Question

A mass m = 0.055 kg of benzene vapor at its boiling point of 80.1 °C is to be condensed by mixing the vapor with water at 36 °C. What is the minimum mass of water required to condense all of the benzene vapor? Assume that the mixing and condensation take place in a perfectly insulating container.

Answer 1

Answer:

Mass of water that is required to condense benzene vapor is 0.1158 kg.

Explanation:

The minimum amount of energy that must be removed from the benzene is its latent heat of vaporization. The latent heat of vaporization for benzene is 390 kJ/kg $\left(L_{v}\right)$ and mass of the benzene is 0.055 kg (m). Therefore for the phase change of benzene vapor to benzene liquid, benzene lost its energy is given by $m \times L_{v}$:                                

(0.055 kg) × (390 kJ/kg) = 21.45 kJ

Loss of energy by benzene is 21.45 kJ.

$\text { Boiling point of the benzene vapor is } 80.1^{\circ} \mathrm{C}$

$\text { Benzene condensed to a temperature of } 36^{\circ} \mathrm{C}$

Using a specific heat for water of 4.2 kJ/kg k

Energy lost by “benzene” = Energy gained by “water”  

21.45 kJ = (mass of substance)(specific heat)(change in temperature)

21.45 kJ = m × c ×∆T

m = mass of a substance (water) (kg)

c = specific heat of water (units J/kg K) = 4.2 kJ/kg k

∆T = change in temperature (Kelvins, K)

∆T = 80.1 – 36

∆T = 44.1

m × 4.2 × 44.1 = 21.45 KJ

m × 185.22 = 21.45 KJ

$\mathrm{m}=\frac{21.45}{185.22}$

m = 0.1158 kg

Mass of water that is required to condense benzene vapor is 0.1158 kg.

Answer 2

The minimum mass of water required to condense all of the Benzene vapor is : 0.1158 kg

Determine the minimum mass of water required

mass of Benzene vapor = 0.055 kg

Temperature of Benzene =  80.1 °C

Temperature of water =  36 °C

First step : Calculate energy lost by Benzene

energy lost = mass of Benzene * latent heat of vaporization of Benzene

                   = 0.0555 * 390 kJ/kg

                   = 21.45 KJ

Next step : Determine the minimum mass of water required to condense

Energy lost by Benzene = Energy gained by water

        21.45 KJ = mass of water * specific heat of water * ΔT

        21.45 KJ = m * 4.2 KJ/kG K * ( 80.1 - 36 )

Therefore Minimum mass ( m ) = 21.45 / ( 185.22 )

                                                   = 0.1158 Kg

Hence we can conclude that The minimum mass of water required to condense all of the Benzene vapor is : 0.1158 kg.

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