Question

What amount of heat (in kJ) is required to convert 10.1 g of an unknown solid (MM = 67.44 g/mol) at -15.4 °C to a liquid at 42.7 °C? (heat capacity of solid = 1.95 J/g･°C; heat capacity of liquid = 1.18 J/g･°C; ∆Hfus = 5.72 kJ/mol; Tf = 28.3°C)

Answer 1

We know that , no. of moles = Mass / Molar mass

No. of moles of unknown solid = 10.1 g / ( 67.44 g /mol ) = 0.1498 mol

Heating of unknown solid from - 15.4 ⁰ C to 42.7 ⁰ C involves following steps.

1) Heating of unknown solid from - 15.4 ⁰ C to 28.3 ⁰ C

2) Melting of unknown solid.

3) Heating of liquid from 28.3 ⁰ C to 42.7 ⁰ C.

We know that, heat required to change temperature of material is given as, q = m x C x T

Where, q is a heat absorbed or given out by material, m is a mass of material , C is a specific heat capacity of material, T is a change in temperature of material.

heat required to change temperature of unknown solid from - 15.4 ⁰ C to 28.3 ⁰ C (q) = 10.1 g 1.95 J / g ⁰ C ( 28.3 ⁰ C - ( - 15.4 ⁰ C) )

q = 10.1 g 1.95 J / g ⁰ C ( 43.7 ⁰ C)

q = 860.67 J

Heat required to change in phase is given as, q= n H

Heat required to melt solid = n H fusion

Heat required to melt unknown solid = 0.1498 mol 5.72 k J / mol = 0.8568 k J = 856.8 J

Heat required to change temperature of unknown liquid from 28.3 ⁰ C to 42.7 ⁰ C (q) = 10.1 g 1.18 J / g ⁰ C ( 42.7 ⁰ C - ( 28.3 ⁰ C) )

q = 10.1 g 1.18 J / g ⁰ C 14.4 ⁰ C

q = 171.6 J

Hence total heat required to Heat unknown solid from - 15.4 ⁰ C to 42.7 ⁰ C = 860.67 J + 856.8 J + 171.6 J

total heat required to Heat unknown solid from - 15.4 ⁰ C to 42.7 ⁰ C = 1889 J

ANSWER : 1889 J