To calculate the mass of a certain number of carbon atoms, you can use the formula:
Mass = Number of atoms × Atomic mass
The atomic mass of carbon (C) is approximately 12 atomic mass units (AMU).
Given that you have 3 × 10^22 carbon atoms, you can calculate the mass as follows:
Mass = (3 × 10^22) × 12 AMU
To simplify the calculation, we can express the number 3 × 10^22 in scientific notation:
Mass = 3 × 12 × 10^22 AMU
Mass = 36 × 10^22 AMU
Now, we can convert the mass to a more convenient form. The atomic mass unit (AMU) is a very small unit, so it is often more practical to express the mass in grams (g). One mole of any substance contains Avogadro's number (approximately 6.022 × 10^23) of particles. Therefore, the molar mass of carbon is 12 grams per mole (g/mol).
To convert from AMU to grams, we use the conversion factor:
1 AMU = 1 g/mol
Thus, the mass can be calculated as:
Mass = 36 × 10^22 AMU × (1 g/mol) / (6.022 × 10^23 AMU/mol)
Mass = 5.976 × 10^-2 g
So, the mass of 3 × 10^22 carbon atoms is approximately 5.976 × 10^-2 grams.