To determine the enthalpy of vaporization of [tex]\( \text{CH}_3\text{OH} \)[/tex] (methanol), follow these steps:
1. Identify and list the given data:
- The amount of heat needed to vaporize methanol, [tex]\( Q \)[/tex], is 14.5 kJ.
- The number of moles of methanol, [tex]\( n \)[/tex], is 0.500 moles.
2. Recall the formula for the enthalpy of vaporization ([tex]\( \Delta H_{\text{vap}} \)[/tex]):
[tex]\[
\Delta H_{\text{vap}} = \frac{Q}{n}
\][/tex]
where:
- [tex]\( \Delta H_{\text{vap}} \)[/tex] is the enthalpy of vaporization in kJ/mol.
- [tex]\( Q \)[/tex] is the heat required in kJ.
- [tex]\( n \)[/tex] is the number of moles of the substance.
3. Substitute the given values into the formula:
[tex]\[
\Delta H_{\text{vap}} = \frac{14.5 \text{ kJ}}{0.500 \text{ moles}}
\][/tex]
4. Perform the division to find the enthalpy of vaporization:
[tex]\[
\Delta H_{\text{vap}} = \frac{14.5}{0.500} = 29.0 \text{ kJ/mol}
\][/tex]
Therefore, the enthalpy of vaporization of [tex]\( \text{CH}_3\text{OH} \)[/tex] is [tex]\( 29.0 \text{ kJ/mol} \)[/tex].
