100=45.5%\\text{Percent Recovery} = \\left( \\frac{25.0\\ \\text{mg}}{55.0\\ \\text{mg}} \\right) \\times 100 = 45.5\\%Percent Recovery=(55.0 mg25.0 mg\u200b)\u00d7100=45.5%<\/p>\n\n\n\n

    \n\n\n\n

    \u2705 Effect of Using 1.0 M HCl Instead of Base<\/strong><\/h3>\n\n\n\n

    During caffeine extraction, we typically add base<\/strong> (like sodium carbonate or sodium hydroxide) to deprotonate acidic components<\/strong> such as tannins and flavonoids, making them more water-soluble and less likely to enter the organic layer<\/strong> (dichloromethane or DCM). Caffeine is a weak base<\/strong>, so in a basic medium, it remains neutral<\/strong> and can partition into DCM<\/strong> during liquid-liquid extraction.<\/p>\n\n\n\n

    If instead we use 1.0 M HCl (hydrochloric acid)<\/strong>, the acidic environment protonates caffeine<\/strong>, forming a cationic (charged) caffeine salt<\/strong>:Caffeine (base)+HCl\u2192Caffeine-H++Cl\u2212\\text{Caffeine (base)} + \\text{HCl} \\rightarrow \\text{Caffeine-H}^+ + \\text{Cl}^-Caffeine (base)+HCl\u2192Caffeine-H++Cl\u2212<\/p>\n\n\n\n

    Charged caffeine salts are more soluble in water<\/strong> and less soluble in dichloromethane<\/strong>. This means:<\/p>\n\n\n\n

      \n
    • Less caffeine will partition into the organic layer<\/strong><\/li>\n\n\n\n
    • Extraction efficiency decreases<\/strong><\/li>\n\n\n\n
    • Percent recovery drops significantly<\/strong><\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      \u2705 Why the Water Extract Was Cooled Before Adding DCM<\/strong><\/h3>\n\n\n\n

      Caffeine extraction involves adding dichloromethane (DCM)<\/strong> to the aqueous extract to separate the neutral caffeine into the organic layer. Before doing this, we cool the water extract<\/strong> to:<\/p>\n\n\n\n

        \n
      1. Prevent evaporation of DCM<\/strong> (DCM has a low boiling point ~40\u00b0C and is volatile)<\/li>\n\n\n\n
      2. Reduce solubility of caffeine in water<\/strong> \u2013 lower temperature favors caffeine partitioning into DCM<\/li>\n\n\n\n
      3. Minimize emulsion formation<\/strong> \u2013 cooling stabilizes layers and improves separation<\/li>\n<\/ol>\n\n\n\n

        In summary, cooling increases extraction efficiency<\/strong>, protects the solvent, and improves layer clarity.<\/p>\n\n\n\n

        \n\n\n\n

        Conclusion<\/strong>:
        You recovered 45.5% of the available caffeine. Using acid instead of base would protonate caffeine and trap it in the aqueous phase. Cooling the water extract helps maximize extraction into the organic layer and supports clean separation.<\/p>\n\n\n\n

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

        The Correct Answer and Explanation is: \u2705 Percent Recovery Calculation Given: Percent Recovery = (actual yield \/ theoretical yield) \u00d7 100Percent Recovery=(25.0 mg55.0 mg)\u00d7100=45.5%\\text{Percent Recovery} = \\left( \\frac{25.0\\ \\text{mg}}{55.0\\ \\text{mg}} \\right) \\times 100 = 45.5\\%Percent Recovery=(55.0 mg25.0 mg\u200b)\u00d7100=45.5% \u2705 Effect of Using 1.0 M HCl Instead of Base During caffeine extraction, we typically add base (like sodium carbonate or sodium hydroxide) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37315","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37315","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37315"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37315\/revisions"}],"predecessor-version":[{"id":37318,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37315\/revisions\/37318"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37315"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37315"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}