Asugar crystal contains approximately 1.2×1017 sucrose (c12h22o11) molecules.
what is its mass in mg?
express your answer using two significant figures.

0.12 mg

Explanation:

Data Given:

no. of molecules of Sucrose (C₁₂H₂₂O₁₁) = 1.2×10¹⁷

mass in mg = ?

Solution:

First we have to find no. of mole

Formula used

      no. of mole = no. of molecules / Avogadro's number

Where

Avogadro's number = 6.022 x 10²³

Put values in above formula

         no. of mole  =  1.2×10¹⁷ / 6.022 x 10²³

          no. of mole  =  3.5×10⁻⁷

Now we have to find mass of sucrose

For this formula will use

      mass in grams = no. of moles x Molar mass . . . . . .(1)

Formula of Sucrose = C₁₂H₂₂O₁₁

Molar mass of C₁₂H₂₂O₁₁ (Sucrose) = 12(12) +22(1) +11(16)

Molar mass of C₁₂H₂₂O₁₁ (Sucrose) = 144 +22 + 176

Molar mass of C₁₂H₂₂O₁₁ (Sucrose) = 342 g/mol

put values in equation 1

                mass in grams = 3.5×10⁻⁷ x 342 g/mol

               mass in grams = 1.2 x 10⁻⁴ g

Convert g to mg

               1 g = 1000 mg

               1.2 x 10⁻⁴ g = 1.2 x 10⁻⁴ x 1000 = 0.12 mg

mass of C₁₂H₂₂O₁₁ (Sucrose) = 0.12 mg