Question

When 0.595 g of biphenyl (C12H10) undergoes combustion in a bomb calorimeter, the temperature rises from 25.4 ∘C to 29.9 ∘C.

Part A

Find ΔErxn for the combustion of biphenyl in kJ/mol biphenyl. The heat capacity of the bomb calorimeter, determined in a separate experiment, is 5.86 kJ/∘C.

Part B

Learning Goal: 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 substance by exactly 1 degree Celsius. This value is the molar heat capacity, which has the symbol Cp.The molar heat capacity is given in the units J/(mol⋅∘C). A second method is to report how much energy it takes to raise the temperature of one gram of a substance by exactly 1 degree Celsius. This value is the specific heat, which has been given the symbol Cs. The units for specific heat are J/(g⋅∘C). The heat capacity of a substance is therefore related to the energy q needed to raise its temperature by an amount ΔT. That is, q=nCpΔT, where n denotes the number of moles of the substance, or q=mCsΔT, where m denotes the number of grams of the substance.

Part 1

It takes 55.0 J to raise the temperature of an 9.90 g piece of unknown metal from 13.0∘C to 24.8 ∘C. What is the specific heat for the metal?

Express your answer with the appropriate units.

Part 2

The molar heat capacity of silver is 25.35 J/mol⋅∘C. How much energy would it take to raise the temperature of 9.90 g of silver by 16.0 ∘C?

Express your answer with the appropriate units.

Part 3

What is the specific heat of silver? Express your answer with the appropriate units.

Answer 1

A)
Q released = C(calorimeter) * delta T
    = 5.86 * (29.9 - 25.4)
    = 26.37 KJ

this heat is released by 0.595 g of C12H10
Molar mass of C12H10 = 12*12 + 10*1 = 154 g/mol
number of moles of C12H10 = mass / molar mass
                                                          = 0.595 / 154
                                                          = 3.864*10^-3 mol

ΔErxn = Q / mol
              = 26.37 KJ / (3.864*10^-3 mol)
              = 6825 KJ/mol

B)
1)
use:
Q = m*C*(Tf-Ti)
55 = 9.9*C*(24.8 - 13)
C = 0.47 J/goC
Answer: 0.47 J/goC

2)
mass of silver = 9.9 g
Molar mass of silver = 107.87 g/mol
number of moles of silver,n = mass / molar mass
                                                      = 9.9 / 107.87
                                                      = 0.0918 mol

Q = n*C*(Tf-Ti)
    = 0.0918*25.35*(16)
   =37.22 J
Answer: 37.22 J

3)
specific heat = molar heat capacity / molar mass
                           = 25.35 / 107.87
                           = 0.235 J/goC
Answer: 0.235 J/goC