{"id":617,"date":"2024-06-19T09:09:45","date_gmt":"2024-06-19T06:09:45","guid":{"rendered":"https:\/\/sisu.ut.ee\/measurement\/self-test-9-a\/"},"modified":"2024-06-19T09:09:45","modified_gmt":"2024-06-19T06:09:45","slug":"self-test-9-a","status":"publish","type":"page","link":"https:\/\/sisu.ut.ee\/measurement\/self-test-9-a\/","title":{"rendered":"Self-test 9 A"},"content":{"rendered":"<div id=\"watupro_quiz\" class=\"quiz-area single-page-quiz\">\n<p id=\"submittingExam7\" style=\"display:none;text-align:center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/img\/loading.gif\" width=\"16\" height=\"16\"><\/p>\n\n<div class=\"watupro-exam-description\" id=\"description-quiz-7\"><p>Here you can test your understanding of the ISO GUM modeling approach and your ability to apply it in practice.<\/p>\n<\/div>\n\n<form action=\"\" method=\"post\" class=\"quiz-form\" id=\"quiz-7\" enctype=\"multipart\/form-data\">\n<div class=\"watu-question \" id=\"question-1\" style=\";\"><div id=\"questionWrap-1\" class=\"   watupro-question-id-20\">\n\t\t\t<div class=\"question-content\"><p>The acidity (expressed as concentration of H<sup>+<\/sup> ions in mol\/l) of an acidic liquid (sample) is measured by titration with KOH solution using phenolphthalein as indicator. 10 ml aliquots of the liquid are titrated. The liquid is measured using a 10 ml pipette. The uncertainty of pipetting (taking into account all uncertainty components) is \u00b1 0.06 ml. Titration was carried out 5 times and the consumed titrant volumes were (all in ml): 12.35, 12.54, 12.21, 12.49 and 12.29. In this case it is safe to assume that the uncertainty of titrant volume originates from two sources: repeatability and uncertainty due to possible systematic effect of finding the end-point. The latter is estimated as \u00b1 0.15 ml. Titrant concentration has been determined in the laboratory earlier and it is (0.1230 \u00b1 0.0015) mol\/l, <em>k<\/em> =2, norm.<\/p>\n<p><span style=\"line-height: 1.6em;\">Find the acidity of the investigated liquid and\u00a0<\/span><span style=\"line-height: 1.6em;\">the standard uncertainty.\u00a0<\/span><\/p>\n<div class=\"accordion-block mb-3\">\n<div id=\"accordion-accordion-6683c25b12875\" class=\"accordion \">\n<div class=\"accordion-item accordion-item--white\">\n<h3 id=\"accordion-6683c25b12875-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b12875-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b12875-collapse-1\">Clue 1<\/button><\/h3>\n<div id=\"accordion-6683c25b12875-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b12875-heading-1\">\n<div class=\"accordion-body\">\n<div>Uncertainty components of <em>c<\/em>(H<sup>+<\/sup>) are: pipetted volume of the sample (<em>u<\/em>(<em>V<\/em><sub>sample<\/sub>)), volume of the titrant (<em>V<\/em><sub>KOH<\/sub>) and concentration of the titrant (<em>c<\/em><sub>KOH<\/sub>). Mathematical model:\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"81\" class=\"alignnone wp-image-260\" style=\"vertical-align: middle;\" title=\"9-1-1.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/18\/9-1-1.png\" alt=\"9-1-1.png\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"accordion-block mb-3\">\n<div id=\"accordion-accordion-6683c25b128752\" class=\"accordion \">\n<div class=\"accordion-item accordion-item--white\">\n<h3 id=\"accordion-6683c25b128752-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b128752-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b128752-collapse-2\">Clue 2<\/button><\/h3>\n<div id=\"accordion-6683c25b128752-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b128752-heading-1\">\n<div class=\"accordion-body\">\n<div>Uncertainty of pipetting has only one component that includes all uncertainty contributors and as it has been presented as \u00b1 0.06 ml without further information on its distribution. It is therefore the safest to assume that it is rectangularly distributed.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"accordion-block mb-3\">\n<div id=\"accordion-accordion-6683c25b128753\" class=\"accordion \">\n<div class=\"accordion-item accordion-item--white\">\n<h3 id=\"accordion-6683c25b128753-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b128753-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b128753-collapse-1\">Clue 3<\/button><\/h3>\n<div id=\"accordion-6683c25b128753-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b128753-heading-1\">\n<div class=\"accordion-body\">\n<div>Uncertainty of titrant volume has two components: uncertainty due to repeatability and uncertainty due to possible systematic effect of finding the end-point. Repeatability uncertainty can be found as the standard deviation of the mean from the titration results. Since the mean value of titrant volume is eventually used for calculating the result, the suitable standard uncertainty estimate is the standard deviation of the mean. The uncertainty due to possible systematic mismatch between the end-point and equivalence point is estimated as \u00b1 0.15 ml and here it is the safest to assume rectangular distribution.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"accordion-block mb-3\">\n<div id=\"accordion-accordion-6683c25b128754\" class=\"accordion \">\n<div class=\"accordion-item accordion-item--white\">\n<h3 id=\"accordion-6683c25b128754-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b128754-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b128754-collapse-1\">Clue 4<\/button><\/h3>\n<div id=\"accordion-6683c25b128754-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b128754-heading-1\">\n<div class=\"accordion-body\">\n<div>Standard uncertainty can be found from expanded uncertainty by dividing the latter by coverage factor. In order to find standard uncertainty from the uncertainty with rectangular distribution it is divided by <img loading=\"lazy\" decoding=\"async\" width=\"25\" height=\"28\" class=\"alignnone wp-image-261\" title=\"9-1-2.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/18\/9-1-2.png\" alt=\"9-1-2.png\">.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"accordion-block mb-3\">\n<div id=\"accordion-accordion-6683c25b128755\" class=\"accordion \">\n<div class=\"accordion-item accordion-item--white\">\n<h3 id=\"accordion-6683c25b128755-heading-1\" class=\"accordion-header\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#accordion-6683c25b128755-collapse-1\" aria-expanded=\"false\" aria-controls=\"accordion-6683c25b128755-collapse-1\">Clue 5<\/button><\/h3>\n<div id=\"accordion-6683c25b128755-collapse-1\" class=\"accordion-collapse collapse\" aria-labelledby=\"accordion-6683c25b128755-heading-1\">\n<div class=\"accordion-body\">\n<div>In case of model that includes only multiplications and divisions is the correct way is to calculate the relative (unitless) standard uncertainties and then combine those according to the following equation:\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"353\" height=\"69\" class=\"alignnone wp-image-262\" style=\"vertical-align: middle;\" title=\"9-1-3.png\" src=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/18\/9-1-3.png\" alt=\"9-1-3.png\" srcset=\"https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/18\/9-1-3.png 353w, https:\/\/sisu.ut.ee\/wp-content\/uploads\/sites\/18\/9-1-3-300x59.png 300w\" sizes=\"auto, (max-width: 353px) 100vw, 353px\"><\/div>\n<\/div>\n<div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div><\/div>\n<div>The acidity of the investigated liquid is:<\/div>\n<div><input type=\"text\" size=\"10\" name=\"gap_20_1\" class=\"watupro-gap answer answerof-20\" value=\"\"><\/div>\n<div>\n<p>The combined standard uncertainty of the found acidity is:<br>\n<input type=\"text\" size=\"10\" name=\"gap_20_2\" class=\"watupro-gap answer answerof-20\" value=\"\"><\/p>\n<\/div>\n<input type=\"hidden\" name=\"question_id[]\" id=\"qID_1\" value=\"20\" class=\"watupro-question-id\"><input type=\"hidden\" id=\"answerType20\" class=\"answerTypeCnt1\" value=\"gaps\"><!-- end question-content--><\/div><!-- end questionWrap--><\/div><\/div><div style=\"display:none\" id=\"question-2\">\n\t<div class=\"question-content\">\n\t\t<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/img\/loading.gif\" width=\"16\" height=\"16\" alt=\"Loading...\" title=\"Loading...\">\u00a0Loading...\t<\/div>\n<\/div>\n\n<br>\n\t\n\t\t\t<div class=\"watupro_buttons flex \" id=\"watuPROButtons7\">\n\t\t  <div id=\"prev-question\" style=\"display:none;\"><input type=\"button\" value=\"&lt; Previous\" onclick=\"WatuPRO.nextQuestion(event, 'previous');\"><\/div>\t\t  \t\t  \t\t   \n\t\t   \t  \t\t<div><input type=\"button\" name=\"action\" class=\"watupro-submit-button\" onclick=\"WatuPRO.submitResult(event)\" id=\"action-button\" value=\"View Results\">\n\t\t<\/div>\n\t\t<\/div>\n\t\t\n\t<input type=\"hidden\" name=\"quiz_id\" value=\"7\" id=\"watuPROExamID\">\n\t<input type=\"hidden\" name=\"start_time\" id=\"startTime\" value=\"2026-04-19 23:29:10\">\n\t<input type=\"hidden\" name=\"start_timestamp\" id=\"startTimeStamp\" value=\"1776641350\">\n\t<input type=\"hidden\" name=\"question_ids\" value=\"\">\n\t<input type=\"hidden\" name=\"watupro_questions\" value=\"20:\">\n\t<input type=\"hidden\" name=\"no_ajax\" value=\"0\">\t\t\t<\/form>\n\t<p>\u00a0<\/p>\n<\/div>\n\n<script type=\"text\/javascript\">\n\/\/jQuery(document).ready(function(){\ndocument.addEventListener(\"DOMContentLoaded\", function(event) { \t\nvar question_ids = \"20\";\nWatuPROSettings[7] = {};\nWatuPRO.qArr = question_ids.split(',');\nWatuPRO.exam_id = 7;\t    \nWatuPRO.post_id = 617;\nWatuPRO.store_progress = 0;\nWatuPRO.curCatPage = 1;\nWatuPRO.requiredIDs=\"0\".split(\",\");\nWatuPRO.hAppID = \"0.32351200 1776630550\";\nvar url = \"https:\/\/sisu.ut.ee\/wp-content\/plugins\/watupro\/show_exam.php\";\nWatuPRO.examMode = 1;\nWatuPRO.siteURL=\"https:\/\/sisu.ut.ee\/measurement\/wp-admin\/admin-ajax.php\";\nWatuPRO.emailIsNotRequired = 0;\nWatuPRO.perDecade = 10;\nWatuPROIntel.init(7);\nWatuPRO.inCategoryPages=1;});    \t \n<\/script>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":280,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-617","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages\/617","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/users\/280"}],"replies":[{"embeddable":true,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/comments?post=617"}],"version-history":[{"count":0,"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/pages\/617\/revisions"}],"wp:attachment":[{"href":"https:\/\/sisu.ut.ee\/measurement\/wp-json\/wp\/v2\/media?parent=617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}