5.3: Energy and Phase Transitions

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Heat Capacity and Phase Changes

Exercise \(\PageIndex{1}\)

How much energy is needed to convert 5.88 g of ice at 0.00 °C to liquid water at 85.0 °C?

Specific heat capacity (ice) = 2.10 J/g*°C
Specific heat capacity (liquid water) = 4.18 J/g*°C
Heat of fusion = 333 J/g

Answer

4.05 * 10³ J

\(q_{1} = m\Delta H_{f} = \left ( 5.88 g \right )\left ( 333 J/g \right ) = 1958.04 J\)

\(q_{2} = mc\Delta T = \left ( 5.88 g \right )\left ( 4.18 J/g*°C \right )\left ( 85 °C - 0 °C \right ) = 2089.164 J\)
q_Total = q₁ + q₂ = 1958.04 J + 2089.164 J = 4047.204 J

Exercise \(\PageIndex{2}\)

Calculate the energy in the form of heat (in kJ) required to convert 125 grams of liquid water at 20.0 °C to steam at 115 °C. Assume that no energy in the form of heat is transferred to the environment. (Heat of fusion = 333 J/g; heat of vaporization = 2256 J/g; specific heat capacities: liquid water = 4.184 J/g*°C, steam = 1.92 J/g*°C)

Answer: 3.28 * 10² kJ

Exercise \(\PageIndex{3}\)

Calculate the energy in the form of heat (in kJ) required to change 81.5 g of liquid water at 30.6 °C to ice at –13.5 °C. Assume that no energy in the form of heat is transferred to the environment. (Heat of fusion = 333 J/g; heat of vaporization = 2256 J/g; specific heat capacities: ice = 2.06 J/g*°C, liquid water = 4.184 J/g*°C)

Answer: -39.8 kJ

Exercise \(\PageIndex{4}\)

What is the minimum mass of ice at 0.0 °C that must be added to 2.50 kg of water to cool the water from 28.0 °C to 9.0 °C? (Heat of fusion = 333 J/g; specific heat capacities: ice = 2.06 J/g*°C, liquid water = 4.184 J/g*°C)

Answer

m = 536 g

\(mc\Delta T = mc\Delta T + m\Delta H_{f}\)

\((2500g)(4.184 J/g*°C)(28 °C - 9 °C) = x(4.184 J/g*°C)(9 °C - 0 °C)+ x(333 J/g)\)

\(198740 = x370.656\)

\(x = \frac{198740}{370.656}\)

x = 536.184 g

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