. 22.4 L = 1 mole Not At STP Chemical reactions happen in MOLES. If you know how much **gas** - change it to moles Use the **Ideal** **Gas** **Law** n = PV/RT If you want to find how much **gas** - use moles to figure out volume V = nRT/P **Example** #1 HCl(g) can be formed by the following reaction 2NaCl(aq) + H 2 SO 4 (aq/

] Average kinetic energy of **ideal** **gas** Where k B = 1.38 10 -23 J K -1. Application of the "Kinetic Molecular Theory" to the **Gas** **Laws** Microscopic justification of the **laws** Pressure **Law** (Gay-Lussac’s **Law**) Effect of a pressure increase at a constant volume Macroscopically: at constant volume the pressure of a **gas** is proportional to its temperature: PV = NkT → P = (const) T **example**: a closed jar/

a pressure of 2.4 atm? PV = nRT The **Ideal** **Gas** **Law** Once you calculate the moles of **gas** you can convert this to a mass (in grams, kilograms, etc.) using what? You may also be given the amount of **gas** in grams and have to convert it to moles in order to plug into the **ideal** **gas** **law** **Example** #12 What is the volume occupied by 36.0/

3 you can determine the fourth. An Empirical Equation - based on experimental evidence. **Ideal** **Gas** **Law** A hypothetical substance - the **ideal** **gas** Think of it as a limit. Gases only approach **ideal** behavior at low pressure (< 1 atm) and high temperature. Use the **laws** anyway, unless told to do otherwise. They give good estimates. **Examples** A 47.3 L container containing 1.62 mol of He is heated/

(L kPa) (K mol) The **Ideal** **Gas** **Law** PV = nRT We now have a new way to count moles of a **gas**. By measuring T, P, and V. We aren’t restricted to STP. n = PV/RT Nothing is required to change, No 1’s and 2’s **Example** How many moles of air are there /reactions happen in MOLES. If you know how much **gas** - change it to moles Use the **Ideal** **Gas** **Law** n = PV/RT If you want to find how much **gas** - use moles to figure out volume V = nRT/P Use the equation in place of 22.4 L **Example** HCl(g) can be formed by the following /

R = 62.4 LmmHg molK If pressure is given in kPa R = 8.314 LkPa molK If pressure is given in atm **Ideal** **Gas** Constant Using the **Ideal** **Gas** **Law** What volume does 9.45g of C 2 H 2 occupy at STP? What volume does 9.45g of C 2 H 2 /and argon are placed in a porous container and allowed to escape, which **gas** will escape faster and how much faster? Grahams **Law** **Example** Calc. Rate of effusion of A = = Rate of effusion of B MBMB MBMB MAMA MAMA Grahams **Law** **Example** Calc. Rate of effusion of He = = Rate of effusion of Ar/

**Ideal** **Gas** **Law**? Combining Boyle’s **Law**, Charles’ **law** & Avogadro’s **Law** we derive the **Ideal** **Gas** **Law**: P V = n R T P = Pressure (atm) V = Volume (L) n = # moles (mol) R = **Gas** Constant (0.0821 L atm /mol K) T = Temperature (K) **Ideal** **gas** **law** calculations are favored at low pressures and high temperatures Let’ Try It! **Example**/C and 1 atm) 1 mole of **gas** occuppies 22.42 L. If not at STP, use the **ideal** **gas** **law** to calculate moles of reactant or volume of product. **Examples** Consider the following reaction: Suppose you heat/

not depend on the path. Given 3 you can determine the fourth. An Empirical Equation - based on experimental evidence. **Ideal** **Gas** **Law** A hypothetical substance - the **ideal** **gas** Think of it as a limit. Gases only approach **ideal** behavior at low pressure (< 1 atm) and high temperature. **Examples** A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85/

3 you can determine the fourth. An Empirical Equation - based on experimental evidence. **Ideal** **Gas** **Law** A hypothetical substance - the **ideal** **gas** Think of it as a limit. Gases only approach **ideal** behavior at low pressure (< 1 atm) and high temperature. Use the **laws** anyway, unless told to do otherwise. They give good estimates. **Examples** A 47.3 L container containing 1.62 mol of He is heated/

the system. In each case, determine the change in internal energy of the system. The First **Law** of Thermodynamics (b) The First **Law** of Thermodynamics **Example** 2 An **Ideal** **Gas** The temperature of three moles of a monatomic **ideal** **gas** is reduced from 540K to 350K as 5500J of heat flows into the **gas**. Find (a) the change in internal energy and (b) the work done by the/

and raises P to 3 atm. 15.2 15.2 Thermodynamic Processes & the First **Law** **Example** 4: First **law** in a Cyclic Process An **ideal** monatomic **gas** is confined in a cylinder by a movable piston. The **gas** starts at A with P = 101.3 kPa, V = .005 m3 and T/Isothermal Expansion (Pave = 172.2 kPa) 15.2 15.2 Thermodynamic Processes & the First **Law** **Example** 4: First **law** in a Cyclic Process An **ideal** monatomic **gas** is confined in a cylinder by a movable piston. The **gas** starts at A with P = 101.3 kPa, V = .005 m3 and T =/

to Kelvin Tk = Tc+273 Tk = 273 Molar Mass Problem Use density form of **ideal** **gas** **law** M = DRT/P Substitute known values: M = (1.40 g/L)(0.0821 L*atm/mol*K)(273K) 1 atm M = 31.4 g/mol **Gas** Stoichiometry Chapter 14, Section 4 **Gas** Stoichiometry – Volume only **Example**: 2C4H10(g) + 13 O2(g) → 8 CO2(g) + 10 H2O(g) Remember: Avogadro/

ml flask. If the sample had a mass of 0.118 g at a pressure of 550.0 Torr, what is the molecular weight of the **gas**? Plan: Use the **Ideal** **gas** **law** to calculate n, then calculate the molar mass. Solution: 1mm Hg 1 Torr 1.00 atm 760 mm Hg P = 550.0 Torr x / = 0.293 PXe = XXe PTotal = 0.293 (2.00 atm) = 0.586 atm for Xe Relative Humidity Pressure of Water in Air Rel Hum = x 100% **Example** : the partial pressure of water at 15oC is 6.54 mm Hg, what is the Relative Humidity? Rel Hum =(6.54 mm Hg/ 12.788 mm Hg )x100% =/

1 atm, the volume of the **gas** is given by **ideal** **gas** **law**, V = nRT / P = (1 mol x 0.08206 L.atm.mol-1.K-1 x 273K) / (1 atm) = 22.42 L Molar Volume of an **ideal** **gas** at STP A Mole of Any **Gas** Occupies a Volume of Approximately 22.4 L at STP **Example**: A sample of N2 **gas** has a volume of 1. 75/

? V = 1.00 L P = 1.50 atm T = 100 oC convert to K = 373 K n = ? Remember R = 0.0821 The **Ideal** **Gas** **Law** **Example** #1 How many moles of a **gas** at 100 oC does it take to fill a 1.00 L flask to a pressure of 1.50 atm? Solve for n: n = PV/RT (1/n = PV/RT (1.50 atm)(1.00 L) (0.0821 atm-L/mol-K)(373K) = 0.0490 mol The **Ideal** **Gas** **Law** **Example** #2 What is the volume occupied by 9.45g of C2H2 at STP? The **Ideal** **Gas** **Law** **Example** #2 What is the volume occupied by 9.45g of C2H2 at STP? First change grams to moles: 9.45g x 1 mol/

that relates the volume of a **gas** to the temperature, pressure and number of moles. Universal **gas** constant R = 0.0821 L atm/mol K **IDEAL** **GAS** **LAW** This relationship is called the **Ideal** **Gas** **Law**, and commonly written as: P V = n R T Temp. in K Pressure in atm Number of moles Volume in Liters **Example** 1: A sample of H2 **gas** has a volume of 8.56/

can determine the number of mols, n, of a **gas** by using pressure, volume, and temperature measurements and the **ideal** **gas** **law**. n = PV/RT The molar mass, M, is the mass, m, divided by the number of mols. M =m/n Putting the two equations together M = m/(PV/RT) = mRT/PV **Example** 5 – Finding M At 301 K and 0.974 atm, 1/

all has to do with the amount of air pressing down on us. Boyle’s **Law** Boyle’s **Law**: 18. Variables = ? 19. Constant = ? 20. Formula = ? 21. **Examples** of system **Gas** **Laws** Studies of the behavior of gases played a major role in the development of physical sciences/atm) (L)atm) (kPa) (mm Hg) L) R = (mol) (K) ! Charles **Law** Boyles **Law** Combined **Gas** **Law** **Ideal** **Gas** **Law** V1 T1 = V2 P1 x V1 = P2 x V2 P1 V1 P2 V2 = T1 T2 Combined **Gas** **Law** **Ideal** **Gas** **Law** P V = n RT Used with only ONE SET OF CONDITIONS When to Use PV = nRT /

Step 4: Convert moles of NH3 to liters of NH3 using the **ideal** **gas** **law**. PV = nRT: (1.02atm) (V) = (0.246mol)(0.0821 L • atm) (304K) mole • K V = 6.02 L of NH3 **Example** 2: Calculate the volume of hydrogen **gas** produced at 0 **Example** 2: Calculate the volume of hydrogen **gas** produced at 0.0°C and 1.00 atm of pressure by reacting/

**Law** of Thermodynamics The equation of the state of the **Ideal** **gas** **Ideal** **gas**: the **gas** which follows the Boyle’s **law**, the Gay-Lussac’s **law**, the charles’ **law**, and the Aavogadro’s **law** The equation of the state: the function connecting the macroscopic quantities of the **ideal** **gas** in equilibrium state. The Equilibrium State, the Zero **Law**/ move irregularly thermally. for **example**: oxygen molecules under the normal temperature and normal pressure. 12-2 The Microscopic Model of Matter, the **law** of Statistics . . ./

conversion factor: 1mol/22.4L or 22.4L/1mol If not at STP, use the **ideal** **gas** **law** to calculate moles or volume of a substance. Can double check using **ideal** **gas** **law** Section 4 **Example** Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate. Calculate the volume/ STP conditions & stoichiometry: At STP 1mol = 22.4L 1.52mol x (22.4L/1mol) = 34.1L CO2 Can double check using **ideal** **gas** **law** **Gas** Density and Molar Mass Recall: D = m/V Let mmolar stand for molar mass mmolar = m/n so n = m/mmolar PV /

use in calculations, P 1 /T 1 = P 2 /T 2 **Example**: pressure cooker A Gay-Lussac’s **Law** Calculation The **gas** in a used aerosol can is at a pressure of 103 kPa at /**Gas** Deviation from **Ideal** Behavior **Ideal** **Gas** **Law** is useful, but all real gases fail to obey it to some degree. At high pressures, real gases do not behave **ideally**. The deviation from **ideal** behavior is small at lower pressures (below 10 atm). Deviations from **Ideal** **Gas** **Law**, Cont. As temperature increases, a **gas** acts more **ideally**. The deviations from **ideal**/

states of an **ideal** **gas** that are permitted by the **ideal** **gas** **law**. It is called the thermodynamic surface for that **gas**. Any changes in the **gas**’ state variables simply reflects movement on this surface. The following diagram illustrates this surface and on it are **examples** of isobaric, / Note: QH and QC here are MAGNITUDES of heat, and are therefore always positive. **Example**: Suppose that the working fluid is an **ideal** **gas**. From the first **law** we have that dU=Q- W. The incremental work done is related to pressure /

where = V/n is the molar volume of the **gas** Any **gas** is presented by the above equation is known as an **ideal** **gas** or perfect **gas** 1 mol of **ideal** **gas** at 0oC and 1 atm occupies 22.415 L, whether the **gas** is argon, nitrogen, or any other single species or mixture of gases **Example** Application of **Ideal** **Gas** **Law** Propane at 120oC and 1 bar absolute passes through a/

ml flask. If the sample had a mass of 0.118 g at a pressure of 550.0 Torr, what is the molecular weight of the **gas**? Plan: Use the **Ideal** **gas** **law** to calculate n, then calculate the molar mass. Solution: 1mm Hg 1 Torr 1.00 atm 760 mm Hg P = 550.0 Torr x x/= 0.293 PXe = XXe PTotal = 0.293 (2.00 atm) = 0.586 atm for Xe Relative Humidity Pressure of Water in Air Rel Hum = x 100% **Example** : the partial pressure of water at 15oC is 6.54 mm Hg, what is the Relative Humidity? Rel Hum =(6.54 mm Hg/ 12.788 mm Hg )x100% =/

Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5 Molar Mass and the **Ideal** **Gas** **Law** Easy to manipulate the **ideal** **gas** **law** to include the molar mass: Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5 Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. **Example** 2 - 15 Calcium Carbide (CaC2) is a hard, gray-black solid that has a melting/

a new way to count moles (amount of matter), by measuring T, P, and V. We aren’t restricted to STP conditions P x V R x T The **Ideal** **Gas** **Law** n = **Examples** u How many moles of air are there in a 2.0 L bottle at 19 ºC and 747 mm Hg? u What is the pressure exerted by 1.8/ g of H 2 **gas** in a 4.3 L balloon at 27 ºC? u Samples 12-5, 12-6 on pages 342 and 343 6. **Ideal** **Gas** **Law** #2 u P x V/

= P i T i = P f T f P i T f T i = P f P f = 3.6 atm Molar Mass and **Gas** Density The **ideal** **gas** **law**, P V = n R T can be used to determine the molar mass of gaseous compounds. The number of moles of a compound = mass of/ in the container. Dalton’s **law** states that the total pressure is the sum of the partial pressures of each **gas** in the mixture. For **example**, consider a mixture of two gases A and B in a closed container Assuming that the pressure is low enough, A and B obey the **ideal** **gas** equation. The fact that A/

get the following: P 1 V 1 / n 1 T 1 = P 2 V 2 / n 2 T 2 **Ideal** **Gas** **Law** The **Ideal** **Gas** **Law** was first written in 1834 by Emil Clapeyron. To "derive" the **Ideal** **Gas** **Law**, write each of the six **gas** **laws** as follows: PV = k 1 V / T = k 2 P / T = k 3 V / n = / found in reference sources – Vary by **gas** type – For **example**: Molar Volume Molar volume is the volume occupied by one mole of **ideal** **gas** at STP. Its value is 22.414 L/mol for any **gas**! – 1 mole = 6.022 x 10 23 particles – 1 mole of **gas** at STP will fit into 11 inch/

are the temperature and pressure at point C? From the graph: P c = 98.0 kPa Using the **ideal** **gas** **law** MFMcGrawChap15d-Thermo-Revised 5/5/1020 **Example** continued: (b) What is the change in internal energy of the **gas** as it is taken from point A to B? This is an isochoric process so W = 0 and U = Q. MFMcGrawChap15d-Thermo-Revised 5/5/

changes are a function of the initial and final temperatures ThermodynamicsM. D. Eastin Combining the First and Second **Laws** **Example**: Air parcels rising through a cloud Most air parcels moving through the atmosphere experience an increase in entropy due/J/kgK ΔS = 38.3 J/kg K After some simplifications, using **ideal** **gas** **law**, and integrating from p 1 to p 2 ThermodynamicsM. D. Eastin Consequences of the Second **Law** Entropy and Potential Temperature: Recall the definition of potential temperature: Valid for /

u There are attractive forces; otherwise, there would be no liquids. The **Ideal** **Gas** **Law** u P V = n R T u Pressure times volume equals the number of moles (n) times the **ideal** **gas** constant (R) times the temperature in Kelvin. The **Ideal** **Gas** **Law** u R = 0.0821 (L atm)/(mol K) u R =/ 8.314 (L kPa)/(mol K) u R = 62.4 (L mm Hg)/(mol K) u The one you choose depends on the unit for pressure! **Example** u How/

R = 0.082058 K mol L atm The **Ideal** **Gas** **Law** = 22.414 LV = P nRT = What is the volume of 1 mol of **gas** at STP? (1 atm) (1 mol)0.082058 K mol L atm (273.15 K) **Example** A helium **gas** cylinder of the sort used to fill balloons have/Waals equation b a Correction for intermolecular attractions. Correction for molecular volume. **examples** Assume that you have 0.500 mol of N 2 in a volume of 0.600L at 300K. Calculate the pressure in the atmosphere using both the **ideal** **gas** **law** and the van der Waals equation. For N2, a = 1./

imploding? **IDEAL** **GAS** **LAW** P = pressure V = volume n = # of moles R = **Ideal** **gas** constant T = temperature (in Kelvin) P V = n R T **Gas** **Law** Constant (R) R: Universal or **ideal** **gas** constant Can be in different units, depending on units used in the equation! 0.082058 L atm/mol K 62.364 L torr/mol K 8.3145 J/mol K Sample Problem **Example** 5.4 **Example** 5.4/

moles At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of **gas** occuppies 22.42 L. If not at STP, use the **ideal** **gas** **law** to calculate moles of reactant or volume of product. **Examples** Mercury can be achieved by the following reaction What volume of oxygen **gas** can be produced from 4.10 g of mercury (II) oxide at STP? At/

x 10 3 kPa) (685 L) mol · K (8.31L · kPa) (621K) n = 251 mol He Sample Problem Using **Ideal** **Gas** **Law** A child’s lungs can hold 2.20 L. How many grams of air do her lungs hold at a pressure of 102 kPa and a/ Solvent – the dissolving medium Solute Solute – the dissolved particles Solvents and Solutes Solutions are homogeneous mixtures. They are also stable mixtures. **Example**: salt (NaCl) does not settle out of the solution when allowed to stand. (provided other conditions, like temperature remain constant) Solute/

state to the final state. Entropy of an **Ideal** **Gas** Consider an arbitrary reversible quasi-static process in which a system consisting of an **ideal** **gas** adsorbs an amount of heat dQ rev. According to the first **law**, dQ rev is related to dE int and/What are possible macrostates and what are their probabilities? What are possible macrostates and what are their probabilities? Entropy, Marble **Example**, Results The most ordered are the least likely The most ordered are the least likely The most disorder is the most/

molar mass of an unknown substance is to heat a weighed sample until it becomes a **gas**; measure the temperature, pressure, and volume; and use the **ideal** **gas** **law**. © 2014 Pearson Education, Inc. Mixtures of Gases Many **gas** samples are not pure, but are mixtures of gases. Dry air, for **example**, is a mixture containing nitrogen, oxygen, argon, carbon dioxide, and a few other gases in/

invent Avogadro’s number! It was named after him 50 years after his death **Ideal** **Gas** **Law** If PV = k AndV = bT AndV = an ThenPV = nT x constant PV = nRT **Ideal** **Gas** **Law** **Ideal** **Gas** **Law** is an Equation of State –Given any three, you can determine the fourth –/= K fp x molality The more you add, the lower it gets. This will only work until you reach saturation. **Examples** **Examples**“Salting” roads in winter Making ice cream antifreeze Ionic vs. covalent substances Ionic substances have a greater effect per mole than /

absolute zero. If you plot volume vs. temperature for any **gas** at constant pressure, the points will all fall on a straight line. Tro, Principles of Chemistry: A Molecular Approach18 **Example** 3: A **gas** has a volume of 2.57 L at 0.00 °C/ P 1 + P 2 + P 3 + … Tro, Principles of Chemistry: A Molecular Approach38 The partial pressure of each **gas** in a mixture can be calculated using the **ideal** **gas** **law**. © 2012 Pearson Education, Inc. Chemistry, The Central Science, 12th Edition Theodore L. Brown; H. Eugene LeMay, Jr.;/

V = n (T/P) = kn V and n are directly related. twice as many molecules Avogadro’s **Law** **Example** : 5.00 L of a **gas** is known to contain 0.965 mol. If the amount of **gas** is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)? 5.00 L/ in mmHg R = 62.4 LmmHg molK If pressure is given in kPa R = 8.31 LkPa molK If pressure is given in atm **Ideal** **Gas** Constant Using the **Ideal** **Gas** **Law** What volume does 9.45g of C 2 H 2 occupy at STP? What volume does 9.45g of C 2 H 2 occupy at STP/

An Empirical Equation - based on experimental evidence. 19 **Ideal** **Gas** **Law** n A hypothetical substance - the **ideal** **gas**. n Gases only approach **ideal** behavior at low pressure (< 1 atm) and high temperature. n Low temperatures and high pressures cause gases to deviate from **ideal**. n Use the **laws** anyway, unless told to do otherwise. They give good estimates. 20 **Examples** n A 47.3 L container containing 1.62/

1 If the number of moles of **gas** are constant in a problem, then we have the combined **gas** **law**… P 1 V 1 T 2 = P 2 V 2 T 1 **Example** #5 1. Assuming that the **gas** behaves **ideally**, how many moles of hydrogen **gas** are in a sample of H 2 /where a corrects for intermolecular forces and b corrects for molecular volume **Example** #6 You want to store 165g of CO 2 **gas** in a 12.5L tank at room temperature (25ºC). Calculate the pressure the **gas** would have using (a) the **ideal** **gas** **law** and (b) the van der Waals equation. (For CO 2/

**Gas** **Laws** The Combined **Gas** **Law**, continued Substitute the given values of P 1, T 1, and T 2 into the equation to obtain the final volume, P 2 : Recall that one mole of a substance contains a number of particles equal to Avogadro’s constant (6.022 × 10 23 ). **example**/ 11 Section 3 **Gas** Volumes and the **Ideal** **Gas** **Law** The **Ideal** **Gas** **Law**, continued The **Ideal** **Gas** Constant, continued Numerical Values of the **Gas** Constant Section 3 **Gas** Volumes and the **Ideal** **Gas** **Law** Chapter 11 The **Ideal** **Gas** **Law**, continued Sample Problem/

piston if V, n, and T are known Temperature of a system if P, V, and n are known Volume of **gas** if P, n, and T are known –Lots of **examples** in text and homework –These are linear relationships, no exponents 41 **Ideal** **Gas** **Ideal** **Gas** **Law** PV=nRT –Simplifies to Boyle’s **Law** when n and T are constant PV = nRT = constant “k” –Simplifies to Charles/

4 L = 1 mole u For **example** How many liters of O 2 at STP are required to produce 20.3 g of H 2 O? Not At STP u Chemical reactions happen in MOLES. u If you know how much **gas** - change it to moles u Use the **Ideal** **Gas** **Law** n = PV/RT u If you/ want to find how much **gas** - use moles to figure out volume V = nRT/P **Example** #1 u HCl(g) can be formed by the following reaction u 2NaCl(aq/

. You have the same number moles. CONVERTING THE **IDEAL** **GAS** **LAW** We start with the **ideal** **gas** **law** PV = nRT We look at the assumptions of each **law** to see what must remain constant If the condition remains constant, we can remove it from the **ideal** **gas** **law** We set the equation equal to the **gas** constant (R) to get the other **gas** **laws** **EXAMPLES** ON THE BOARD STOICHIOMETRY REVISITED With gases, we sometimes/

temperature changes from 20 o C to 15 o C? **Examples** with Combined **Gas** **Law** A certain sample of **gas** has a volume of 0.452 L measured at 87 o C and 0.620 atm. What is its volume at 1 atm and 0 o C? The **Ideal** **Gas** **Law** P, V, T, and n The Combined **Gas** **Law** Takes into account P, T, and V but not/

58,60,62 Objectives Perform **gas** stoichiometry calculations Describe volume ratios Relate **gas** temperature to Kinetic Energy Perform calculations using Grahams **Law** of Effusion Describe the dependence of **gas** variables **Gas** Stoichiometry We can perform stoichiometry with gases Must use the **ideal** **gas** **law** –Use the **ideal** **gas** **law** to find moles –Use at beginning or the end –Perform normal stoichiometry Balanced equation Mole ratios Molar masses **Example** 4.55 grams of/

1 x 10 -3 m 3. **ideal** **gas** constant is also known as the universal **gas** constant 10.3 **Gas** **Laws** and Absolute Temperature **Example** 10.4: A **gas** has a volume of 0.20 m 3/**Gas** **Laws** and Absolute Temperature **Example** 10.5: An **ideal** **gas** in a container of volume 1000 cm 3 (one liter) at 20.0°C has a pressure of 1.00 x 10 4 N/m 2. Determine the number of **gas** molecules and the number of moles of **gas** in the container. 10.3 **Gas** **Laws** and Absolute Temperature: Check for Understanding 1. The temperature used in the **ideal** **gas** **law**/

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