Question

Which is the least expensive source of enery in kilojoules per dollar, a box of breakfast cereal that weighs 32 ounces and costs $4.23, or a liter of isooctane (Density 0.6916 g/mL) that costs $0.45? Compare the nutritionl value of the cereal with the heat produced by combustion of the isooctane under standard conditions. A 1.0 -ounce serving of the cereal provides 130 calories

Answer 1

Step-by-step explanation:

1) 1.0 ounce serving of the cereal provides 130 calories.

Then 32 ounces of breakfast cereal will provide :

=
`32* 130 cal =4160 cal`

Cost of 32 ounces of cereal = $4.23

Energy from cereal with respect to dollar:

`(4160 cal)/(\$4.23)=983.45 cal/\$`

2) Density of iso-octane = d = 0.6916 g/mL

Mass of the iso-octane = m

Volume of iso-octane = V = 1 L

`m=d* V=0.6916 g/mL* 1L = 0.6916 g`

Moles of isooctane =
`(0.6916 g)/(114 g/mol)=0.006066 mol`

Heat of combustion of isooctane = 5450 kJ/mol

Heat released on combustion of 0.006066 moles of isooctane:

`0.006066 mol* 5450 kJ/mol=33.0633 kJ`

1 kJ = 239.006 cal

`33.0633 kJ=33.0633* 239.006 cal=7,904.23 cal`

Cost of 0.6916 g or 1 L of isooctane = $0.45

Energy from isooctane with respect to dollar:

`(7,904.23 cal)/(\$0.45)=17,564.95 cal/\$`

We can generate large amount of energy by combustion of isooctane than the energy we getting from cereal:

17,564.95 cal/$ > 983.45 cal/$

But isooctane is an indigestible by human body so, it will be good to have cereals.