Phase Changes

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Physical Chemistry › Phase Changes

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What amount of heat must be added to a 20-gram sample of ice in order to raise the temperature from $-5^\circ C$ to $35^\circ C$ ?

$\Delta H^\circ_f=333\frac{J}{g}$

$c_{water}=2.1\frac{J}{g^\circ C}$

$c_{ice}=4.184\frac{J}{g^\circ C}$

This question requires three steps:

1. We need to raise the temperature of the ice from to degrees Celsius.

2. We need to melt the ice.

3. We need to raise the temperature of the water from to degrees Celsius.

Steps one and three can use the equation:

$q = mc\Delta T$

Step 2 requires the enthalpy of fusion to be multiplied by the mass of the water sample.

$q = (\Delta H_{fusion})(m)$

Finding these three added heats will give us the total amount of heat needed to raise the temperature from $-5^\circ C$ to $35^\circ C$ .

$q = mc_{ice}\Delta T + \Delta H_{fusion}(m) + mc_{water}\Delta T$

$q = (20g)(2.1\frac{J}{g^{\circ} C})(5^{\circ} C) + (333J)(20g) + (20g)(4.184\frac{J}{g^{\circ} C})(35^{\circ} C)$