4. A cube of sugar (C6H12O)6 has a density of 1.58 g/cm3. If the cube contains 4.706 x 1023 carbon atoms, what is the length of each side of the cube in centimeters?
The molar mass of C6H12O)6 is 292 g/mol.
Answers
The side of the cube is 11.8 cm
Explanation:
Given:
A cube of sugar containing 4.076 × 10²³ carbon atoms has density = 1.58 g/cc
To find out:
Length of the sides of the cube
Solution:
Given molar mass of sugar = 292 g/mole
i.e. 1 mole of sugar will have weight = 292 grams
1 mole of sugar will contain = 6.023 × 10²³ molecules of sugar
and 1 sugar molecules contains = 6 carbon atoms
Therefore, 1 mole of sugar will contain = 6 × 6.023 × 10²³ carbon atoms
Thus, 4.076 × 10²³ carbon atoms will be in = (6 × 6.023 × 10²³)/(4.076 × 10²³)
= 8.87 moles
Weight of the sugar cube = 8.87 × 292 = 2590.04 gram
Volume of sugar = weight/density
= 2590.04/1.58
= 1639.27 cc
Therefore, sides of sugar cube = ∛(1639.27) = 11.8 cm
Hope this answer is helpful.
Know More:
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