13.A student mixed 5.00 g (0.0594 mol) of solid cyclohexane, C6H12, (84.18 g mol–1) at its melting temperature of 6.6°C with 50.0 g (0.594 mol) of liquid cyclohexane at 50.0°C in an open yet insulated container. After thermal equilibrium was established, the temperature of the mixture was 44.5°C. The specific heat capacity of liquid cyclohexane is 1.809 J g–1K–1, and is assumed to be constant over the temperature interval.From this information, what is the molar enthalpy of fusion, ΔHfusion, of cyclohexane?

The molar enthalpy of fusion, ΔHfusion, of cyclohexane is 6.9 kJ/mol.

Well, well, well! It seems like we have a melting mess on our hands. Let's put on our thermodynamic clown nose and tackle this question!

To find the molar enthalpy of fusion (ΔHfusion), we need to calculate the amount of heat absorbed or released during the phase change from solid to liquid. Are you ready to dance with some numbers? Great!

First, we need to determine the heat absorbed by the solid cyclohexane during the phase change, which can be calculated using the formula:

q = msΔT

Where q is the heat absorbed or released, m is the mass, s is the specific heat capacity, and ΔT is the change in temperature.

The heat absorbed by the solid cyclohexane is equal to the heat released by the liquid cyclohexane:

q solid = -q liquid

Now, let's calculate the heat absorbed by the solid:

q solid = msΔT
= (5.00 g)(1.809 J g–1K–1)(44.5°C - 6.6°C)

And the heat released by the liquid:

q liquid = msΔT
= (50.0 g)(1.809 J g–1K–1)(44.5°C - 50.0°C)

Since q solid = -q liquid, we can equate the two equations:

(5.00 g)(1.809 J g–1K–1)(44.5°C - 6.6°C) = -(50.0 g)(1.809 J g–1K–1)(44.5°C - 50.0°C)

Now, we can solve for the molar enthalpy of fusion, ΔHfusion:

ΔHfusion = q solid / mol solid
= [ (5.00 g)(1.809 J g–1K–1)(44.5°C - 6.6°C) ] / 0.0594 mol

Now, pull out your trusty calculator and crunch those numbers!

And there you have it, my friend! The molar enthalpy of fusion, ΔHfusion, of cyclohexane. I hope this answer melted away any confusion you had!

To calculate the molar enthalpy of fusion (ΔHfusion) of cyclohexane, we can use the following equation:

ΔHfusion = Qfusion / moles of cyclohexane

First, let's calculate the heat gained by the solid cyclohexane during its fusion (Qfusion):

Qfusion = mass of solid cyclohexane * specific heat capacity of liquid cyclohexane * change in temperature

Qfusion = 5.00 g * 1.809 J g–1K–1 * (44.5°C - 6.6°C)

Now, let's calculate the moles of cyclohexane involved in the fusion (moles of cyclohexane):

moles of cyclohexane = mass of solid cyclohexane / molar mass of cyclohexane

moles of cyclohexane = 5.00 g / 84.18 g mol–1

Finally, let's substitute these values into the equation to calculate ΔHfusion:

ΔHfusion = Qfusion / moles of cyclohexane

ΔHfusion = (5.00 g * 1.809 J g–1K–1 * (44.5°C - 6.6°C)) / (5.00 g / 84.18 g mol–1)

After performing the calculation, the molar enthalpy of fusion (ΔHfusion) of cyclohexane will be obtained.

To determine the molar enthalpy of fusion (ΔHfusion) of cyclohexane, you can use the equation for heat transfer:

q = (m1 * Cp1 * ΔT1) + (m2 * Cp2 * ΔT2) + ΔHfusion

Where:
q is the total heat transferred (in joules)
m1 and m2 are the masses of the solid and liquid cyclohexane respectively (in grams)
Cp1 and Cp2 are the specific heat capacities of the solid and liquid cyclohexane respectively (in J g–1K–1)
ΔT1 and ΔT2 are the temperature changes of the solid and liquid cyclohexane respectively (in Kelvin)
ΔHfusion is the molar enthalpy of fusion of cyclohexane (in joules per mole)

Let's substitute the given values into the equation:

q = (5.00 g * 1.809 J g–1K–1 * (44.5°C - 6.6°C)) + (50.0 g * 1.809 J g–1K–1 * (44.5°C - 50.0°C)) + ΔHfusion

Simplifying the equation:

q = 590.77 J + (-536.45 J) + ΔHfusion
q ≈ 54.32 J + ΔHfusion

Since the system is open, the total heat transferred (q) is zero. Therefore, we can set q equal to zero:

0 = 54.32 J + ΔHfusion

Rearranging the equation to isolate ΔHfusion:

ΔHfusion = -54.32 J

The molar enthalpy of fusion (ΔHfusion) for cyclohexane is approximately -54.32 J/mol.