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  • Given: - The heat of fusion for a substance is <img alt="180 \mathrm{~J} / \mathrm{g}." src="https://

Given: - The heat of fusion for a substance \mathrm{X} is 180 \mathrm{~J} / \mathrm{g}.

- The heat of vaporization for substance\mathrm{X} is 800 \mathrm{~J} / \mathrm{g}.

- The molar mass of substance \mathrm{X} is 60 \mathrm{~g} / \mathrm{mol}.

- Initial temperature of substance \mathrm{X} is \mathrm{15^{\circ} \mathrm{C}.}

- Final temperature of the vaporized substance \mathrm{X} is 100^{\circ} \mathrm{C}.

- The specific heat capacity of substance \mathrm{X} (liquid) is 3.5 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}.

- The specific heat capacity of vaporized substance \mathrm{X} is 2.0 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}.
Calculate the enthalpy change for the following process: Heating 30 \mathrm{~g} of substance \mathrm{X} at \mathrm{-5^{\circ} \mathrm{C}} to vaporized substance \mathrm{X} at \mathrm{100^{\circ} \mathrm{C}.}

Option: 1

16525 J


Option: 2

-16525 J


Option: 3

16000 J


Option: 4

-16000 J


Answers (1)

best_answer

Step 1: Calculate the heat required to raise the temperature of substance \mathrm{X} from -5^{\circ} \mathrm{C} to 0^{\circ} \mathrm{C}.

                                        q_1=m \times C_{\mathrm{X}}, \text { liquid } \times \Delta T
Where: -m=30 \mathrm{~g} (mass of substance X ) \mathrm{- C_{\mathrm{X}}, \, liquid =3.5 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}}(specific heat capacity of substance

\mathrm{\mathrm{X})-\Delta T=0-(-5)^{\circ} \mathrm{C}=5^{\circ} \mathrm{C}}

                                        \mathrm{ q_1=30 \mathrm{~g} \times 3.5 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C} \times 5^{\circ} \mathrm{C}=525 \mathrm{~J} }

Step 2: Calculate the heat required to melt substance \mathrm{X} at 0^{\circ} \mathrm{C} to substance \mathrm{X} at 0^{\circ} \mathrm{C}.

                                        q_2=m \times \Delta H_{\text {fusion }}

Where: \mathrm{-m=30 \mathrm{~g}} (mass of substance \mathrm{X} ) \mathrm{-\Delta H_{\text {fusion }}=180 \mathrm{~J} / \mathrm{g}} (heat of fusion for substance \mathrm{X} )

                                     \mathrm{ q_2=30 \mathrm{~g} \times 180 \mathrm{~J} / \mathrm{g}=5400 \mathrm{~J} }

Step 3: Calculate the heat required to raise the temperature of substance \mathrm{X} from \mathrm{0^{\circ} \mathrm{C}} to \mathrm{100^{\circ} \mathrm{C}. }

                                     \mathrm{q_3=m \times C_{\mathrm{X}, \text { liquid }} \times \Delta T}
Where: -m=30 \mathrm{~g} (mass of substance \mathrm{X} )\mathrm{ -C_{\mathrm{X}}, liquid =3.5 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}} (specific heat capacity of substance \mathrm{X})-\Delta T=100^{\circ} \mathrm{C}-0^{\circ} \mathrm{C}=100^{\circ} \mathrm{C}

                                    \mathrm{ q_3=30 \mathrm{~g} \times 3.5 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C} \times 100{ }^{\circ} \mathrm{C}=10500 \mathrm{~J} }

The total heat for the process is \mathrm{q_{\text {total }}=q_1+q_2+q_3=525 \mathrm{~J}+5400 \mathrm{~J}+ 10500 \mathrm{~J}=16525 \mathrm{~J}}. So, option A is correct

Posted by

himanshu.meshram

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