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Chapter 17: Problem 44

The enthalpy of vaporization of ethanol is 38.7 kJ/mol at its boiling point \(\left(78^{\circ} \mathrm{C}\right) .\) Determine $\Delta S_{\mathrm{sys}}, \Delta S_{\mathrm{surr}},\( and \)\Delta S_{\mathrm{univ}}$ when 1.00 mole of ethanol is vaporized at \(78^{\circ} \mathrm{C}\) and 1.00 atm.

Short Answer

Expert verified
In conclusion, when 1 mole of ethanol is vaporized at 78°C and 1 atm, the change in entropy of the system (ΔS_sys) is \(110.16 J/mol\cdot K\), the change in entropy of the surroundings (ΔS_surr) is \(-110.16 J/mol\cdot K\), and the change in entropy of the universe (ΔS_univ) is \(0 J/mol\cdot K\).

Step by step solution

01

Convert enthalpy of vaporization to J/mol

We are given that the enthalpy of vaporization of ethanol is 38.7 kJ/mol. To convert this value to J/mol, we will multiply by 1000: 38.7 kJ/mol * 1000 J/kJ = 38,700 J/mol Now, the enthalpy of vaporization of ethanol is 38,700 J/mol.
02

Calculate ΔS_sys

To calculate the change in entropy of the system (ΔS_sys), we will use the formula: ΔS_sys = ΔHvap/T First, we need to convert the boiling point temperature from Celsius to Kelvin by adding 273.15: T = 78°C + 273.15 = 351.15 K Now, we can calculate ΔS_sys: ΔS_sys= (38,700 J/mol) / (351.15 K)= 110.16 J/mol·K The change in entropy of the system is 110.16 J/mol·K.
03

Calculate ΔS_surr

To calculate the change in entropy of the surroundings (ΔS_surr), we will use the following formula: ΔS_surr = -ΔHvap/T Using the previously calculated values for ΔHvap (38,700 J/mol) and T(351.15 K): ΔS_surr = -(38,700 J/mol) / (351.15 K) = -110.16 J/mol·K The change in entropy of the surroundings is -110.16 J/mol·K.
04

Calculate ΔS_univ

To calculate the change in entropy of the universe (ΔS_univ), we will add ΔS_sys and ΔS_surr: ΔS_univ = ΔS_sys + ΔS_surr = 110.16 J/mol·K + (-110.16 J/mol·K) = 0 J/mol·K The change in entropy of the universe is 0 J/mol·K. In conclusion, the change in entropy of the system (ΔS_sys) is 110.16 J/mol·K, the change in entropy of the surroundings (ΔS_surr) is -110.16 J/mol·K, and the change in entropy of the universe (ΔS_univ) is 0 J/mol·K when 1 mole of ethanol is vaporized at 78°C and 1 atm.

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Most popular questions from this chapter

Choose the substance with the larger positional probability in each case. a. 1 mole of \(\mathrm{H}_{2}\) (at \(\mathrm{STP} )\) or 1 mole of $\mathrm{H}_{2}\left(\text { at } 100^{\circ} \mathrm{C}, 0.5 \mathrm{atm}\right)$ b. 1 mole of \(\mathrm{N}_{2}(\text { at } \mathrm{STP})\) or 1 mole of \(\mathrm{N}_{2}(\text { at } 100 \mathrm{K}, 2.0 \mathrm{atm})\) c. 1 mole of \(\mathrm{H}_{2} \mathrm{O}(s)\) (at \(0^{\circ} \mathrm{C} )\) or 1 \(\mathrm{mole}\) of $\mathrm{H}_{2} \mathrm{O}(l)\left(\mathrm{at} 20^{\circ} \mathrm{C}\right)$

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Consider the following energy levels, each capable of holding two particles: $$\begin{array}{l}{E=2 \mathrm{kJ}} \\ {E=1 \mathrm{kJ}} \\ {E=0 \quad \underline{X X}}\end{array}$$ Draw all the possible arrangements of the two identical particles (represented by X) in the three energy levels. What total energy is most likely, that is, occurs the greatest number of times? Assume that the particles are indistinguishable from each other.
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