Question

Which has more atoms: a 1-g sample of carbon-12 or a 1-g sample of carbon-13? explain?

Answer 1

Carbon-12

Step-by-step explanation:

Let's consider Avogadro's number: 1 mole of atoms has 6.02 × 10²³ atoms.

The molar mass of the isotope carbon-12 is 12 g/mol. The atoms contained in 1 g of ¹²C are:

`1g^(12)C.(1mol^(12)C)/(12g^(12)C) .(6.02 * 10^(23)atom ^(12)C)/(1mol^(12)C) =5.0 * 10^(22)atom ^(12)C`

The molar mass of the isotope carbon-13 is around 13 g/mol. The atoms contained in 1 g of ¹³C are:

`1g^(13)C.(1mol^(13)C)/(13g^(13)C) .(6.02 * 10^(23)atom ^(13)C)/(1mol^(13)C) =4.6 * 10^(22)atom ^(13)C`

There are more atoms in a 1-g sample of ¹²C than in a 1-g sample of ¹³C.

Answer 2

From the Avogadro's constant 1 mole = 6.022 × 10^23 atoms
1g of Carbon-12 contains = 1/12 = 0.083 moles
Therefore; 0.083 moles × 6.022×10^23
= 4.9983 × 10^22 atoms
1g of Carbon-13 contains = 1/13 = 0.077 moles
= 4.6370 × 10^22 atoms
Therefore; Carbon-12 has more atoms than Carbon-13