Respuesta :
Answer:
First question
[tex]Q = 36826 \ J[/tex]
Second question
[tex]Q = 52299.7 \ J[/tex]
Explanation:
From the question we are told that
The melting point of Ethanol is [tex]T_m = -114 ^oC[/tex]
The boiling point of Ethanol is [tex]T_b = 78^ oC[/tex]
The enthalpy of fusion of Ethanol is [tex]F = 5.02 \ kJ / mol = 5.02 *10^{3}\ kJ / mol[/tex]
The enthalpy of vaporization of Ethanol is [tex]L = 38.56 \ kJ / mol = 38.56 *10^{3} \ J / mol[/tex]
The specific heat of solid Ethanol is [tex]c_e = 0.97 \ J/ g \cdot K[/tex]
The specific heat of liquid Ethanol is [tex]c_l = 2.3 \ J / g \cdot K[/tex]
The mass of the Ethanol given is [tex]m = 35.0 \ g[/tex]
Considering the first question
The initial temperature is [tex]T_i = 27^oC[/tex]
The final temperature is [tex]T_f = 120^oC[/tex]
Generally the heat required too raise the Ethanol to its boiling point is mathematically represented as
[tex]Q_1 = m * c_l * (T_b - T_i)[/tex]
=> [tex]Q_1 = 35.0 * 2.3 * ( 78 - 27)[/tex]
=> [tex]Q_1 =4106 \ J[/tex]
Genially the number of moles of Ethanol given is mathematically represented as
[tex]n = \frac{m}{Z}[/tex]
Here Z is the molar mass of Ethanol with value [tex]Z = 46 g/mol[/tex]
So
[tex]n = \frac{35}{46 }[/tex]
=> [tex]n = 0.7609 \ mol[/tex]
Generally the heat of vaporization of the Ethanol is mathematically represented as
[tex]Q_2 = n * L[/tex]
=> [tex]Q_2 =0.7809 * 38.56 * 10^{3}[/tex]
=> [tex]Q_2 =29339 \ J[/tex]
Generally the heat required too raise the Ethanol from its boiling point to [tex]T_f[/tex] is mathematically represented as
[tex]Q_3 = m * c_l * (T_f - T_b)[/tex]
=> [tex]Q_3 = 35 * 2.3 * (120 - 78 )[/tex]
=> [tex]Q_3 = 3381 \ J[/tex]
Generally the total heat required is
[tex]Q = Q_1 + Q_2 + Q_3[/tex]
=> [tex]Q = 4106 + 29339 + 3381[/tex]
=> [tex]Q = 36826 \ J[/tex]
Considering the second question
The initial temperature is [tex]T_i = -120^oC[/tex]
The final temperature is [tex]T_f = 120^oC[/tex]
Generally the heat required too raise the Ethanol to its melting point is mathematically represented as
[tex]Q_1 = m * c_e * (T_m - T_i)[/tex]
=> [tex]Q_1 = 35.0 * 0.97 * ( -114 - (- 120) )[/tex]
=> [tex]Q_1 = 203.7 \ J[/tex]
Generally the heat of fusion of the Ethanol is mathematically represented as
[tex]Q_2 = n * F[/tex]
=> [tex]Q_2 =0.7809 * 5.02 *10^{3}[/tex]
=> [tex]Q_2 =3920 \ J[/tex]
Generally the heat required too raise the Ethanol to its boiling point is mathematically represented as
[tex]Q_3 = m * c_l * (T_b - T_m)[/tex]
=> [tex]Q_3 = 35.0 * 2.3 * ( 78 - (- 114) )[/tex]
=> [tex]Q_3 =15456 \ J[/tex]
Generally the heat of vaporization of the Ethanol is mathematically represented as
[tex]Q_4 = n * L[/tex]
=> [tex]Q_4 =0.7809 * 38.56 * 10^{3}[/tex]
=> [tex]Q_4 =29339 \ J[/tex]
Generally the heat required too raise the Ethanol from its boiling point to [tex]T_f[/tex] is mathematically represented as
[tex]Q_5 = m * c_l * (T_f - T_b)[/tex]
=> [tex]Q_5 = 35 * 2.3 * (120 - 78 )[/tex]
=> [tex]Q_5 = 3381 \ J[/tex]
Generally the total heat required is
[tex]Q = Q_1 + Q_2 + Q_3+Q_4 + Q_5[/tex]
=> [tex]Q = 203.7 + 3920 + 15456 +29339+3381[/tex]
=> [tex]Q = 52299.7 \ J[/tex]
