# 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}

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