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A sample of 100 \mathrm{~g} of ice at -10^{\circ} \mathrm{C} is heated until it completely vaporizes into steam at 100^{\circ} \mathrm{C}. Calculate the change in entropy during each phase transition and the total change in entropy for the entire process. Given the specific heat capacity of ice is 2.09 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right), the specific heat capacity of water is 4.18 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right), the heat of fusion of ice is 334 \mathrm{~J} / \mathrm{g},the heat of vaporization of water is 2260 \mathrm{~J} / \mathrm{g},and the molar gas constant is 8.314 \mathrm{~J} /(\mathrm{mol} \mathrm{K}).

Option: 1

650.31 \mathrm{~J} / \mathrm{K}


Option: 2

732.15 \mathrm{~J} / \mathrm{K}


Option: 3

505.26 \mathrm{~J} / \mathrm{K}


Option: 4

478.25 \mathrm{~J} / \mathrm{K}


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_{\text {ice }} \cdot c_{\text {ice }} \cdot \Delta T

Where: -m_{\text {ice }}$ is the mass of the ice $-c_{\text {ice }}$ is the specific heat capacity of ice - $\Delta T is the temperature change

Substitute the given values:

Q_{\text {ice }}=100 \mathrm{~g} \cdot 2.09 \mathrm{~J} /\left(\mathrm{g}^{\circ} \mathrm{C}\right) \cdot\left(0{ }^{\circ} \mathrm{C}-\left(-10^{\circ} \mathrm{C}\right)\right)
Q_{\text {ice }}=2090 \mathrm{~J}

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_{\text {ice }} \cdot \Delta H_{\text {fusion }}

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

Substitute the given value:
Q_{\text {fusion }}=100 \mathrm{~g} \cdot 334 \mathrm{~J} / \mathrm{g}
Q_{\text {fusion }}=33400 \mathrm{~J}

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_{\text {water }} \cdot c_{\text {water }} \cdot \Delta T
\mathrm{Where: -m_{\text {water }} \text{is the mass of the water} -c_{\text {water }}}

the specific heat capacity of water Substitute the given values:
Q_{\text {water }}=100 \mathrm{~g} \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 }}=41800 \mathrm{~J}

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_{\text {water }} \cdot \Delta H_{\text {vaporization }}

\mathrm{Where: -\Delta H_{\text {vaporization }}}  is the heat of vaporization of water Substitute the given value:
Q_{\text {vaporization }}=100 \mathrm{~g} \cdot 2260 \mathrm{~J} / \mathrm{g}
Q_{\text {vaporization }}=226000 \mathrm{~J}

Step 5: Calculate the total heat transfer during the entire process:
Q_{\text {total }}=Q_{\text {ice }}+Q_{\text {fusion }}+Q_{\text {water }}+Q_{\text {vaporization }}

Substitute the calculated values:
Q_{\text {total }}=2090 \mathrm{~J}+33400 \mathrm{~J}+41800 \mathrm{~J}+226000 \mathrm{~J}
Q_{\text {total }}=302590 \mathrm{~J}

Step 6: Calculate the change in entropy for each phase transition: Entropy change during fusion:
\Delta S_{\text {fusion }}=\frac{Q_{\text {fusion }}}{T_{\text {fusion }}}
\mathrm{Where: - T_{\text {fusion }} }  is the melting point of ice in Kelvin (263.15 \mathrm{~K}) Substitute the values:
\Delta S_{\text {fusion }}=\frac{33400 \mathrm{~J}}{263.15 \mathrm{~K}}
\Delta S_{\text {fusion }}=126.80 \mathrm{~J} / \mathrm{K}

Entropy change during vaporization:
\Delta S_{\text {vaporization }}=\frac{Q_{\text {vaporization }}}{T_{\text {vaporization }}}

Where: -T_{\text {vaporization }}  is the boiling point of water in Kelvin (373.15 \mathrm{~K})   Substitute the values:
\Delta S_{\text {vaporization }}=\frac{226000 \mathrm{~J}}{373.15 \mathrm{~K}}
\Delta S_{\text {vaporization }}=605.35 \mathrm{~J} / \mathrm{K}

Step 7: Calculate the total change in entropy for the entire process:
\Delta S_{\text {total }}=\Delta S_{\text {fusion }}+\Delta S_{\text {vaporization }}
\Delta S_{\text {total }}=126.80 \mathrm{~J} / \mathrm{K}+605.35 \mathrm{~J} / \mathrm{K}
\Delta S_{\text {total }}=732.15 \mathrm{~J} / \mathrm{K}

Answer: The change in entropy during fusion is 126.80 \mathrm{~J} / \mathrm{K},the change in entropy during vaporization is 605.35 \mathrm{~J} / \mathrm{K}, and the total change in entropy for the entire process is 732.15 \mathrm{~J} / \mathrm{K}.
Therefore, the correct option is (B).

Posted by

jitender.kumar

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