The specific heat capacity of arsenic is 0.33 J °C−1 g−1. (a) Calculate the energy required to raise the temperature of 201.4 g As from 273 K to 298 K. J (b) Calculate the energy required to raise the temperature of 1.0 mole of As by 1.0°C (called the molar heat capacity of arsenic). J °C−1 mol−1 (c) It takes 1.26 kJ of energy to heat a sample of pure arsenic from 13.2°C to 15.2°C. Calculate the mass of the sample of arsenic. g

a)1661.55 J of energy is required

b) the molar heat capacity = 24.7 J /mol*°C

c) We need 1909 grams of arsenic

Explanation:

Step 1: Data given

The specific heat capacity of arsenic is 0.33 J/g*K

Mass of As = 201.4 grams

Initial temperature = 273 K

Final temperature = 298 K

Step 2: Calculate the energy required to raise the temperature of 201.4 g As from 273 K to 298 K.

Q =m*c*ΔT

⇒with Q = the energy needed = TO BE DETERMINED

⇒with m = the mass of As = 201.4 grams

⇒with c = the specific heat capacity of Arsenic = 0.33 J/*K

⇒with ΔT = the change of temperature = 298 - 273 = 25 K

Q = 201.4 g * 0.33 J/g*K * 25 K

Q = 1661.55 J

Step 3: Calculate the energy required to raise the temperature of 1.0 mole of As by 1.0°C (called the molar heat capacity of arsenic)

Atomic mass of Arsenic = 74.9 g/mol

1 mol As has a mass of 74.9 grams

∆H = (moles * molar mass)* C* ∆T

⇒with  ∆H= the molar heat capacity= TO BE DETERMINED

⇒with moles = 1.0 mol

⇒with molar mass = 74.9 g/mol

⇒with c= the specific heat capacity of arsenic = 0.33 J/g*°C

⇒with ΔT = the change of temperature = 1.0 °C

∆H = (1.0 mol * 74.9 g/mol) * (0.33J/g*°C) * 1 °C

∆H = 24.7 J /mol*°C

Step 4: It takes 1.26 kJ of energy to heat a sample of pure arsenic from 13.2°C to 15.2°C. Calculate the mass of the sample of arsenic

Q = m*c*ΔT

⇒with Q = the energy required = 1.26 kJ = 1260 J

⇒with m = the mass of arsenic = TO BE DETERMINED

⇒with c= the specific heat capacity of arsenic = 0.33 J/g°C

⇒with ΔT = the change of temperature = T2 - T1 = 15.2 °C - 13.2 °C = 2.0 °C

1260 J = m * 0.33 J/g°C * 2.0 °C

m = 1909 grams

We need 1909 grams of arsenic

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