Question

Question #a540a

Answer 1

Find all heats according to temperature decrease and phase changes and add them. Answer is:

`Q_(t ot)=62.6509kJ`

Explanation:

First you need to understand what phase transitions it faces. From the melting and boiling points you know that:

Transition 1 Temperature cooling : Gas `92^oC->78.4^oC`

Transition 2 Phase change : Condensation at `78.4^oC`

Transition 3 Temperature cooling : Liquid `78.4^oC->-16^oC`

Since the melting point of `-114.5^oC` is not met, the ethanol does not become solid.

The 3 energies you need to estimate are the three transitions mentioned above.

Transition 1

The energy is given as a temperature decrease `ΔT_1`:

`Q_1=n*c_(p(gas))*ΔT=m/(Mr)*c_(p(gas))*ΔT_1`

Note: this equation uses mols instead of grams because the heat capacity is given in J/(K*mol).

`Mr_(C_2H_5OH)=2*12+1*6+16=46g/(mol)`

`Q_1=20/16*65.7*(92-78.4)g/(g/(mol))*J/(K*mol)*K`

`Q_1==1116,9J=1.1169kJ`

Transition 2

The energy is given for the phase transition:

`Q_2=ΔH_(vap)*n=ΔH_(vap)*m/(Mr)=38.56*20/16 (kJ)/(mol)*g/(g/(mol))`

`Q_2=48.2kJ`

Transition 3

The energy is given as a temperature decrease `ΔT_3`:

`Q_3=n*c_(p(liq))*ΔT=m/(Mr)*c_(p(liq))*ΔT_3`

`Q_3=20/16*113*(78.4-(-16))g/(g/(mol))*J/(K*mol)*K`

`Q_3=13334J=13.334kJ`

Total energy

The total energy is:

`Q_(t ot)=Q_1+Q_2+Q_3=1.1169kJ+48.2kJ+13.334kJ`

`Q_(t ot)=62.6509kJ`

Water as medium

If the case was water, than the properties would change. Most important properties are boiling and melting points. Water boils at `100^oC` so no phase change would occur since the top temperature is `92^oC`. However, since `-16^oC` is lower than the melting point `0^oC`, water would undergo a phase change as a solid, so enthalpy of fusion should be calculated. Also, water would have different heat capacities. Finally, the molecular weight would be different `(Mr_(H_2O)=2*1+16=18g/(mol))` In short, the heat you would need to find would be equal to:

`Q_(t ot)=Q_1+Q_2+Q_3`

But their values would be equal to:

`Q_1=n*c_(p_(liq))*ΔT_1`
`(ΔT_1=92-0)`

`Q_2=ΔH_(fusion)*n`

`Q_3=n*c_(p_(solid))*ΔT_3`
`(ΔT_3=0-(-16))`