Final answer:
To calculate the heat evolved when 250.0 mL of methanol is burned, you need to convert from the given enthalpy of combustion per mole of methane to methanol and then calculate the heat evolved per mole of methanol. The answer is approximately 19.53 kJ.
Step-by-step explanation:
To calculate the heat evolved when 250.0 mL of methanol is burned, we need to use the enthalpy of combustion per mole of methanol. However, the enthalpy of combustion per mole of methane is given in the provided information, so we will need to convert from methane to methanol.
The balanced equation for the combustion of methane is: CH4 + 2O2 → CO2 + 2H2O.
The molar mass of methane is approximately 16 g/mol, while the molar mass of methanol is approximately 32 g/mol. Therefore, 2.5 g of methane is equivalent to 2.5/16 mol of methane. To convert this to moles of methanol, we need to consider that the balanced equation shows a 1:1 ratio between methane and methanol, so the number of moles of methanol is also 2.5/16.
Now, we can use the given information that 2.5 g of methane produces 125 kJ of heat. To find the heat evolved when 250.0 mL of methanol is burned, we need to calculate the heat evolved per mole of methanol, and then multiply it by the number of moles of methanol.
So, the heat evolved per mole of methane is 125 kJ/mol, and the number of moles of methanol is 2.5/16. Therefore, the heat evolved when 250.0 mL of methanol is burned would be (125 kJ/mol) * (2.5/16 mol) = 19.53 kJ.