Calculate the mass, in grams, of each of the following.
a) 1.2×10^23 gold atoms
b) 2.78×10^22 helium atoms
c) 2.0×10^23 lead atoms
d) 7.6×10^21 uranium atoms
There are 6.022 x 10^23 atoms in 1 mole; therefore, # moles = 1.2 x ^23/6.022 x 10^23 = ??
Then moles = grams/molar mass. Solve for grams.
To calculate the mass of each of the following, we will use the concept of molar mass.
The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol).
a) 1.2×10^23 gold atoms:
The molar mass of gold (Au) is 197.0 g/mol.
To calculate the mass, we use the formula:
Mass = number of atoms × molar mass
Mass = 1.2 × 10^23 atoms × (197.0 g/mol)
Mass = 2.34 × 10^25 g
Therefore, the mass of 1.2×10^23 gold atoms is 2.34 × 10^25 grams.
b) 2.78×10^22 helium atoms:
The molar mass of helium (He) is 4.0026 g/mol.
Mass = 2.78 × 10^22 atoms × (4.0026 g/mol)
Mass = 1.112 × 10^23 g
Therefore, the mass of 2.78×10^22 helium atoms is 1.112 × 10^23 grams.
c) 2.0×10^23 lead atoms:
The molar mass of lead (Pb) is 207.2 g/mol.
Mass = 2.0 × 10^23 atoms × (207.2 g/mol)
Mass = 4.144 × 10^25 g
Therefore, the mass of 2.0×10^23 lead atoms is 4.144 × 10^25 grams.
d) 7.6×10^21 uranium atoms:
The molar mass of uranium (U) is 238.03 g/mol.
Mass = 7.6 × 10^21 atoms × (238.03 g/mol)
Mass = 1.811 × 10^24 g
Therefore, the mass of 7.6×10^21 uranium atoms is 1.811 × 10^24 grams.
To calculate the mass of each of the given substances, we need to use the concept of molar mass and Avogadro's number:
1) Determining the molar mass:
a) The molar mass of gold (Au) is 196.97 g/mol.
b) The molar mass of helium (He) is 4.00 g/mol.
c) The molar mass of lead (Pb) is 207.2 g/mol.
d) The molar mass of uranium (U) is 238.03 g/mol.
2) Utilizing Avogadro's number:
Avogadro's number (6.022 x 10^23) represents the number of particles in one mole of a substance, which includes atoms, molecules, or ions.
Now, let's calculate the mass of each substance:
a) 1.2×10^23 gold atoms:
To find the mass, we need to divide the number of atoms by Avogadro's number and then multiply by the molar mass:
Mass = (1.2×10^23) / (6.022 x 10^23) * 196.97 g/mol
Mass ≈ 3.90 grams
b) 2.78×10^22 helium atoms:
Mass = (2.78×10^22) / (6.022 x 10^23) * 4.00 g/mol
Mass ≈ 0.0461 grams
c) 2.0×10^23 lead atoms:
Mass = (2.0×10^23) / (6.022 x 10^23) * 207.2 g/mol
Mass ≈ 68.5 grams
d) 7.6×10^21 uranium atoms:
Mass = (7.6×10^21) / (6.022 x 10^23) * 238.03 g/mol
Mass ≈ 0.19 grams
Therefore, the mass of each substance is approximately:
a) 3.90 grams
b) 0.0461 grams
c) 68.5 grams
d) 0.19 grams
A.) 65g
B.)0.187g
C.)79g
D.)3g