The length in miles of 1.00 mole of zinc atoms will be 9.8 × 10¹⁰ miles
Stoichiometry & Conversion
From the question, we are to determine the length in miles of the zinc atoms.
First, we will calculate the number of atoms present
Using the formula,
Number of atoms = Number of moles × Avogadro's constant
From the given information,
Number of moles of zinc atoms = 1.00 mole
Then,
Number of zinc atoms present = 1.00 × 6.022 × 10²³
Number of zinc atoms present = 6.022 × 10²³ atoms.
Now, from the given information
The diameter of a zinc atom is 2.60 Å
Therefore,
The diameter of 6.022 × 10²³ atoms of zinc will be
6.022 × 10²³ × 2.60 Å = 15.6572 × 10²³ Å
If 1 × 10¹⁰ Å = 1 m
Then,
15.6572 × 10²³ Å will be [tex]\frac{15.6572 \times 10^{23} }{1 \times 10^{10} } [/tex] m
Therefore
15.6572 × 10²³ Å = 1.56572 × 10¹⁴ m
Convert to km
1.56572 × 10¹⁴ m = 1.56572 × 10¹¹ km
Now, we will convert from km to miles
If 1.6 km = 1 mile
Then,
1.56572 × 10¹¹ km will [tex]\frac{1.56572 \times 10^{11} }{1.6} [/tex] miles
[tex]\frac{1.56572 \times 10^{11} }{1.6} [/tex] = 0.978575 ×10¹¹ miles
= 9.78575 × 10¹⁰ miles
≅ 9.8 × 10¹⁰ miles
Hence, the length in miles of 1.00 mole of zinc atoms will be 9.8 × 10¹⁰ miles
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