To determine which compound will experience the largest change in temperature during evaporation, we look at the enthalpy of evaporation values for each compound. The enthalpy of evaporation ([tex]\(\Delta H_{\text{evap}}\)[/tex]) indicates the amount of energy required to convert a liquid into a gas. Compounds with larger (more negative) enthalpy values will generally undergo a more significant temperature change because more energy is involved in the phase transition process.
Here are the provided enthalpy of evaporation values for the given compounds:
1. Methane ([tex]\(CH_4\)[/tex]) has an enthalpy of evaporation of -84900 J/mol.
2. Propane ([tex]\(CH_3CH_2CH_3\)[/tex]) has an enthalpy of evaporation of -222000 J/mol.
3. Pentane ([tex]\(CH_3CH_2CH_2CH_2CH_3\)[/tex]) has an enthalpy of evaporation of -275000 J/mol.
We can compare these values to find which compound will experience the largest temperature change. The compound with the most negative enthalpy change during evaporation will undergo the greatest temperature change because it requires the most energy for the phase change.
By comparing the enthalpy values:
- Methane: -84900 J/mol
- Propane: -222000 J/mol
- Pentane: -275000 J/mol
Pentane ([tex]\(CH_3CH_2CH_2CH_2CH_3\)[/tex]) has the most negative enthalpy value of -275000 J/mol. Therefore, pentane will experience the largest change in temperature during evaporation.
Thus, the compound that will experience the largest change in temperature during evaporation for 30 seconds at room temperature is [tex]\( \mathbf{CH_3CH_2CH_2CH_2CH_3} \)[/tex] (pentane).
