Question

If the average molecular mass of compounds in food is 50.0 g, how many molecules are there in 1.00 kg of food?

9. (1.204 × 10²⁶)
10. (2.408 × 10²⁵)
11. (6.022 × 10²⁴)
12. (1.204 × 10²⁵)

Answer 1

To find the number of molecules in 1.00 kg of food with an average molecular mass of 50.0 g, you convert the mass to moles and then multiply by Avogadro's number. This results in 1.204 × 10²µ molecules.

Step-by-step explanation:

If the average molecular mass of compounds in food is 50.0 g, to calculate the number of molecules in 1.00 kg of food, we can use Avogadro's number, which is the number of units (atoms, molecules, etc.) in one mole of a substance. Avogadro's number is 6.022 × 10²³ units per mole. Since the average molecular mass is 50.0 g, we need to first convert 1.00 kg (which is 1000 g) to moles. This is done by dividing the total mass of the food by the average molecular mass of the compounds in the food:

Number of moles = Total mass of food / Average molecular mass = 1000 g / 50.0 g/mol = 20 moles

Then, to find the total number of molecules, we multiply the number of moles by Avogadro's number:

Number of molecules = Number of moles × Avogadro's number = 20 mol × 6.022 × 10²³ molecules/mol = 1.204 × 10²µ molecules