Question

What amount of heat (in kJ) is required to convert 19.8 g of an unknown liquid (MM = 83.21 g/mol) at 19.2 °C to a gas at 93.5 °C? (specific heat capacity of liquid = 1.58 J/g･°C; specific heat capacity of gas = 0.932 J/g･°C; ∆Hvap = 22.5 kJ/mol; normal boiling point, Tb = 57.3°C)

Answer 1

The total energy required to convert the unknown liquid to gas at the given temperature is 7.215 kJ.

The given parameters;

• mass of the unknown liquid, m = 19.8 g
• molar mass of liquid = 83.21 g/mol
• initial temperature of the liquid, = 19.2 °C
• boiling point temperature of the liquid, = 57.3°C
• final temperature of the liquid = 93.5 °C

The total heat required to convert the liquid to gas is calculated as follows;

H = Heat to raise to boiling temp. + Heat to vaporize the liquid + Heat of gas vapor

The heat required to raise the temperature of the liquid to boiling point;

$H_1 = mc\Delta t\\\\H_1 = 19.8 \times 1.58 \times (57.3 - 19.2)\\\\H_1 = 1,191.92 \ J\\\\H_1 = 1.1919 \ kJ$

The number of moles of the liquid is calculated as;

$moles= \frac{19.8 \ g}{83.21 \ g/mol} = 0.238 \ mol$

The heat required to vaporize the liquid;

$H_2 = n H_{vap}\\\\H _2 = 0.238 \times 22.5\\\\H_2 = 5.355\ kJ$

The heat of the gas vapor is calculated as;

$H_3 = mc_g \Delta t\\\\H_3 = 19.8 \times 0.932 \times (93.5- 57.3)\\\\H_3 = 668.02 \ J\\\\H_3 = 0.668 \ kJ$

The total energy required to convert the unknown liquid to gas at the given temperature is calculated as;

$H_{total} = 1.1919 \ kJ \ + \ 5.355 \ kJ \ + \ 0.668 \ kJ\\\\H_{total} = 7.215 \ kJ$

Thus, the total energy required to convert the unknown liquid to gas at the given temperature is 7.215 kJ.

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