General Chemistry Principles, Patterns, and Applications, 2011

Now suppose you wish to report the number of kilocalories of energy contained in a 7.00 oz piece of
chocolate in units of kilojoules per gram. To obtain an answer in kilojoules, we must convert 7.00 oz to
grams and kilocalories to kilojoules. Food reported to contain a value in Calories actually contains that
same value in kilocalories. If the chocolate wrapper lists the caloric content as 120 Calories, the chocolate
contains 120 kcal of energy. If we choose to use multiple steps to obtain our answer, we can begin with the
conversion of kilocalories to kilojoules:
120 kcal9(1000 calkcal) \
(4.184 J1 cal) / (1 kJ1000 J) = 502 kJ
We next convert the 7.00 oz of chocolate to grams:
7.00 oz(28.35 g1 oz) = 199 g
The number of kilojoules per gram is therefore
502 kJ199 g = 2.52 kJ / g
The discrepancy between the two answers is attributable to rounding to the correct number of significant
figures for each step when carrying out the calculation in a stepwise manner. Recall that all digits in the
calculator should be carried forward when carrying out a calculation using multiple steps. In this problem,
we first converted kilocalories to kilojoules and then converted ounces to grams. Skill Builder ES2 allows
you to practice making multiple conversions between units in a single step.
S K I L L BUILDER ES2
a. Write a single equation to show how to convert cm/min to km/h; cal/oz to J/g;
lb/in. 2 to kg/m 2 ; and °C/s to K/h.
b. How many Calories are contained in an 8.0 oz serving of green beans if their fuel value is
1.5 kJ/g?
c. Gasoline has a fuel value of 48 kJ/g. How much energy in joules can be obtained by filling
an automobile’s 16.3 gal tank with gasoline, assuming gasoline has a density of 0.70
g/mL?
Solution:
a. Our goal is to convert 1.5 kJ/g to Calories in 8 oz:
b. Our goal is to use the energy content, 48 kJ/g, and the density, 0.70 g/mL, to obtain the number
of joules in 16.3 gal of gasoline:
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