To understand the concepts of heat capacity, specific heat, and molar heat capac

Question

To understand the concepts of heat capacity, specific heat, and molar heat capacity. Heat capacity, C. is the amount of energy required to raise the temperature of a substance by exactly 1 degree Celsius. The energy needed to warm an object increases as the mass of that object increases. We see this in our everyday life. For example, we know that it takes much more energy to heat a large tank of water than a small cup. Because of this dependence on mass, experimentally determined heat capacities are always reported in terms of the amount of the substance that is heated. One method is to report how much energy it takes to raise the temperature of one mole of a substances by exactly 1 degree Celsius. This value is the molar heat capacity, which has the symbol C_p. The molar heat capacity is given in the units J/(mol middot degree C). A second method is to report how much energy it takes to raise the temperature of one gram of a substance exactly 1 degree Celsius. This value is the specific heat, which has been g symbol C_s. The units for specific heat are J/(g middot degree C). The heat capacity of a substances is therefore related to the energy q needed to raise its temperature by an amount delta T. That is, q = nC_p delta T, where n denotes the number of moles of the substance, or q = mC_s delta T, where m denotes the number of grams of the substances. It takes 50.0 J to raise the temperature of an 9.60 g piece of unknown 13.0 degree C to 25.0 degree C. What is the specific heat for the metal? Express your answer with the appropriate units. C_s = .434 The next two questions pertain to silver They have nothing to do with unknown metal described in Part A. The molar heat capacity of silver is 25.35 J/mol middot degree C. How much energy would it take to raise the temperature of 9.80 g of silver by 14.2 degree C? Express your answer with the appropriate units. q = What is the specific heat of silver? Express your answer with the appropriate units.

Explanation / Answer

A)

Q = m*C*(Tf-Ti)

50.0 J = 9.80g * C * (25.0 - 13.0) oC

C = 0.425 J/g.oC

Answer: 0.425 J/goC or 0.425 J/gK

B)

molar mass of Ag = 108 g/mol

So,

number of mol of silver,

n = mass / molar mass

= 9.80 g / 108 g/mol

= 0.09074 mol

Q= n*C*delta T

= 0.09074 mol * 25.35 J/mol.oC*14.2 oC

= 32.66 J

Answer: 32.66 J

C)

specific heat = molar heat / molar mass

= 25.35 J/mol.oC / 108 g/mol

= 0.235 J/g.oC

Answer: 0.235 J/g.oC

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