To calculate the mass of sodium (Na) metal containing the same number of atoms as 12g of carbon (C), we need to use the concept of molar mass and Avogadro's number.
The molar mass of an element represents the mass of one mole of that element, and it is expressed in grams/mol. Avogadro's number (N_A) is the number of atoms or molecules per mole and is approximately 6.022 × 10^23.
First, we need to determine the number of moles of carbon in 12g. The molar mass of carbon (C) is approximately 12.01 g/mol. So, the number of moles (n) of carbon can be calculated as:
n = mass / molar mass n = 12g / 12.01 g/mol ≈ 0.999 mole
Since 1 mole of any substance contains Avogadro's number (N_A) of atoms, the number of atoms in 0.999 moles of carbon is approximately:
number of atoms = n * N_A number of atoms = 0.999 * 6.022 × 10^23 ≈ 6.015 × 10^23
Now, we can calculate the mass of sodium (Na) that contains the same number of atoms:
number of atoms = n * N_A mass = number of atoms / N_A mass = 6.015 × 10^23 / 6.022 × 10^23 ≈ 0.998g
Therefore, the mass of sodium (Na) containing the same number of atoms as 12g of carbon (C) is approximately 0.998 grams.