Answer :
The mass in grams of 6.5×10²⁰ molecules of aspirin (C₉H₈O₄) is 0.194 g
From Avogadro's hypothesis,
6.02×10²³ molecules = 1 mole of C₉H₈O₄
- Next, we shall determine the mass of 1 mole of C₉H₈O₄.
1 mole of C₉H₈O₄ = (12×9) + (1×8) + (16×3)
= 180 g
Therefore, we can say that:
6.02×10²³ molecules = 180 g of C₉H₈O₄
- With the above information, we can obtain the mass of 6.5×10²⁰ molecules of aspirin (C₉H₈O₄). This can be obtained as follow:
6.02×10²³ molecules = 180 g of C₉H₈O₄
Therefore,
6.5×10²⁰ molecules = [tex]\frac{180 * 6.5*10^{20} }{6.02*10^{23}}\\\\[/tex]
6.5×10²⁰ molecules = 0.194 g
Thus, the mass of 6.5×10²⁰ molecules of aspirin (C₉H₈O₄) is 0.194 g
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The mass in grams of the aspirin is 0.194 g
From the question,
We are to determine the mass in grams of 6.5×10²⁰ molecules of aspirin (C₉H₈O₄)
First, we will determine the number of moles of aspirin present
Using the formula
[tex]Number\ of\ moles = \frac{Number\ of\ molecules}{Avogadro's\ constant}[/tex]
Avogadro's constant = 6.022 × 10²³ mol⁻¹
From the given information
Number of molecules of aspirin = 6.5×10²⁰ molecules
∴ Number of moles of aspirin present = [tex]\frac{6.5 \times 10^{20} }{6.022 \times 10^{23} }[/tex]
Number of moles of aspirin present = 0.0010793756 moles
Number of moles of aspirin present = 1.0793756 ×10⁻³ mole
Now, to determine the mass of aspirin present
From the formula
Mass = Number of moles × Molar mass
Molar mass of aspirin = 180.158 g/mol
∴ Mass of aspirin = 0.0010793756 × 180.158
Mass of aspirin = 0.194458 g
Mass of aspirin = 0.194 g
Hence, the mass in grams of the aspirin is 0.194 g
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