At 1 atm, how much energy is required to heat 75.0 g of H_2O(s) at -20.0 degrees C to H_2O(g) at...

Question:

At 1 atm, how much energy is required to heat {eq}75.0\ g {/eq} of {eq}\rm H_2O(s) {/eq} at {eq}\rm -20.0 ^\circ C {/eq} to {eq}\rm H_2O(g) {/eq} at {eq}155.0 ^\circ C {/eq}?

Phase change

Energy is needed to change the phase of a substance. During a phase change, the temperature does not change but energy is either added or subtracted for the phase change to occur. The temperature only changes when the phase change have finished.

Answer and Explanation:

{eq}H_{2}O_{(s)} (-20^{o}C) -> H_{2}O_{(s)} (0^{o}C) -> H_{2}O_{(l)} (0^{o}C) -> H_{2}O_{(l)} (100^{o}C) -> H_{2}O_{(g)} (100^{o}C) -> H_{2}O_{(g)} (155^{o}C) {/eq}

Constants to be used:

{eq}\Delta _{fus}H= 333.6 J/g {/eq}

{eq}\Delta _{vap}H= 2257 J/g {/eq}

{eq}specific\ heat\ of\ ice= 2.087 J/g^{o}C {/eq}

{eq}specific\ heat\ of\ water= 4.184 J/g^{o}C {/eq}

{eq}specific\ heat\ of\ steam= 2.000 J/g^{o}C {/eq}

Compute energy needed for each step in the diagram above:

1. To raise the temperature of ice to {eq}0^{o}C {/eq}:

{eq}Q_{1}= mc\Delta T {/eq}

{eq}Q_{1}=(75g)(2.087J/g^{o}C)(20.0^{o}C) {/eq}

{eq}Q_{1}= 3130.5 J {/eq}

2. To melt the ice

{eq}Q_{2}=m\Delta _{fus}H {/eq}

{eq}Q_{2}= (75g)(333.6 J/g) {/eq}

{eq}Q_{2}=25020 J {/eq}

3. To heat the water

{eq}Q_{3}= mc\Delta T {/eq}

{eq}Q_{3}=(75g)(4.184J/g^{o}C)(100^{o}C) {/eq}

{eq}Q_{3}=2928.8 J {/eq}

4. To boil the water

{eq}Q_{4}=m\Delta _{vap}H {/eq}

{eq}Q_{4}= (75g)(2257J/g) {/eq}

{eq}Q_{4}=169275J {/eq}

5. To heat the steam

{eq}Q_{5}= mc\Delta T {/eq}

{eq}Q_{5}= (75g)(2.000 J/g^{o}C)(55^{o}C) {/eq}

{eq}Q_{5}= 8250 J {/eq}

6. Total energy needed

{eq}Q_{t}=Q_{1}+ Q_{2} + Q_{3} + Q_{4} + Q_{5} {/eq}

{eq}Q_{t}= 208604.3 J= 208.6043 kJ {/eq}


Learn more about this topic:

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Phase Changes and Heating Curves

from Chemistry 101: General Chemistry

Chapter 6 / Lesson 3
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