The specific heat capacity of silver is 0.24 J/°C ·g. A) Calculate the energy required to raise the temperature of 150.0 g Ag from 273 K to 298 K.
B) Calculate the energy required to raise the temperature of 1.0 mole of Ag by 1.08C (called the molar heat capacity of silver).
C. It takes 1.25 kJ of energy to heat a sample of pure silver from 12.08°C to 15.28°C. Calculate the mass of the sample of silver.

A) 900 J

B) 27.96 J

C) 1,628 J ≅ 1.63 kJ

Explanation:

The heat absorbed by the metal (silver) - or energy required to heat it -  is calculated as:

heat = mass x Cp x ΔT

Where Cp is the heat capacity (0.24 J/°C ·g) and ΔT is the change in temperature (final T - initial T).

A) Given:

mass = 150.0 g

final T = 298 K = 25°C

initial T = 273 K = 0°C

We calculate the energy in J to raise the temperature:

heat = mass x Cp x (final T - initial T)

       = 150 .0 g x 0.24 J/°C ·g x (25°C - 0°C )

       = 900 J

B) Given:

moles Ag= 1.0 mol

ΔT = 1.08°C

We first calculate the mass of silver (Ag) by multiplying the moles of Ag by the molar mass of Ag (MM = 107.9 g/mol)

mass = moles x MM = 1.0 mol Ag x 107.9 g/mol Ag = 107.9 g

Then, we calculate the heat required:

heat = mass x Cp x ΔT = 107.9 g x 0.24 J/°C ·g x 1.08°C = 27.96 J

C) Given:

heat = 1.25 kJ = 1,250 J

final T = 15.28°C

initial T = 12.08°C

We first calculate the change in temperature:

ΔT = final T - initial T = 15.28°C - 12.08°C = 3.2°C

Then, we calculate the mass of silver:

mass = heat/(Cp x ΔT) = 1,250 J/(0.24 J/°C ·g x 3.2°C) = 1,628 J ≅ 1.63 kJ

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