0.92g of ethanol raised the temperature of 100g of water from 298K to 312.3K when...

Explanation

To determine the heat of combustion of ethanol, we first need to find the amount of heat released by burning 0.92g of ethanol, and then convert that to kJ/mol.

First, we can find the amount of heat released using the formula:

\(\Delta Q = mc\Delta T\)

Where \(\Delta Q\) is the heat released, \(m\) is the mass of water, \(c\) is the specific heat capacity of water, and \(\Delta T\) is the change in temperature.

Using the given values: \(m = 100g\), \(c = 4.2 Jg^{-1}K^{-1}\), and \(\Delta T = 312.3K - 298K = 14.3K\), we can calculate the heat released:

\(\Delta Q = (100g)(4.2 Jg^{-1}K^{-1})(14.3K) = 6006 J\)

Now we need to determine the number of moles of ethanol in 0.92g. The molecular formula of ethanol is \(C_2H_5OH\), so its molar mass is:

\(2(C) + 6(H) + 1(O) + 1(H) = 2(12) + 6(1) + 16 + 1 = 46 g/mol\)

To find the number of moles, we divide the mass by the molar mass:

\(0.92g / 46 g/mol = 0.02 mol\)

Finally, we can find the heat of combustion per mole of ethanol by dividing the heat released by the number of moles:

\(\frac{6006 J}{0.02 mol} = 300300 J/mol \approx 300 KJ/mol\)

Since the heat of combustion is exothermic, the value should be negative. Therefore, the correct answer is:

Option C: -300KJ mol\(^{-1}\)