To calculate the final temperature of the water when sodium hydroxide dissolves, we can use the heat energy equation and the molar heat of solution. Here’s a step-by-step approach:<\/p>\n\n\n\n
Step 1: Calculate the moles of sodium hydroxide (NaOH)<\/h3>\n\n\n\n
The molar mass of sodium hydroxide (NaOH) is approximately 40.0 g\/mol.moles of NaOH=mass of NaOHmolar mass of NaOH=5.00\u2009g40.0\u2009g\/mol=0.125\u2009mol\\text{moles of NaOH} = \\frac{\\text{mass of NaOH}}{\\text{molar mass of NaOH}} = \\frac{5.00 \\, \\text{g}}{40.0 \\, \\text{g\/mol}} = 0.125 \\, \\text{mol}moles of NaOH=molar mass of NaOHmass of NaOH\u200b=40.0g\/mol5.00g\u200b=0.125mol<\/p>\n\n\n\n
Step 2: Calculate the heat released during dissolution<\/h3>\n\n\n\n
The molar heat of solution (\u0394H_soln) of sodium hydroxide is -445.1 kJ\/mol, which means that for every mole of NaOH dissolved, 445.1 kJ of energy is released (exothermic process).Heat released=moles of NaOH\u00d7\u0394Hsoln=0.125\u2009mol\u00d7(\u2212445.1\u2009kJ\/mol)=\u221255.64\u2009kJ\\text{Heat released} = \\text{moles of NaOH} \\times \\Delta H_{\\text{soln}} = 0.125 \\, \\text{mol} \\times (-445.1 \\, \\text{kJ\/mol}) = -55.64 \\, \\text{kJ}Heat released=moles of NaOH\u00d7\u0394Hsoln\u200b=0.125mol\u00d7(\u2212445.1kJ\/mol)=\u221255.64kJ<\/p>\n\n\n\n
Since the heat is released, we treat the heat energy as positive when it goes into the water.Qwater=55.64\u2009kJQ_{\\text{water}} = 55.64 \\, \\text{kJ}Qwater\u200b=55.64kJ<\/p>\n\n\n\n
Step 3: Convert heat energy to joules<\/h3>\n\n\n\n
We need to convert kJ to joules, because the specific heat capacity of water is usually given in J\/g\u00b0C.Qwater=55.64\u2009kJ\u00d71000\u2009J\/kJ=55640\u2009JQ_{\\text{water}} = 55.64 \\, \\text{kJ} \\times 1000 \\, \\text{J\/kJ} = 55640 \\, \\text{J}Qwater\u200b=55.64kJ\u00d71000J\/kJ=55640J<\/p>\n\n\n\n
Step 4: Use the formula for heat transfer to calculate the temperature change<\/h3>\n\n\n\n
The formula for heat transfer is:Q=m\u22c5c\u22c5\u0394TQ = m \\cdot c \\cdot \\Delta TQ=m\u22c5c\u22c5\u0394T<\/p>\n\n\n\n
Where:<\/p>\n\n\n\n
- \n
- QQQ is the heat energy (in joules),<\/li>\n\n\n\n
- mmm is the mass of the water (in grams),<\/li>\n\n\n\n
- ccc is the specific heat capacity of water (4.18 J\/g\u00b0C),<\/li>\n\n\n\n
- \u0394T\\Delta T\u0394T is the change in temperature (in \u00b0C).<\/li>\n<\/ul>\n\n\n\n
For 1.000 L of water, the mass of the water is 1000 g (since 1 L of water is approximately 1000 g). Now, we can solve for the temperature change \u0394T\\Delta T\u0394T:55640\u2009J=1000\u2009g\u00d74.18\u2009J\/g\u00b0C\u00d7\u0394T55640 \\, \\text{J} = 1000 \\, \\text{g} \\times 4.18 \\, \\text{J\/g\u00b0C} \\times \\Delta T55640J=1000g\u00d74.18J\/g\u00b0C\u00d7\u0394T\u0394T=55640\u2009J1000\u2009g\u00d74.18\u2009J\/g\u00b0C=13.3\u2009\u00b0C\\Delta T = \\frac{55640 \\, \\text{J}}{1000 \\, \\text{g} \\times 4.18 \\, \\text{J\/g\u00b0C}} = 13.3 \\, \\text{\u00b0C}\u0394T=1000g\u00d74.18J\/g\u00b0C55640J\u200b=13.3\u00b0C<\/p>\n\n\n\n
Step 5: Calculate the final temperature<\/h3>\n\n\n\n
The initial temperature of the water is 20.0\u00b0C. The final temperature will be the initial temperature plus the temperature change:Tfinal=20.0\u00b0C+13.3\u00b0C=33.3\u00b0CT_{\\text{final}} = 20.0\u00b0C + 13.3\u00b0C = 33.3\u00b0CTfinal\u200b=20.0\u00b0C+13.3\u00b0C=33.3\u00b0C<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
The final temperature of the water is 33.3\u00b0C<\/strong>.<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
The dissolution of sodium hydroxide is an exothermic process, meaning it releases heat into the water. Since the heat released is transferred to the water, the water temperature increases. By using the molar heat of solution, we calculated the heat released during the dissolution process. We then used the specific heat capacity of water to determine how much the temperature of the water would increase, leading to the final temperature of 33.3\u00b0C.<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-727.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"The molar heat of solution (\u00ce\u201dHsoln) of sodium hydroxide is -445.1 kJ\/mol. In a certain experiment, 5.00 g of solid sodium hydroxide is completely dissolved in 1.000 L of 20.0 \u00c2\u00b0C water in a foam cup calorimeter. Assuming no heat loss, calculate the final temperature of the water. The Correct Answer and Explanation is: To […]<\/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-257236","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257236","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=257236"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257236\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=257236"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=257236"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=257236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}