Question

A researcher studying the nutritional value of a new candy places a 3.60 g sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.79 ∘ C. If the heat capacity of the calorimeter is 29.60 kJ ⋅ K − 1 , how many nutritional Calories are there per gram of the candy?

Answer 1

Answer : The nutritional Calories present per gram of the candy are 5.48 cal/g.

Explanation :

First we have to calculate the heat given off by the combustion of this candy.

`q=c* \Delta T`

where,

q = heat released by the reaction = ?

c = specific heat of calorimeter =
`29.60kJ/K`

`\Delta T` = change in temperature =
`2.79^oC=2.79K` (Change in kelvin temperature = Change in Celsius temperature)

Now put all the given values in the above formula, we get:

`q=(29.60kJ/K)* (2.79K)`

`q=82.58kJ`

Now we have to convert heat from kJ to cal.

Conversion used : 1 cal = 4.186 kJ

As, 4.186 kJ heat = 1 cal

So, 84.58 kJ heat =
`(82.58kJ)/(4.186kJ)* 1cal=19.73cal`

Now we have to calculate the nutritional Calories are there per gram of the candy.

Amount of nutritional Calories =
`(19.73cal)/(3.60g)=5.48cal/g`

Therefore, the nutritional Calories present per gram of the candy are 5.48 cal/g.