6.8 Enthalpy of Formation

The standard enthalpy of formation (ΔH°f) is the enthalpy change when 1 mole of a compound forms from its elements in their standard states (298 K, 1 atm). By convention ΔH°f = 0 for elements in their standard states (like O2(g), C(graphite)). We need ΔH°f because it lets you get ΔH°rxn without doing calorimetry for every reaction—use the CED formula ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants). That’s just Hess’s law in table form: add/subtract formation enthalpies using stoichiometric coefficients. Why it matters for the AP exam: Learning Objective 6.8.A expects you to calculate reaction enthalpies from standard ΔH°f values (use correct signs, states, and coefficients). If you want practice, see the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and work problems from the AP practice set (https://library.fiveable.me/practice/ap-chemistry).

Use the formula from the CED: ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants). Steps: (1) write the balanced equation with correct stoichiometric coefficients, (2) look up each species’ standard enthalpy of formation (ΔH°f) from a table (elements in their standard states have ΔH°f = 0), (3) multiply each ΔH°f by its coefficient, (4) sum the products’ terms and subtract the sum for the reactants. Result is the standard enthalpy change at 298 K and 1 atm. This is an application of Hess’s law—you’re adding formation reactions. Show units (kJ or kJ·mol−1), include sign, and report correct significant figures for the AP exam. Example (no real numbers): for A + 2B → C, ΔH°rxn = [1·ΔH°f(C)] − [1·ΔH°f(A) + 2·ΔH°f(B)]. For more review and examples, see the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej), the Unit 6 overview (https://library.fiveable.me/ap-chemistry/unit-6), and practice problems (https://library.fiveable.me/practice/ap-chemistry).

Enthalpy of formation (ΔH°f) is the enthalpy change for forming 1 mole of a compound from its elements in their standard states (298 K, 1 atm). It’s a single, tabulated value (per mole) you’ll find in tables. Enthalpy of reaction (ΔH°rxn) is the heat change for any chemical equation—it depends on stoichiometry and can be positive or negative. How they connect: AP expects you to use ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants) (Hess’s law). So you use standard ΔH°f values (elements in their standard states have ΔH°f = 0) to calculate the enthalpy for the whole reaction. On the exam you’ll be asked to compute ΔH°rxn from ΔH°f entries, so memorize the idea and practice problems in the Topic 6.8 study guide (Fiveable) (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej). For extra practice, check Unit 6 resources and the AP-style problem sets (https://library.fiveable.me/ap-chemistry/unit-6 and https://library.fiveable.me/practice/ap-chemistry).

Think of ΔH°reaction = ΣΔH°f(products) − ΣΔH°f(reactants) as “total energy to make products from elements minus total energy to make reactants from elements.” Breakdown: - ΔH°f (standard enthalpy of formation) = enthalpy change to form 1 mole of a compound from its elements in their standard states (298 K, 1 atm). Units: kJ/mol. - Σ means sum over each species, and you must multiply each ΔH°f by its stoichiometric coefficient from the balanced equation. - Subtract products minus reactants because Hess’s law: the enthalpy change for the overall reaction equals the sum of formation steps for products minus that for reactants. - Remember: ΔH°f for any element in its standard state = 0 (e.g., O2(g), C(graphite)). On the AP exam you’ll use tables of ΔH°f and apply this formula (CED 6.8.A). Want more worked examples and practice? Check the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and the practice set (https://library.fiveable.me/practice/ap-chemistry).

The standard enthalpy of formation, ΔH°f, is defined as the enthalpy change for forming 1 mole of a compound from its elements in their standard states (298 K, 1 atm). By convention we set the reference point so that every pure element in its standard state has ΔH°f = 0. That’s not because the element has no energy, but because we need a common baseline to compare reaction enthalpies (so ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants) works cleanly). Choosing zero for elements prevents double-counting and makes Hess’s law calculations consistent across tables. On the AP exam you’ll always use these tabulated ΔH°f values (elements: zero) when applying the ΔH°rxn formula from the CED (6.8.A.1). For a quick refresher, see the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and try practice problems (https://library.fiveable.me/practice/ap-chemistry).

Use the ΔH°f values for the actual chemical species and phases shown in your balanced equation, then apply ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants). Key tips: - Pick the value that matches the chemical formula and phase (g, l, s, aq). Tables list different numbers for different phases. - Multiply each ΔH°f by its stoichiometric coefficient before summing. - Elements in their standard states (O2(g), C(graphite), H2(g), etc.) have ΔH°f = 0—don’t include a nonzero value for them. - Use standard-state values (298 K, 1 atm) unless the problem says otherwise. The result will be in kJ per mole of reaction as written. - If a species isn’t listed, build it from formation reactions (Hess’s law) or use given combustion/ion formation data if supplied. Tables sometimes include ions—use those only when the problem is about ionic species. For step-by-step examples and AP-style practice, check the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and more practice problems (https://library.fiveable.me/practice/ap-chemistry).

The little degree symbol in ΔH°f means “standard”—ΔH°f is the standard enthalpy (molar enthalpy) of formation. Standard conditions are 1 atm pressure and usually 298 K (25°C). A standard enthalpy of formation is the enthalpy change for making 1 mol of a compound from its elements in their standard states. Elements in their standard states have ΔH°f = 0 by definition. Why that matters: AP problems use tables of ΔH°f (standard values) so you can apply the CED formula ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants). If you don’t use standard values (or forget the reference state), your sign or magnitude will be wrong. For exam practice and examples, see the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and try practice problems (https://library.fiveable.me/practice/ap-chemistry).

Step-by-step (AP-style) strategy for enthalpy of formation problems: 1. Write the target reaction and check it’s balanced. 2. Use the formula ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants) (CED 6.8.A.1). 3. From a ΔH°f table, pick values for each species at standard state (298 K, 1 atm). Remember ΔH°f = 0 for elements in their standard states (O2, H2, C(graphite)). 4. Multiply each ΔH°f by its stoichiometric coefficient before summing. Watch signs (exothermic negative, endothermic positive). 5. Compute ΔH°rxn and report units (kJ per mol of reaction as written). Use significant figures per given data. 6. If a species’ phase differs from the table, convert or use formation value for the correct phase (Hess’s law). Quick example: for H2 + 1/2 O2 → H2O(l), ΔH°rxn = ΔH°f(H2O,l) − [ΔH°f(H2)+½ΔH°f(O2)] = ΔH°f(H2O,l) − 0. For guided practice and tables, see the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and more problems at (https://library.fiveable.me/practice/ap-chemistry).

Think of enthalpy (H) as a state function—it depends only on the chemical identity and amounts of reactants or products, not on the path. Standard enthalpies of formation (ΔH°f) are the enthalpies to make 1 mol of each substance from elements in their standard states. To get the reaction enthalpy you compare the total energy stored in products to the total energy stored in reactants: ΔH°rxn = Σ(ΔH°f of products × coefficients) − Σ(ΔH°f of reactants × coefficients). We subtract reactants because we’re asking “how much more (or less) enthalpy do the products have than the reactants?” If products have lower enthalpy than reactants, ΔH°rxn is negative (exothermic); if higher, it’s positive (endothermic). This is just Hess’s law applied to formation reactions: build products from elements and undo the formation of reactants, then take the net change. For step-by-step examples and AP-style practice, check the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and tons of practice problems (https://library.fiveable.me/practice/ap-chemistry).

Standard conditions for enthalpy (the "standard state") mean each substance is at 1 atm and at 298 K (25°C); standard enthalpies of formation ΔH°f in tables are given for those conditions. STP (standard temperature and pressure) usually means 1 atm and 273.15 K (0°C) and is mainly used for gas-volume calculations (ideal gas relations). Why it matters: ΔH° is temperature dependent, so a ΔH°f listed in a table applies to 298 K, not STP. If you need ΔH at a different T (like 273 K), you must correct it (using heat capacities or Hess’s law if you have relevant data). For AP Chem: always use ΔH°f (standard enthalpy of formation) at the standard state 298 K, 1 atm when calculating ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants). For review and practice, see the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and more practice problems (https://library.fiveable.me/practice/ap-chemistry).

Think of ΔH°f as the enthalpy change to make 1 mol of a compound from its elements in their standard states. Two quick rules to remember: - Elements in their standard states have ΔH°f = 0 (e.g., O2(g), C(graphite)). - ΔH°f can be negative or positive—negative if making the compound releases energy (most stable products, like many ionic solids and oxides), positive if forming the compound requires net energy input (less common; some unstable or strained species). Memory tricks: - “Stable product → negative”: ionic salts and most oxides formed from elements usually have negative ΔH°f. - “Uncommon/strained → maybe positive”: molecules that are hard to assemble from elements (highly strained rings, some radicals, or unusual oxidation states) can have positive ΔH°f. - Always use the table on the exam—you won’t be asked to guess signs without data. For reaction ΔH°, use ΣΔH°f(products) − ΣΔH°f(reactants) (CED 6.8.A.1, Hess’s law). For more practice and tables/examples, check the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and Unit 6 overview (https://library.fiveable.me/ap-chemistry/unit-6). If you want lots of practice problems, try the AP practice bank (https://library.fiveable.me/practice/ap-chemistry).

Good question—short answer: we use tables because measuring every compound’s standard enthalpy of formation directly is impractical, sometimes impossible, and would give inconsistent results. Why: a ΔH°f is defined for forming 1 mol of a compound from elements in their standard states at 298 K and 1 atm, so you need a standard reference. Some “formation” reactions can’t be run (elements don’t combine cleanly or produce unstable intermediates), or they’re hazardous. Calorimetry measures only specific experiments (and has heat losses and different conditions), so values would vary lab-to-lab. Instead we measure a few robust reactions (combustions, heats of reaction), use Hess’s law to combine them, and compile standardized ΔH°f tables. That gives consistent, comparable data you can plug into ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants) on the exam (CED 6.8.A.1). For practice applying this and exam-style problems, see the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and lots of practice questions (https://library.fiveable.me/practice/ap-chemistry).

If a compound’s standard enthalpy of formation (ΔH°f) isn’t in your table, don’t panic—use Hess’s law. The exam expects you to get ΔH°rxn from ΔH°f via ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants), so build a thermochemical pathway that uses known values (remember elements in their standard states have ΔH°f = 0 at 298 K, 1 atm). Common approaches: - Combine known formation reactions of related species to algebraically get the missing ΔH°f. - Use experimental enthalpies (like ΔH°combustion) plus known ΔH°f values to solve for the unknown ΔH°f by Hess’s law. - As a last resort, use bond enthalpies to estimate ΔH (less accurate—state it’s an estimate). On the AP exam, clearly show the Hess cycle, cancel intermediate steps, and state standard conditions. For worked examples and practice problems on this topic, see the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and more Unit 6 review (https://library.fiveable.me/ap-chemistry/unit-6). For extra practice, check Fiveable’s AP Chem practice problems (https://library.fiveable.me/practice/ap-chemistry).

Enthalpy of formation (ΔH°f) is the enthalpy change to make 1 mol of a compound from its elements in their standard states. Microscopically, any reaction enthalpy is the net of bond breaking (endothermic) and bond forming (exothermic). A ΔH°f value encodes that net for forming the compound from elements—it already includes the energy cost to break whatever bonds in elemental forms and the energy released when new bonds form. Use Hess’s law: ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants) to get reaction enthalpies without tracking every individual bond. On the AP exam you’ll be expected to calculate ΔH°rxn from tables of ΔH°f (CED 6.8.A.1), so practice translating bond-breaking/−forming intuition into the ΣΔH°f formula. For a focused review, see the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and more unit resources (https://library.fiveable.me/ap-chemistry/unit-6).

Short answer: you’re seeing different ΔH°f numbers because sources aren’t always using the same reference conditions, physical states, or rounding—so check the table’s assumptions before using it. Details you should know for AP Chem (CED-aligned): - Standard enthalpy of formation, ΔH°f, is defined for forming 1 mol of a compound from its elements in their standard states (298 K, 1 atm). Use ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants) (CED 6.8.A). - Differences come from: (1) reported physical state (e.g., H2O(l) vs H2O(g) have very different ΔH°f), (2) temperature—most tables give 298 K but some use other temps, (3) rounding or different experimental/compilation sources, (4) whether the value is for a specific ionic form or a gas/condensed phase. Elements in their standard states have ΔH°f = 0 by definition. Before solving, always note the table’s temperature and the compound’s state. For more on examples and practice, check the Topic 6.8 study guide (https://library.fiveable.me/ap-chemistry/unit-6/enthalpy-formation/study-guide/glO3L5mcfcUwCd0ODBej) and try extra problems at (https://library.fiveable.me/practice/ap-chemistry).