Question

A sugar crystal contains approximately 2.2×1017 sucrose (c12h22o11) molecules. part a what is its mass in mg?

Answer 1

The mass of a sugar crystal with 2.2×1017 sucrose molecules is found by calculating the number of moles and multiplying by the molar mass of sucrose (342.297 g/mol), then converting to milligrams.

Step-by-step explanation:

To find the mass of a sugar crystal with approximately 2.2×1017 sucrose (C12H22O11) molecules, we need to use the molar mass of sucrose. The molar mass of sucrose is 342.297 grams per mole. Since one mole of a compound contains Avogadro's number (approximately 6.022×1023) of molecules, we can use the following steps to calculate the mass:

1. Calculate moles of sucrose: moles = number of molecules ÷ Avogadro's number = 2.2×1017 molecules ÷ 6.022×1023 molecules/mole.
2. Convert moles to grams using the molar mass: mass in grams = moles × molar mass of sucrose.
3. Finally, convert the mass from grams to milligrams by multiplying by 1,000, since there are 1,000 milligrams in a gram.

Performing these calculations will give us the mass of the crystal in milligrams (mg).

Answer 2

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
mass = 3.6544 x 10^-7 x 342 = 1.249 x 10^-4 grams = 0.12498 mg