A sugar crystal contains approximately 1.8 × 1017 sucrose (C12H22O11) molecules. What is its mass in milligrams?
Here, we are going to calculate the mass of sugar crystal containing approximately 1.8 x 1017 sucrose molecules.
One mole of any species is that quantity in number having a mass equal to its atomic or molecular mass in grams.
The number of particles (atoms, molecules or ions) present in 1 mole of any substance is fixed, with a value of 6.022 × 1023. This is an experimentally obtained value. This number is called the Avogadro Constant or Avogadro Number.
Therefore, 1 mole = molar mass
1 mole = Avogadro number of particles
Combining the two statements, we get,
Mass of Avogadro’s number of particles = Molar mass
Therefore, mass of given number of particles = (Molar mass / Avogadro's number) x given number of particles
The mass of given sucrose sample = (given number of particles/Avogadro's number) x molar mass
Now, molar mass of sucrose(C12H22O11) = (12 x atomic mass of C) + (22 x atomic mass of H) + (11 x atomic mass of O)
= (12 x 12.0107) + (22 x 1.0079) + (11 x 15.9994)
= 144.1284 + 22.1738 + 175.9934
= 342.2956 g/mol
Given number of sucrose molecules = 1.8 x 1017 molecules
Therefore, mass of the sugar crystal = [(1.8 x 1017)/(6.022 × 1023)] x 342.2956 g/mol
= (0.299 x 10-6) x 342.2956 g
= 102.346 x 10-6 g
= 102.346 x 10-6 x 1000 mg [1 g = 1000 mg]
= 0.102 mg.
Thus, mass of the sugar crystal is 0.102 mg.