Question

Calculate the amount of heat needed to boil 120.g of acetic acid (HCH3CO2), beginning from a temperature of 16.7°C.

Answer 1

Answer:

The total amount of heat needed = 72.2116  kJ

Explanation:

Given that ;

the mass of acetic acid = 120.0 g

The initial temperature $T_1$ = 16.7 °C  = (16.7 + 273.15 ) K = 298.85 K

The standard molar mass of acetic acid = 60.052  g/mol

Thus ; we can determine the number of moles of acetic acid;

number of moles of acetic acid = mass of acetic acid/ molar mass of acetic acid

number of moles of acetic acid = 120.0 g/ 60.052 g/mol

number of moles of acetic acid =  1.998 moles

For acetic acid:

The standard boiling point  $T_2$ = 118.1 °C = ( 118.1 + 273.15 ) K = 391.25 K

The enthalpy of vaporization of acetic acid $\Delta H_{vap}$ = 23.7 kJ/mol

The heat capacity of acetic acid   c = 2.043  J/g.K

The change in temperature Δ T = $T_2 - T_1$

Δ T = (391.25 - 289.85)K

Δ T = 101.4 K

The amount of heat needed to bring the liquid acetic acid at 16.7°C to its boiling point is ;

q = mcΔT

From our values above;

q = 120 g ×  2.043  J/g.K × 101.4 K

q = 24859.2  J

q = 24859 /1000 kJ

q = 24.859 kJ

we have earlier calculated our number of moles o f acetic acid to be 1.998 moles;

Thus;

The needed amount of heat = $\Delta_{vap} *numbers \ of \ moles$

The needed amount of heat = $23.7 \ kJ/mol * 1.998 \ moles$

The needed amount of heat = 47.3526 kJ

Hence;

The total amount of heat needed = 24.859 kJ + 47.3526 kJ

The total amount of heat needed = 72.2116  kJ