Questions: Calculate the heat, in kJ, that would be involved in condensing 15.8 g of CH3OH. (ΔHvap=38.0 kJ / mol)

Solution Steps

The chemical formula for methanol is \(\mathrm{CH}_3\mathrm{OH}\). To find the molar mass, we sum the atomic masses of all the atoms in the formula:

• Carbon (C): \(1 \times 12.01 \, \text{g/mol} = 12.01 \, \text{g/mol}\)
• Hydrogen (H): \(4 \times 1.008 \, \text{g/mol} = 4.032 \, \text{g/mol}\)
• Oxygen (O): \(1 \times 16.00 \, \text{g/mol} = 16.00 \, \text{g/mol}\)

Adding these together gives the molar mass of methanol:

\[ \text{Molar mass of } \mathrm{CH}_3\mathrm{OH} = 12.01 + 4.032 + 16.00 = 32.042 \, \text{g/mol} \]

To find the number of moles of methanol in 15.8 g, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

\[ \text{Number of moles} = \frac{15.8 \, \text{g}}{32.042 \, \text{g/mol}} \approx 0.4929 \, \text{mol} \]

The heat involved in condensing methanol is given by the formula:

\[ q = n \times \Delta \mathrm{H}_{\text{vap}} \]

where \(n\) is the number of moles and \(\Delta \mathrm{H}_{\text{vap}}\) is the enthalpy of vaporization.

\[ q = 0.4929 \, \text{mol} \times 38.0 \, \text{kJ/mol} = 18.731 \, \text{kJ} \]

Final Answer