How many atoms in total are present in 1 kg of sugar?a)7.92 x 1025 atomsb)6 x 1023 atomsc)6.022 x 1025atomsd)1000 atomsCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

One molecule of sugar (C₁₂H₂₂O₁₁) = 45 atoms
Number of moles of sugar = 1000/342 = 2.92
Number of molecules = 2.92 x 6.023 x 10²³
= 17.60 x 10²³
molecules Number of atoms = 45 x 17.60 x 10²³
= 7.92 x 10²⁵ atoms

Answer

One molecule of sugar (C₁₂H₂₂O₁₁) = 45 atoms
Number of moles of sugar = 1000/342 = 2.92
Number of molecules = 2.92 x 6.023 x 10²³
= 17.60 x 10²³
molecules Number of atoms = 45 x 17.60 x 10²³
= 7.92 x 10²⁵ atoms

Answer

The molar mass of sugar, which is the amount of mass in one mole of sugar, is approximately 342.3 g/mol. To calculate the number of atoms in 1 kg of sugar, we first need to convert the mass of sugar to moles using the molar mass.

Conversion of mass to moles:
1 kg of sugar = 1000 g of sugar
Number of moles of sugar = (mass of sugar)/(molar mass of sugar)
= 1000 g / 342.3 g/mol
≈ 2.92 mol

Since 1 mole of any substance contains Avogadro's number of particles (6.022 x 10^23 atoms), we can calculate the number of atoms in 2.92 moles of sugar.

Number of atoms in 2.92 mol of sugar = 2.92 mol x (6.022 x 10^23 atoms/mol)
≈ 1.77 x 10^24 atoms

However, this calculation is for 2.92 moles of sugar, and we need to find the number of atoms in 1 kg of sugar. To find the number of atoms in 1 kg, we can multiply the number of atoms in 2.92 moles by the ratio of the number of moles in 1 kg to the number of moles in 2.92 moles.

Number of atoms in 1 kg of sugar = (1 kg / 342.3 g/mol) x (6.022 x 10^23 atoms/mol) x (2.92 mol / 1 kg)
≈ 7.92 x 10^25 atoms

Hence, the correct answer is option A) 7.92 x 10^25 atoms.

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