{"id":205681,"date":"2025-03-25T08:10:13","date_gmt":"2025-03-25T08:10:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=205681"},"modified":"2025-03-25T08:10:18","modified_gmt":"2025-03-25T08:10:18","slug":"dimethylamine-ch32nh-is-a-weak-base-kb-5-4-x-104","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/25\/dimethylamine-ch32nh-is-a-weak-base-kb-5-4-x-104\/","title":{"rendered":"Dimethylamine, (CH3)2NH, is a weak base ( Kb = 5.4 x 10?4)"},"content":{"rendered":"\n

Dimethylamine, (CH3)2NH, is a weak base ( Kb = 5.4 x 10?4). What is the pH of a 0.50 M solution and what is the percent dissociation?
A) 12.2, 3.2%
B) 0.016, 3.2%
C) 8.5, 6.3 x 10?4 %
D) 1.8, 3.2%
E) 5.5, 6.3 x 10?4 %<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To determine the pH<\/strong> and percent dissociation<\/strong> of a 0.50 M dimethylamine ((\\text{CH}_3)_2\\text{NH}), follow these steps:<\/p>\n\n\n\n

Step 1: Write the Base Dissociation Equation<\/strong><\/h3>\n\n\n\n

[
(\\text{CH}_3)_2\\text{NH} + H_2O \\rightleftharpoons (\\text{CH}_3)_2\\text{NH}_2^+ + OH^-
]<\/p>\n\n\n\n

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

    \n
  • Base dissociation constant, (K_b = 5.4 \\times 10^{-4})<\/li>\n\n\n\n
  • Initial concentration, ( C = 0.50 ) M<\/li>\n<\/ul>\n\n\n\n

    Step 2: Set Up ICE Table<\/strong><\/h3>\n\n\n\n
    Species<\/th>Initial (M)<\/th>Change (M)<\/th>Equilibrium (M)<\/th><\/tr><\/thead>
    ((\\text{CH}_3)_2\\text{NH})<\/td>0.50<\/td>(-x)<\/td>(0.50 – x)<\/td><\/tr>
    ((\\text{CH}_3)_2\\text{NH}_2^+)<\/td>0<\/td>(+x)<\/td>(x)<\/td><\/tr>
    (\\text{OH}^-)<\/td>0<\/td>(+x)<\/td>(x)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Using the Kb expression<\/strong>:
    [
    K_b = \\frac{[\\text{OH}^-][(\\text{CH}_3)_2\\text{NH}_2^+]}{[(\\text{CH}_3)_2\\text{NH}]}
    ]<\/p>\n\n\n\n

    [
    5.4 \\times 10^{-4} = \\frac{x^2}{0.50 – x}
    ]<\/p>\n\n\n\n

    Since ( K_b ) is small, assume ( x \\ll 0.50 ), so ( 0.50 – x \\approx 0.50 ):<\/p>\n\n\n\n

    [
    5.4 \\times 10^{-4} = \\frac{x^2}{0.50}
    ]<\/p>\n\n\n\n

    [
    x^2 = (5.4 \\times 10^{-4}) \\times 0.50
    ]<\/p>\n\n\n\n

    [
    x^2 = 2.7 \\times 10^{-4}
    ]<\/p>\n\n\n\n

    [
    x = \\sqrt{2.7 \\times 10^{-4}}
    ]<\/p>\n\n\n\n

    [
    x = 0.0164 \\text{ M} = [\\text{OH}^-]
    ]<\/p>\n\n\n\n

    Step 3: Find pOH and pH<\/strong><\/h3>\n\n\n\n

    [
    \\text{pOH} = -\\log (0.0164)
    ]<\/p>\n\n\n\n

    [
    \\text{pOH} = 1.78
    ]<\/p>\n\n\n\n

    [
    \\text{pH} = 14 – 1.78 = 12.2
    ]<\/p>\n\n\n\n

    Step 4: Find Percent Dissociation<\/strong><\/h3>\n\n\n\n

    [
    \\% \\text{Dissociation} = \\left( \\frac{x}{C} \\right) \\times 100
    ]<\/p>\n\n\n\n

    [
    = \\left( \\frac{0.0164}{0.50} \\right) \\times 100
    ]<\/p>\n\n\n\n

    [
    = 3.28\\% \\approx 3.2\\%
    ]<\/p>\n\n\n\n

    Final Answer:<\/strong><\/h3>\n\n\n\n

    [
    \\boxed{A) \\text{ pH } = 12.2, \\text{ Percent Dissociation } = 3.2\\%}
    ]<\/p>\n\n\n\n

    Now, here’s an image representing the dissociation of dimethylamine in water:<\/p>\n\n\n\n

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

    Dimethylamine, (CH3)2NH, is a weak base ( Kb = 5.4 x 10?4). What is the pH of a 0.50 M solution and what is the percent dissociation?A) 12.2, 3.2%B) 0.016, 3.2%C) 8.5, 6.3 x 10?4 %D) 1.8, 3.2%E) 5.5, 6.3 x 10?4 % The correct answer and explanation is : To determine the pH and […]<\/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-205681","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205681","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=205681"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205681\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=205681"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=205681"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=205681"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}