[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-343373-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-343373-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","solving-integrated-rate-law-problems-using-the-graphing-calculator-mt-whitney-high-school-ap-chemistry","Solving Integrated Rate Law Problems Using the Graphing Calculator - Mt. Whitney High School AP Chemistry","","Guide for solving integrated rate law problems with a graphing calculator for AP Chemistry. It reviews the zero-, first-, and second-order linearization strategies, then applies them to the NO2 + CO reaction where rate depends only on [NO2] below 225°C. The procedure walks through entering time and concentration data into lists, enabling diagnostics, running LinReg(ax+b) regressions, identifying reaction order via correlation, extracting the rate constant k, and using the integrated law to predict [NO2] at a specified time.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/solving-integrated-rate-law-problems-using-the-graphing-calculator-mt-whitney-high-school-ap-chemistry/343373/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/solving-integrated-rate-law-problems-using-the-graphing-calculator-mt-whitney-high-school-ap-chemistry/343373.png","ImageObject",300,407,{"name":42,"@type":43},"Himbo","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-31","2026-09-22",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"Why does graphing time versus different transformed concentrations help determine reaction order?","Question",{"text":63,"@type":64},"For each possible order, the integrated rate law becomes linear only after applying the correct transformation (concentration, ln(concentration), or 1/concentration). The linearity and correlation indicate the correct order.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are the data entered on the TI graphing calculator in this method?",{"text":68,"@type":64},"Time values are entered into one list (L1) and [NO2] values into another list (L2). The calculator then stores ln[NO2] in L3 and 1/[NO2] in L4.",{"name":70,"@type":61,"acceptedAnswer":71},"How does the process use linear regression results to choose the reaction order?",{"text":72,"@type":64},"The method turns on diagnostics and performs LinReg(ax+b) on the appropriate lists. It checks the correlation (r2 and r); the order is the one whose regression gives the closest correlation to 1.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},343373,1790825367,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":96,"preview_page_count":4},687197100911,"https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697","Solving Integrated Rate Law Problems Using the Graphing Calculator  \nMt. Whitney High School AP Chemistry  \nThe old-fashioned (and tedious) method for determining the order of a reaction from experimental data was to graph the data points by hand. Since linear graphs resulting from relationships of concentration with time depend on the order of the reaction, this method usually required three separate graphs:  \nTime vs. concentration for zero order reactions  \nTime vs. ln(concentration) for first order reactions  \nTime vs. (1/concentration) for second order reactions  \nThe graphing calculator greatly simplifies the process. We will use the following problem from Zumdahl, chapter 12:  \nThe rate of the reaction  \nNO2(g) + CO(g) Æ NO(g) + CO2(g)  \nDepends only on the concentration of nitrogen dioxide below 225°C. At a temperature below 225°C the following data were collected:  \n\n| Time (s) | [NO2](mol/L) |\n| --- | --- |\n| 0 | 0.500 |\n| 1.20 x 103 | 0.444 |\n| 3.00 x 103 | 0.381 |\n| 4.50 x 103 | 0.340 |\n| 9.00 x 103 | 0.250 |\n| 1.80 x 104 | 0.174 |\n\nDetermine the rate law, the integrated law, and the value of the rate constant. Calculate [NO2] at  \n2.70 x 104 s after the start of the reaction.  \nStep 1: Enter the data in a list  \n…Æ“EDIT”Æ 1:Edit Æ Í This opens the list window. If there are contents in the  \nlists, then use the “up” cursor to move into the uppermost field – the list header (L 1 , L2 , L3…) . Once there, press‘and then the “down” cursor. This clears the list field.  \nNow enter the values for time in L 1 and concentration in L2 . We will use L3 and L4 to store values corresponding to ln[ NO2] .  \nGo to the header of L3 and press µ y Á Í . This places values of ln[NO2] in List 3.  \nGo to the header of L4 and press À ¥ y Á Í . This places values of 1/[NO2] in List 4.  \nThe contents of L2 , L3 and L4 should now appear as it does in the picture.  \nStep 2: Turn on Diagnostics  \nIn order to analyze the linearity of our data, we need to turn on the statistical diagnostics. This will provide us with correlation coefficients when we perform a linear regression.  \nOpen the Catalog function: y Æ À and then scroll down to “DiagnosticOn” and press Í , and then Í a second time. The diagnostic functions are now on.  \nStep 3: Perform Linear Regressions  \nPress…~ (CALC), press Í . Scroll down to 4:LinReg(ax+b) and press Í .  \nWe will now perform a linear regression on the contents of L 1 and L2 . We would also like to store the resulting linear equation for later use. We will store it in under the o function. The homescreen should now say“LinReg(ax+b)”. Press y À ¢ y Á ¢ 􀁲 ~ (Y-VARS, 1:Function) Í and Select “1:Y1”. Press Í . The screen should now appear as it does to the right.  \nPress Í once again, the screen should look like it does below:  \nThe values of r2 and r give us a sense of how closely our data correlates to a linear equation. The closer these values are to 1, the better the correlation. In this case, the correlation is not very close. This indicates that there is not a linear relationship between time (t) and [ NO2], so thereaction is not zero order.  \nRepeat the process from the top of the page, exploring linear relationships between t (L 1) and ln[NO2](L3) which would indicate a first order relationship.  \nPress…~ (CALC), press Í . Scroll down to 4:LinReg(ax+b) and press Í .  \nWe will now perform a linear regression on the contents of L 1 and L3. We would also like to store the resulting linear equation for later use. We will store it in under the o function. The homescreen should now say“LinReg(ax+b)”. Press y À ¢ y  ¢ 􀁲 ~ (Y-VARS, 1:Function) Í and Select “1:Y2”. Press Í . Press Í once again, the screen should look like it does at the right.  \nRepeat the process from the top of the page, exploring linear relationships between t (L 1) and 1/[ NO2](L4) which would indicate a second order relationship.  \nPress…~ (CALC), press Í . Scroll down to 4:LinReg(ax+b) and press Í .  \nWe will now perform a linear regression on t","cbCaiaTUepAQOeF2","https://ap.wps.com/l/cbCaiaTUepAQOeF2","pdf",148421,"English","# Solving Integrated Rate Law Problems Using the Graphing Calculator\n## Background: Linearized Forms by Reaction Order\n## Problem Setup: NO2 + CO Reaction and Collected Data\n## Calculator Procedure: Enter Data into Lists\n## Enable Diagnostics and Interpret Correlation\n## Determine Order with Linear Regressions\n## Extract Rate Constant k and Predict [NO2] at Later Time","[{\"question\":\"Why does graphing time versus different transformed concentrations help determine reaction order?\",\"answer\":\"For each possible order, the integrated rate law becomes linear only after applying the correct transformation (concentration, ln(concentration), or 1/concentration). The linearity and correlation indicate the correct order.\"},{\"question\":\"How are the data entered on the TI graphing calculator in this method?\",\"answer\":\"Time values are entered into one list (L1) and [NO2] values into another list (L2). The calculator then stores ln[NO2] in L3 and 1/[NO2] in L4.\"},{\"question\":\"How does the process use linear regression results to choose the reaction order?\",\"answer\":\"The method turns on diagnostics and performs LinReg(ax+b) on the appropriate lists. It checks the correlation (r2 and r); the order is the one whose regression gives the closest correlation to 1.\"}]","Solving Integrated Rate Law Problems Using the Graphing Calculator - Mt. Whitney High School AP Chemistry | PDF",1790050950]