{"id":1288,"date":"2020-06-23T15:10:48","date_gmt":"2020-06-23T19:10:48","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/chbe220\/?post_type=chapter&p=1288"},"modified":"2020-08-11T15:39:18","modified_gmt":"2020-08-11T19:39:18","slug":"describing-reaction-rate","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/chbe220\/chapter\/describing-reaction-rate\/","title":{"raw":"Definitions of Reaction Rate and Extent of Reactions","rendered":"Definitions of Reaction Rate and Extent of Reactions"},"content":{"raw":"
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Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nBy the end of this section, you should be able to:\r\n\r\nDefine <\/strong>Reaction rate and r<\/span>eaction extent<\/span>\r\n\r\nCalculate<\/strong> the reaction rate for the reaction, t<\/span>he rate of formation of compounds and the r<\/span>eaction extent<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n

Reaction Rate<\/h2>\r\nA reaction rate shows the rates of production of a chemical species. It can also show the rate of consumption of a species; for example, a reactant. In general though, we want an overall common reaction rate to describe changes in a chemical system.\r\n\r\nLet's look at an example. Say we have reaction represented as: [latex]A + 2B \u2192 3C + D [\/latex]\r\n\r\nFor this system reaction rate can be expressed as follows:\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
<\/div>\r\n
\r\n
\r\n

[latex]r = \\frac{d[D]}{dt}[\/latex]<\/p>\r\nThe reaction rate is represented by the letter \"r\" or the Greek letter upsilon \"[latex]\\upsilon[\/latex]\"\r\n\r\nNOTE: I will stick with r as upsilon looks like \"[latex]\\nu[\/latex]\" which we will use to represent the stoichiometric coefficient\r\n\r\nAbove we have written the reaction rate as if a substance with a coefficient of 1<\/strong> was reacting (or being produced). This is the typical form of an overall reaction rate describing a reaction.\r\n\r\nRearranging the above equation, we can find the rate of production\/consumption for any species based on this overall reaction rate, note that stoichiometric coefficients are\u00a0positive for products and negative for reactants:\r\n

[latex]r_{A}=\\frac{d[A]}{dt}=-\\nu_{A}\u00d7r=(-1)\u00d7r[\/latex]<\/p>\r\n

[latex]r_{B}=\\frac{d[B]}{dt}=-\\nu_{B}\u00d7r=(-2)\u00d7r[\/latex]<\/p>\r\n

[latex]r_{C}=\\frac{d[C]}{dt}=\\nu_{C}\u00d7r=3\u00d7r[\/latex]<\/p>\r\n

[latex]r_{D}=\\frac{d[D]}{dt}=\\nu_{D}\u00d7r=1\u00d7r[\/latex]<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

\r\n
<\/div>\r\n
\r\n
\r\n\r\nThe general equation for calculating the reaction rate:\r\n\r\nGeneral notation: J is used to denote any compound involved in the reaction.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n\r\n\r\n\r\n
[latex] r = \\frac{1}{\\nu}\\frac{d[J]}{dt} [\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n
\r\n

Reaction rate at a given time can also be found from the graph of concentration of components in a system vs. time:<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

\r\n
<\/div>\r\n
\r\n
\r\n\r\n\"\"\r\n
\r\n

Exercise: Calculating the Reaction Rate<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nIf we have the reaction\r\n

[latex] 2 NOBr_{(g)} \u21cc 2 NO_{(g)} + Br_{2(g)}[\/latex]<\/p>\r\nand we measure that the rate of formation of NO is 1.6 mmol\/(L\u00b7s), what are the overall reaction rate, and the rate of formation of [latex]Br_{2}[\/latex] and [latex]N\\!O\\!Br[\/latex]?\r\n\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

\r\n

Solution<\/h3>\r\nStep 1:<\/strong> Determine the overall reaction rate from the rate of formation for NO.\r\n\\begin{align*}\r\nr & = \\frac{1}{\\nu_{j}} \\frac{d[NO]}{dt} \\\\\r\n& = \\frac{1}{2} \\left( 1.6 \\frac{mmol}{L\u00b7s}\\right)\\\\\r\n& = 0.8\\frac{mmol}{L\u00b7s}\r\n\\end{align*}\r\n\r\nStep 2:<\/strong> Use the reaction rate to determine rate of formation for the other compounds\r\nNOTE: <\/strong>rate of formation is positive for products and negative for reactants\r\n\\begin{align*}\r\n\\frac{d[Br_{2}]}{dt}& = r \\\\\r\n& = 0.8\\frac{mmol}{L\u00b7s}\r\n\\end{align*}\r\n\r\n\\begin{align*}\r\n\\frac{d[NOBr]}{dt}& = -2r \\\\\r\n& = -1.6\\frac{mmol}{L\u00b7s}\r\n\\end{align*}\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
<\/div>\r\n<\/div>\r\n
\r\n
\r\n
\r\n\r\nReaction rates can be given in a variety of units over time. In this class we will just explore molarity<\/strong> and partial pressure<\/strong>, although other forms exist.\r\n\r\nMolarity<\/strong> - molar concentration - expressed in units of [latex]\\frac{mol}{volume * time}[\/latex] (eg. [latex]\\frac{mol}{L*s}[\/latex] )\r\n\r\nPartial pressure<\/strong> - the pressure produced by one gaseous component if it occupies the whole system volume at the same temperature, commonly used for gasses - units of [latex]\\frac{pressure}{time} [\/latex]( eg. [latex]\\frac{Pa}{s}[\/latex] )\r\n\r\n<\/div>\r\n

Extent of Reaction<\/h2>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n
\r\n

We use the extent of reaction ([latex]\\xi[\/latex]) to describe the change in an amount of a reacting speicies J.<\/p>\r\n\r\n\r\n\r\n\r\n
[latex]d n_{j} = \\nu_{j} d\\xi[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n
    \r\n \t
  • [latex]dn_{j}[\/latex] = change in the number of moles of a certain substance<\/span><\/li>\r\n \t
  • [latex]\\nu_{j}[\/latex] = the stoichiometric coefficient<\/li>\r\n \t
  • [latex]d\\xi[\/latex] = the extent of reaction<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
    \r\n
    <\/div>\r\n
    \r\n
    \r\n\r\nWe can get a relationship between the reaction extent and the rate of reaction when the system volume is constant:\r\n\r\n\r\n\r\n
    [latex] r = \\frac{1}{V} \\frac{d\\xi}{dt} = \\frac{1}{\\nu_{j}} \\frac{1}{V} \\frac{dn_{j}}{dt}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n
    [latex]V[\/latex]= volume<\/blockquote>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
    \r\n
    <\/div>\r\n<\/div>","rendered":"
    \n
    \n
    \n
    \n
    \n

    Learning Objectives<\/p>\n<\/header>\n

    \n

    By the end of this section, you should be able to:<\/p>\n

    Define <\/strong>Reaction rate and r<\/span>eaction extent<\/span><\/p>\n

    Calculate<\/strong> the reaction rate for the reaction, t<\/span>he rate of formation of compounds and the r<\/span>eaction extent<\/span><\/p>\n<\/div>\n<\/div>\n

    Reaction Rate<\/h2>\n

    A reaction rate shows the rates of production of a chemical species. It can also show the rate of consumption of a species; for example, a reactant. In general though, we want an overall common reaction rate to describe changes in a chemical system.<\/p>\n

    Let’s look at an example. Say we have reaction represented as: [latex]A + 2B \u2192 3C + D[\/latex]<\/p>\n

    For this system reaction rate can be expressed as follows:<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n
    <\/div>\n
    \n
    \n

    [latex]r = \\frac{d[D]}{dt}[\/latex]<\/p>\n

    The reaction rate is represented by the letter “r” or the Greek letter upsilon “[latex]\\upsilon[\/latex]”<\/p>\n

    NOTE: I will stick with r as upsilon looks like “[latex]\\nu[\/latex]” which we will use to represent the stoichiometric coefficient<\/p>\n

    Above we have written the reaction rate as if a substance with a coefficient of 1<\/strong> was reacting (or being produced). This is the typical form of an overall reaction rate describing a reaction.<\/p>\n

    Rearranging the above equation, we can find the rate of production\/consumption for any species based on this overall reaction rate, note that stoichiometric coefficients are\u00a0positive for products and negative for reactants:<\/p>\n

    [latex]r_{A}=\\frac{d[A]}{dt}=-\\nu_{A}\u00d7r=(-1)\u00d7r[\/latex]<\/p>\n

    [latex]r_{B}=\\frac{d[B]}{dt}=-\\nu_{B}\u00d7r=(-2)\u00d7r[\/latex]<\/p>\n

    [latex]r_{C}=\\frac{d[C]}{dt}=\\nu_{C}\u00d7r=3\u00d7r[\/latex]<\/p>\n

    [latex]r_{D}=\\frac{d[D]}{dt}=\\nu_{D}\u00d7r=1\u00d7r[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n
    <\/div>\n
    \n
    \n

    The general equation for calculating the reaction rate:<\/p>\n

    General notation: J is used to denote any compound involved in the reaction.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n
    \n\n\n\n
    [latex]r = \\frac{1}{\\nu}\\frac{d[J]}{dt}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
    \n
    \n

    Reaction rate at a given time can also be found from the graph of concentration of components in a system vs. time:<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n
    <\/div>\n
    \n
    \n

    \"\"<\/p>\n

    \n
    \n

    Exercise: Calculating the Reaction Rate<\/p>\n<\/header>\n

    \n

    If we have the reaction<\/p>\n

    [latex]2 NOBr_{(g)} \u21cc 2 NO_{(g)} + Br_{2(g)}[\/latex]<\/p>\n

    and we measure that the rate of formation of NO is 1.6 mmol\/(L\u00b7s), what are the overall reaction rate, and the rate of formation of [latex]Br_{2}[\/latex] and [latex]N\\!O\\!Br[\/latex]?<\/p>\n

     <\/p>\n<\/div>\n<\/div>\n

    \n

    Solution<\/h3>\n

    Step 1:<\/strong> Determine the overall reaction rate from the rate of formation for NO.
    \n\\begin{align*}
    \nr & = \\frac{1}{\\nu_{j}} \\frac{d[NO]}{dt} \\\\
    \n& = \\frac{1}{2} \\left( 1.6 \\frac{mmol}{L\u00b7s}\\right)\\\\
    \n& = 0.8\\frac{mmol}{L\u00b7s}
    \n\\end{align*}<\/p>\n

    Step 2:<\/strong> Use the reaction rate to determine rate of formation for the other compounds
    \nNOTE: <\/strong>rate of formation is positive for products and negative for reactants
    \n\\begin{align*}
    \n\\frac{d[Br_{2}]}{dt}& = r \\\\
    \n& = 0.8\\frac{mmol}{L\u00b7s}
    \n\\end{align*}<\/p>\n

    \\begin{align*}
    \n\\frac{d[NOBr]}{dt}& = -2r \\\\
    \n& = -1.6\\frac{mmol}{L\u00b7s}
    \n\\end{align*}<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

    \n
    <\/div>\n<\/div>\n
    \n
    \n
    \n

    Reaction rates can be given in a variety of units over time. In this class we will just explore molarity<\/strong> and partial pressure<\/strong>, although other forms exist.<\/p>\n

    Molarity<\/strong> – molar concentration – expressed in units of [latex]\\frac{mol}{volume * time}[\/latex] (eg. [latex]\\frac{mol}{L*s}[\/latex] )<\/p>\n

    Partial pressure<\/strong> – the pressure produced by one gaseous component if it occupies the whole system volume at the same temperature, commonly used for gasses – units of [latex]\\frac{pressure}{time}[\/latex]( eg. [latex]\\frac{Pa}{s}[\/latex] )<\/p>\n<\/div>\n

    Extent of Reaction<\/h2>\n<\/div>\n<\/div>\n
    \n
    \n
    \n

    We use the extent of reaction ([latex]\\xi[\/latex]) to describe the change in an amount of a reacting speicies J.<\/p>\n\n\n\n
    [latex]d n_{j} = \\nu_{j} d\\xi[\/latex]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    where:<\/p>\n

      \n
    • [latex]dn_{j}[\/latex] = change in the number of moles of a certain substance<\/span><\/li>\n
    • [latex]\\nu_{j}[\/latex] = the stoichiometric coefficient<\/li>\n
    • [latex]d\\xi[\/latex] = the extent of reaction<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n

      We can get a relationship between the reaction extent and the rate of reaction when the system volume is constant:<\/p>\n\n\n\n
      [latex]r = \\frac{1}{V} \\frac{d\\xi}{dt} = \\frac{1}{\\nu_{j}} \\frac{1}{V} \\frac{dn_{j}}{dt}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      where:<\/p>\n

      [latex]V[\/latex]= volume<\/p><\/blockquote>\n<\/div>\n<\/div>\n<\/div>\n

      \n
      <\/div>\n<\/div>\n","protected":false},"author":948,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1288","chapter","type-chapter","status-publish","hentry"],"part":1286,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1288","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/users\/948"}],"replies":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/comments?post=1288"}],"version-history":[{"count":9,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1288\/revisions"}],"predecessor-version":[{"id":2602,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1288\/revisions\/2602"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/parts\/1286"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1288\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/media?parent=1288"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapter-type?post=1288"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/contributor?post=1288"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/license?post=1288"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}