Question

Consider 1.5g of rubbing alcohol (c3h8o) placed on a 150.g block of aluminum at 25

c. if all of the rubbing alcohol evaporates at 25 c, what is the final temperature of the aluminum?

Answer 1

Answer : The final temperature of Aluminium is 17° C

Explanation :

The rubbing alcohol evaporates at 25 °C . That means it changes from liquid state to gaseous state. This process is known as Vaporization and the amount of heat it absorbs is known as enthalpy of vaporization.

Step 1 : Find moles of alcohol

We have 1.5 g of C₃H₈O.

Let us find the moles of alcohol.

`Mole = (Mass)/(MolarMass)`

Molar mass of rubbing alcohol is 60.1 g/mol

`mole = (1.5g)/(60.1g/mol) = 0.025 mol`

Step 2 : Find heat absorbed by given amount of alcohol

The enthalpy of vaporization of rubbing alcohol is 45 kJ/mol

The amount of heat absorbed by alcohol can be calculated as follows.

`q_(alcohol) = \bigtriangleup H_(vap) * moles`

`q_(alcohol) = (45kJ)/(mol) * 0.025mol = 1.12 kJ`

So during the process of evaporation, alcohol absorbs 1.12 kJ of heat.

This heat is taken from the aluminium.

Step 3 : Equate the q values for alcohol and aluminium

Therefore we have ,
`q_(alcohol) = - q_(Al)`

`q_(Al) = -1.12 kJ`

Step 4 : Find delta T for Al using the heat value found in the above step

Heat lost by Aluminium can be calculated using following equation

`q = m * C * \bigtriangleup T`

Here q is the amount of heat lost by Al. We need to convert q from kJ to J

`1.12 kJ * (1000J)/(1kJ) = 1120 J`

C is the specific heat of Al which is 0.9 J/gC

ΔT is the change in temperature of Aluminium.

m is the mass of Al which is 150 g.

Let us plug in the values and solve for ΔT

`-1120J = 150g * 0.9 J/gC * \bigtriangleup T`

`\bigtriangleup T= (-1120J)/(0.9J/gC * 150g)`

`\bigtriangleup T = -8.3 C`

Step 5 : Find final temperature using delta T

But ΔT is the difference in final temperature and initial temperature.

`\bigtriangleup T = T_(f) - T_(i)`

`-8.3 = T_(f) - 25 C`

`T_(f) = 25 C - 8.3 C`

`T_(f)= 16.7 C`

The final temperature of Aluminium is 17° C