Answer to Question #174400 in Chemistry for Ava Brooke

Question

A 13.97 g sample of ice is heated from -10 ^oC to its melting point of 0 ^oC and then melted completely. Next it is raised to its boiling point of 100 ^oC and boiled completely. Finally the sample is heated to 111 ^oC. How much energy was absorbed by the sample? (Answer in kJ pay close attention to units!)

S_ice=2.1 J/g^oC Delta H_f = 6.02 kJ/mol

S_steam=1.7 J/g^oC Delta H_v = 2.26 kJ/g

Answer 1

Solution:

Moles of H₂O = Mass of H₂O / Molar mass of H₂O

The molar mass of H₂O is 18.0153 g mol^-1.

Hence,

Moles of H₂O = 13.97 g / 18.0153 g mol^-1 = 0.77545 mol

Moles of H₂O = 0.77545 mol

This problem can be summarized thusly:

1) Ice is heated from -10°C to 0°C.

The heat absorbed is calculated by using the specific heat of ice (S_ice = 2.1 J/g°C) and the equation:

q = m × S × ΔT

q₁ = m × S_ice × (T_f - T_i)

q₁ = 13.97 g × 2.1 J/g°C × (0 - (-10))°C = 293.37 J = 0.29337 kJ

q₁ = 0.29337 kJ

2) Ice is melted at 0°C. The heat absorbed is calculated by multiplying the moles of ice by the molar heat of fusion (ΔH_f).

q₂ = ΔH_f × n = 6.02 kJ/mol × 0.77545 mol = 4.66821 kJ

q₂ = 4.66821 kJ

3) Water at 0°C is heated to 100°C. The heat absorbed is calculated by using the specific heat of water (S_water = 4.2 J/g°C) and the equation: q = m × S × ΔT

q₃ = m × S_water × (T_f - T_i)

q₃ = 13.97 g × 4.2 J/g°C × (100 - 0)°C = 5867.4 J = 5.8674 kJ

q₃ = 5.8674 kJ

4) Water is vaporized to steam at 100°C. The heat absorbed is calculated by multiplying the grams of water by the heat of vaporization (ΔH_v) in kJ/g.

q₄ = ΔH_v × m = 2.26 kJ/g × 13.97 g = 31.5722 kJ

q₄ = 31.5722 kJ

5) Steam is heated from 100°C to 111°C. The heat absorbed is calculated by using the specific heat of steam (S_steam = 1.7 J/g°C) and the equation: q = m × S × ΔT

q₅ = m × S_steam × (T_f - T_i)

q₅ = 13.97 g × 1.7 J/g°C × (111 - 100)°C = 261.239 J = 0.26124 kJ

q₅ = 0.26124 kJ

q = q₁ + q₂ + q₃ + q₄ + q₅

q = 0.29337 kJ + 4.66821 kJ + 5.8674 kJ + 31.5722 kJ + 0.26124 kJ = 42.66242 kJ = 42.66 kJ

q = 42.66 kJ

Answer: 42.66 kJ of energy was absorbed by the sample.