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Question

Which has more number of atoms, 100 grams of sodium or 100grams of iron (given, atomic mass of Na=23u, Fe=56u100g)?


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Solution

Step 1: Given data

Amount of sodium = 100g

Amount of iron = 100g

Atomic mass of sodium = 23u

Atomic mass of iron = 56u

Step 2: Formula used

One mole of any substance(molecular weight in grams) contains 6.022×1023 number of atoms. This is known as the Avogadro's number.

Therefore, unitary method is used to calculate the number of atoms in 100g of sodium and iron.

Step 3: Calculation of the number of atoms in 100g sodium

Weight of one mole of sodium = 23g

Using Avagadro's number,

Number of atoms 23g of sodium = 6.022×1023

Number of atoms 1g of sodium = 6.022×102323

Number of atoms 100g of sodium = 6.022×102323×100=2.6182×1024

Step 4: Calculation of the number of atoms in 100g iron

Weight of one mole of iron = 56g

Using Avagadro's number,

Number of atoms 56g of iron = 6.022×1023

Number of atoms 1g of iron = 6.022×102356

Number of atoms 100g of iron = 6.022×102356×100=1.0753×1024

Hence, 100 grams of sodium has more atoms than 100grams of iron.


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