What mass of ethanol #C_2H_5OH(l)# must be burned to supply 500.0 kJ of heat?

The enthalpy of combustion of ethanol is widely quoted in the public domain and is 1360 kJ/mol.

Therefore in order to supply 500 kJ of heat you would need to burn (500/1360) = 0.368 moles of ethanol.

The molecular weight of ethanol is 46.07 g/mol, so the mass required would be 0.368 x 46.07 = 16.95 g.

This is based on 100% ethanol - in practise ethanol will have a certain water content, and this of course does not burn or generate heat. If you have a water content of, say, 2%, then the mass of ethanol required would need to be slightly increased to compensate for this.

To find the mass of ethanol (C2H5OH) that must be burned to supply 500.0 kJ of heat, we need to use the molar enthalpy of combustion (ΔHc) for ethanol, which is the amount of heat released when one mole of ethanol is burned completely.

The molar enthalpy of combustion for ethanol is approximately -1367 kJ/mol.

We can use the following equation to find the mass of ethanol:

[ \text{Mass of ethanol} = \frac{\text{Heat required}}{\text{Molar enthalpy of combustion}} ]

Given:

• Heat required = 500.0 kJ
• Molar enthalpy of combustion for ethanol = -1367 kJ/mol

Substituting the values into the equation:

[ \text{Mass of ethanol} = \frac{500.0 , \text{kJ}}{-1367 , \text{kJ/mol}} ]

[ \text{Mass of ethanol} \approx -0.366 , \text{mol} ]

Since mass cannot be negative, we take the absolute value:

[ \text{Mass of ethanol} \approx 0.366 , \text{mol} ]

Now, we need to convert moles to grams:

[ \text{Molar mass of ethanol (C2H5OH)} = 46.07 , \text{g/mol} ]

[ \text{Mass of ethanol} = 0.366 , \text{mol} \times 46.07 , \text{g/mol} ]

[ \text{Mass of ethanol} \approx 16.86 , \text{g} ]

So, approximately 16.86 grams of ethanol must be burned to supply 500.0 kJ of heat.