The average fuel value of sugars is 17 kjmol a 2.0 l pitcher sweetened kool-aid contains 400 g sugar what the in kj 500-ml serving kool-aid?

$$n = \frac {mass} {molar \space mass}$$

The molar mass of sugar (sucrose) is 342.3 g/mol. Therefore, the number of moles of sugar in 400 g of sugar is:

$$n = \frac {400 \space g} {342.3 \space g/mol} = 1.17 mol$$

Step 2: Calculate the energy content of 1.17 mol of sugar.

The average fuel value of sugars is 17 kJ/mol. Therefore, the energy content of 1.17 mol of sugar is:

$$Energy = n \times \Delta H_{sugar}$$

$$Energy = (1.17 \space mol) \times (17 kJ \space mol^{−1}) = 20.0 \space kJ$$

Step 3: Calculate the energy content of a 500-ml serving of Kool-Aid.

Since a 2.0-liter pitcher of sweetened Kool-Aid contains 400 g of sugar, a 500-ml serving (1/4 of the pitcher) contains:

$$400 \space g \times \frac {1}{4} = 100 \space g \space sugar$$

The number of moles of sugar in 100 g of sugar is:

$$n = \frac {mass} {molar \space mass}$$

$$n = \frac {100 \space g} {342.3 \space g/mol} = 0.29 mol$$

Therefore, the energy content of a 500-ml serving of Kool-Aid is:

$$Energy = n \times \Delta H_{sugar}$$

$$Energy = (0.29 \space mol) \times (17 kJ \space mol^{−1}) = 5.0 \space kJ$$

Therefore, the energy content of a 500-ml serving of Kool-Aid is 5.0 kJ.