A sugar crystal contains approximately 1.4×1017 sucrose (C12H22O11) molecules. What is its mass in milligrams? Express using 2 sig figs

From the periodic table:

mass of carbon = 12 grams

mass of hydrogen = 1 grams

mass of oxygen = 16 grams

molar mass of surcose = 12(12) + 22(1) + 11(16) = 342 grams

number of molecules = number of moles x Avogadro's number

number of moles = number of molecules / Avogadro's number

number of moles = (2.2x10^17) / (6.02x10^23) = 3.6544 x 10^-7 moles

number of moles = mass / molar mass

mass = number of moles x molar mass

= 1.7 x 10^17/6.022 x 10^23.

Our process would be just turning the molecules of sucrose to the moles by dividing using Avogadro's number (6.02 x 10^23), which will give us the moles we need. In order to find the mass of the sucrose, you have to multiply the moles by the molar mass of sucrose in order to find the mass, and then multiply by it 1000 to change it to mg.

Here are the formulas:

Number of moles = Number of molecules / Avogadro's number

Mass = Moles x Molar mass

Number of moles = (1.4 x 10^17) / (6.02 x 10^23) = 2.3255814 x 10^-7 moles

Now that we have the moles, we can multiply them by Sucrose's molar mass, which can be calculated by using the masses listed in the periodic table.

Carbon's Molar Mass = 12g/mol (There are 12 atoms of Carbon in sucrose)

Hydrogen's Molar mass = 1.01g/mol (22 atoms of Hydrogen in sucrose)

Oxygen's Molar mass = 16g/mol (11 atoms of oxygen in sucrose)

Now we just add them together:

((12)x(12)) + ((1.01)x(22)) + ((16)x(11)) = 342.22g/mol is the molar mass of Sucrose

Now back to the question, you multiply the moles of sucrose by its molar mass to get the mass in grams

(2.3255814 x 10^-7) x (342.22) = 0.0000796 grams

Now to get it in milligrams, you multiply the answer above by 1000

0.0000796 x 1000 = 0.079 mg (already in 2 sig figs)

Therefore there are 0.079 milligrams of sucrose in the sugar crystal.

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