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A sample of ice at -20^{\circ} \mathrm{C} is heated until it becomes steam at 100^{\circ} \mathrm{C}.Calculate the total heat required to first raise the temperature of the ice to its melting point and then convert it to steam. Given the specific heat capacity of ice is 2.09 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right), the heat of fusion of ice is 334 \mathrm{~J} / \mathrm{g},the specific heat capacity of water is 4.18 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right),and the heat of vaporization of water is 2260 \mathrm{~J} / \mathrm{g}.

Option: 1

1.60 \mathrm{~kJ} / \mathrm{mol}


Option: 2

0.437 \mathrm{~kJ} / \mathrm{mol}


Option: 3

20.30 \mathrm{~kJ} / \mathrm{mol}


Option: 4

2.50 \mathrm{~kJ} / \mathrm{mol}


Answers (1)

best_answer

Step 1: Calculate the heat required to raise the temperature of the ice to its melting point \left(0^{\circ} \mathrm{C}\right) :

Q_{\text {ice }}=m \cdot c_{\text {ice }} \cdot \Delta T

Where:
m is the mass of the ice
c_{\text {ice }} is the specific heat capacity of ice
\Delta Tis the temperature change

Substitute the given values:
\begin{gathered} Q_{\text {ice }}=m \cdot 2.09 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right) \cdot\left(0^{\circ} \mathrm{C}-\left(-20^{\circ} \mathrm{C}\right)\right) \\ Q_{\text {ice }}=41.8 \mathrm{~m} \mathrm{~J} / \mathrm{g} \end{gathered}


Step 2: Calculate the heat required for the fusion of ice at its melting point \left(0^{\circ} \mathrm{C}\right) :

Q_{\text {fusion }}=m \cdot \Delta H_{\text {fusion }}

Where:
\Delta H_{\text {fusion }} \text { is the heat of fusion of ice }

Substitute the given value:

Q_{\text {fusion }}=m \cdot 334 \mathrm{~J} / \mathrm{g}

Step 3: Calculate the heat required to raise the temperature of the water from its melting point \left(0^{\circ} \mathrm{C}\right) to its boiling point \left(100^{\circ} \mathrm{C}\right) :
Q_{\text {water }}=m \cdot c_{\text {water }} \cdot \Delta T

Where:
c_{\text {water }} \text { is the specific heat capacity of water }
Substitute the given values:
Q_{\text {water }}=m \cdot 4.18 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right) \cdot\left(100^{\circ} \mathrm{C}-0{ }^{\circ} \mathrm{C}\right)
Q_{\text {water }}=418 \mathrm{~m} \mathrm{~J} / \mathrm{g}

Step 4: Calculate the heat required for the vaporization of water at its boiling point \left(100^{\circ} \mathrm{C}\right) :
Q_{\text {vaporization }}=m \cdot \Delta H_{\text {vaporization }}
Where:
\Delta H_{\text {vaporization }} \text { is the heat of vaporization of water }

Substitute the given value:
Q_{\text {vaporization }}=m \cdot 2260 \mathrm{~J} / \mathrm{g}

Step 5: Calculate the total heat required:

Q_{\text {total }}=Q_{\text {ice }}+Q_{\text {fusion }}+Q_{\text {water }}+Q_{\text {vaporization }}
Substitute the calculated values:

Q_{\text {total }}=41.8 \mathrm{~m} \mathrm{~J} / \mathrm{g}+m \cdot 334 \mathrm{~J} / \mathrm{g}+418 \mathrm{~m} \mathrm{~J} / \mathrm{g}+m \cdot 2260 \mathrm{~J} / \mathrm{g}
Q_{\text {total }}=(2613.8+2278) \mathrm{m} \mathrm{J} / \mathrm{g}

Answer: The total heat required to first raise the temperature of the ice to its melting point and then convert it to steam is approximately 4891.8 \mathrm{~m} \mathrm{~J} / \mathrm{g}.

 

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