Question

How much energy is released when 2.65kg of diethyl ether ((C2H5)2O) freezes? The heat of fusion for diethyl ether is 7.27 kJ/mol.

Answer 1

M=2.65kg=2650g
M=74g/mol

n = m/M = 2650g/74g/mol ≈ 35.81mol

Heat of fusion = 7.27kJ/mol

If            7.27kJ -------------  energy is in  --------------- 1mol
than           x      -------------  energy is in  --------------- 35.81mol

x = [35.81mol*7.27kJ]/1mol = 260.3387kJ

Answer 2

The amount of energy released when ${{\text{(}}{{\text{C}}_2}{{\text{H}}_5}{\text{)}}_2}{\text{O}}$ freezes is $\boxed{{\text{259}}{\text{.92 kJ}}}$.

Further explanation:

Heat of fusion measures the amount of energy needed to heat given mass of a solid to change its state into liquid. Also, it represents the amount of energy given up when a given mass of liquid solidifies.

When a substance converts from its phase from solid to liquid, the change in enthalpy $\left({\Delta H}}}\right)$ is positive, and if the substance transforms from liquid state to solid state then the change in enthalpy$\left({\Delta H}}}\right)$ is negative.

The expression to relate the energy released and heat of solidification is as follows:

${\text{Energy released}}={\text{n}}\times\left({{\Delta }}{{\text{H}}_{{\text{solidification}}}}}\right)$

Given mass of ${{\text{(}}{{\text{C}}_2}{{\text{H}}_5}{\text{)}}_2}{\text{O}}$ is 2.65 kg.

The conversion factor to convert mass in (g) from (kg) is written as follows:

${\text{1kg}}=1000\;{\text{g}}$

So, 2.65 kg of mass is converted into (g) as follows:

$\begin{aligned}{\text{Mass}}&=\,\left({2.65\;{\text{kg}}} \right)\left( {\frac{{{\text{1000}}\;{\text{g}}}}{{{\text{1}}\;{\text{k}}{\text{g}}}}}\right)\\&={\text{2650 g}}\\\end{aligned}$

Molar mass of ${{\text{(}}{{\text{C}}_2}{{\text{H}}_5}{\text{)}}_2}{\text{O}}$ is 74.12 g/mol.

The moles of ${{\text{(}}{{\text{C}}_2}{{\text{H}}_5}{\text{)}}_2}{\text{O}}$can be calculated as follows:

$\begin{aligned}{\text{number of moles }}&=\frac{{{\text{mass of (}}{{\text{C}}_2}{{\text{H}}_5}{{\text{)}}_2}{\text{O}}}}{{{\text{molar mass of (}}{{\text{C}}_2}{{\text{H}}_5}{{\text{)}}_2}{\text{O}}}}\\&=\frac{{{\text{2650 g}}}}{{{\text{74}}{\text{.12}}\;{\text{g/mol}}}}\\&=35.752{\text{ mol}}\\\end{aligned}$

The heat of fusion for diethyl ether${{\text{(}}{{\text{C}}_2}{{\text{H}}_5}{\text{)}}_2}{\text{O}}$is 7.27 kJ/mol and therefore the heat of solidification for diethyl ether${{\text{(}}{{\text{C}}_2}{{\text{H}}_5}{\text{)}}_2}{\text{O}}$is -7.27 kJ/mol.

The formula to calculate the amount of energy released is as follows:

${\text{Amount of energy}}={\text{number of moles}}\times{\Delta }}{{\text{H}}_{{\text{solidification}}}}{\text{ }}$        …… (1)

Substitute 35.752 mol for number of moles and -7.27 kJ/mol for ${\Delta }}{{\text{H}}_{{\text{solidification}}}}$ in the equation (1).

$\begin{aligned}{\text{Amount of energy}}&=\left({35.752\;{\text{mol}}}\right)\left({-7.27{\text{kJ/mol}}}\right)\\&=-259.92{\text{ kJ}}\\\end{aligned}$

Therefore, the amount of energy released is ${\mathbf{259}}{\mathbf{.92 kJ}}$.

Learn more:

1. Determine the coefficients are needed to balance the equation for the complete combustion of methane? brainly.com/question/1971314

2. Determine the energy required to break the hydrogen bond?brainly.com/question/10278354

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Thermodynamics

Keywords: Heat of fusion, number of moles, enthalpy, enthalpy change, released, absorbed, 259.91 kJ, 7.27kJ/mol, and 35.752 mol.