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Heat Problems

Heat Problems. There are a few problems that deal with heat: Heat as enthalpy Specific heat Heat of fusion Heat of vaporization. Enthalpy. Enthalpy is the total energy of a system It is represented by a H .

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Heat Problems

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  1. Heat Problems • There are a few problems that deal with heat: • Heat as enthalpy • Specific heat • Heat of fusion • Heat of vaporization

  2. Enthalpy • Enthalpy is the total energy of a system • It is represented by a H. • If the pressure remains constant, the enthalpy increase of a sample of matter equals the energy as heat that is received. • This remains true even during a chemical reaction or a change of state occurs. • It also indicates the totalkinetic energy of the particles in a sample

  3. So to calculate Enthalpy, we have to visit molar heat capacity • Molar heat capacity of a pure substance is the energy as heat needed to increase the temperature of 1 mol of a substance by 1K • It is symbolized by C • It has a unit of J/(mol.K) • Formula: q=nCT • Heat = (amount in moles) (molar heat capacity) (change in temperature) • Note: moles are used so you may have to do some gram to mole problems. • Table 1 on Page 343 has many Molar Heat Capacities of Elements and Compounds.

  4. Examples • The molar heat capacity of tungsten is 24.2 J/(mol.K).Calculate the energy as heat needed to increase the temperature of 0.40 mol of tungsten by 10.0 K. • Suppose a sample of water increased in temperature by 3.5 K when the sample absorbed 856 J of energy as heat. Calculate the number of moles of water if the molar heat capacity is 50.5 J /(mol.K). What is the mass of that water?

  5. Molar Enthalpy Change • Since enthalpy “equals the energy as heat that is received”, we can rewrite the heat equation to: • H = nCT • Enthalpy change = (moles)(molar heat capacity) (change in temperature) • The enthalpy change for one mole of a pure substance is known as the molar enthalpy change.

  6. Examples • The molar heat capacity of Al(s) is 24.2 J/K.mol. Calculate the molar enthalpy change when Al(s) is cooled from 128.5 C to 22.6 C. • Lead has a molar heat capacity of 26.4 J/K.mol. What molar enthalpy change occurs when lead is cooled from 302 C to 275 C?

  7. Molar Heat Capacity is related to Specific Heat • Specific heat is the energy as heat needed to raise the temperature of one gram of substance by one Kelvin. • Symbolized by cp • This is why an iron gets hot faster than a pot of water • There are two equations that involve specific heat 1) Molar Mass (g/mol) x cp (J/K.g) = C (J/K.mol) 2) q = m x cp x T

  8. Example Problem • If the molar heat capacity of nitrogen (N2) is 29.1 (J/K.mol), what is nitrogen’s specific heat? • Calculate the specific heat of a substance if a 35 g sample absorbs 48 J as the temperature is raised from 293 K to 313 K • cp= 48 J/[35gx(313K-293K)] = 0.069 J/gK

  9. Two more heat equations • Heat of fusion (Lf) • Heat involved in melting or freezing a substance • Heat of vaporization (Lv) • Heat involved in evaporation or condensing a substance • As a phase change occurs, all energy is being used for the change so the temperature will not change. • So, during a phase change, heat equals the mass (m) times a value (L) for that material (q=m x L)

  10. Example Problem • If the heat of fusion of water is 80 cal/g, what is the amount of heat energy required to change 15.0 grams of ice at 0C to 15.0 grams of water at 0C?

  11. How do they all fit together? This is Figure 17 from page 394 from the book As heat is added, temperature increases linearly (q=nCT) Except, when a phase change occurs, because all the heat is going into changing the phase (q=m L, note no T)

  12. Try Practice Problems 2-4 on page 61 • 0.385 J/gK • 329 K • 3.6 kJ

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