Question

Determine the numbers of atoms in each of the following 5.40 g B 0.250 mol k 0.0384 mol k 0.02550 g pt 1.00 x 10^-10 g Au,

Answer 1

The answers are the following:
1. 3.01 x 10^23 atoms B
solution: (5.40/10.81)(6.022x10^23) 
2. 1.51 x 10^23 atoms S
solution: (.250)(6.022x10^23) 
3. 2.31 x 10^22 atoms K
solution: (.0384)(6.022x10^23) 
4. 7.872 x 10^19 atoms Pt
solution: (.02550/195.08)(6.022x10^23) 
5. 3.06 x 10^11 atoms Au
solution: (1.00x10^-10/196.97)(6.022x10^23)

Answer 2

Answer:

a) 5.40 g B : $3.012\times 10^{23}$ atoms

b) 0.250 mol K : $1.51\times 10^{23}$ atoms

c) 0.0384 mol K : $0.23\times 10^{23}$ atoms

d) 0.02550 g Pt: $7.8\times 10^{19}$ atoms

e)  $1.00\times 10^-{10} g$ Au: $0.03\times 10^{13}$ atoms

Explanation:

According to avogadro's law, 1 mole of every substance occupies 22.4 L at STP and contains avogadro's number $6.023\times 10^{23}$ of particles.

To calculate the moles, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text {Molar mass}}$

a) 5.40 g B

$\text{Number of moles}=\frac{\text{Given mass}}{\text {Molar mass}}=\frac{5.40g}{11g/mol}=0.5moles$

1 mole of boron contains = $6.023\times 10^{23}$ atoms

Thus 0.5 moles  of boron contain =$\frac{6.023\times 10^{23}}{1}\times 0.5=3.012\times 10^{23}$ atoms

b) 0.250 mol K

1 mole of potassium (K) contains = $6.023\times 10^{23}$ atoms

Thus 0.250 moles of potassium contain =$\frac{6.023\times 10^{23}}{1}\times 0.250=1.51\times 10^{23}$ atoms

c) 0.0384 mol K

1 mole of potassium (K) contains = $6.023\times 10^{23}$ atoms

Thus 0.0384 moles of potassium (K) contain =$\frac{6.023\times 10^{23}}{1}\times 0.0384=0.23\times 10^{23}$ atoms

d) 0.02550 g Pt

$\text{Number of moles}=\frac{\text{Given mass}}{\text {Molar mass}}=\frac{0.02550 g}{195g/mol}=1.3\times 10^{-4}moles$

1 mole of platinum contains = $6.023\times 10^{23}$ atoms

Thus $1.3\times 10^{-4}moles$ of platinum contain=$\frac{6.023\times 10^{23}}{1}\times 1.3\times 10^{-4}=7.8\times 10^{19}$ atoms

e) $1.00\times 10^-{10}g$ Au,

$\text{Number of moles}=\frac{\text{Given mass}}{\text {Molar mass}}=\frac{1.00\times 10^{-10}g}{197g/mol}=0.005\times 10^{-10}moles$

1 mole of gold contains = $6.023\times 10^{23}$ atoms

Thus $0.005\times 10^{-10}moles$ of platinum contain=$\frac{6.023\times 10^{23}}{1}\times 0.005\times 10^{-10}=0.03\times 10^{13}$ atoms