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Answer :
[tex]\boxed{0.508{\text{ g}}}[/tex] is the mass of [tex]1.70 \times {\text{1}}{{\text{0}}^{{\text{21}}}}\;{\text{molecules}}[/tex] of aspirin.
Further Explanation:
Avogadro’s number is a mathematical number that determines the number of atoms or molecules in one mole of the substance. The value of Avogadro’s number is [tex]{\text{6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}\;{\text{units}}[/tex]. These units can either be atoms or molecules.
There are [tex]{\text{6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}\;{\text{molecules}}[/tex] in one mole of aspirin. Therefore the number of moles in [tex]1.70 \times {\text{1}}{{\text{0}}^{{\text{21}}}}\;{\text{molecules}}[/tex] of aspirin can be calculated as follows:
[tex]\begin{aligned}{\text{Moles of aspirin}}&= \left( {1.70 \times {\text{1}}{{\text{0}}^{{\text{21}}}}\;{\text{molecules}}} \right)\left( {\frac{{1{\text{ mol}}}}{{6.022 \times {\text{1}}{{\text{0}}^{{\text{23}}}}\;{\text{molecules}}}}} \right)\\&= 0.002823{\text{ mol}}\\\end{aligned}[/tex]
The moles of aspirin can be calculated by the following formula.s
[tex]{\text{Moles of aspirin}}=\dfrac{{{\text{Mass of aspirin}}}}{{{\text{Molar mass of aspirin}}}}[/tex] …… (1)
Rearrange equation (1) for the mass of aspirin.
[tex]{\text{Mass of aspirin}} = \left( {{\text{Moles of aspirin}}} \right)\left( {{\text{Molar mass of aspirin}}} \right)[/tex] …… (2)
The molar mass of aspirin [tex]\left( {{{\text{C}}_{\text{9}}}{{\text{H}}_{\text{8}}}{{\text{O}}_{\text{4}}}} \right)[/tex] can be calculated as follows:
[tex]{\text{Molar mass of }}{{\text{C}}_{\text{9}}}{{\text{H}}_{\text{8}}}{{\text{O}}_{\text{4}}} = \left[ \begin{aligned}9\left( {{\text{Atomic mass of C}}} \right)+\hfill\\8\left({{\text{Atomic mass of H}}} \right)+\hfill\\4\left( {{\text{Atomic mass of O}}} \right) \hfill\\\end{aligned} \right][/tex] …… (3)
Substitute 12.01 g for the atomic mass of C, 1.008 g for the atomic mass of H and 15.99 g for the atomic mass of O in equation (3).
[tex]\begin{aligned}{\text{Molar mass of }}{{\text{C}}_{\text{9}}}{{\text{H}}_{\text{8}}}{{\text{O}}_{\text{4}}} &= \left[ {9\left( {{\text{12}}{\text{.01 g}}} \right) + 8\left( {{\text{1}}{\text{.008 g}}} \right) + 4\left( {{\text{15}}{\text{.99 g}}} \right)} \right]\\&= \left[ {108.09{\text{ g}} + 8.064{\text{ g}} + 63.96{\text{ g}}} \right]\\&= 180.114{\text{ g/mol}}\\\end{aligned}[/tex]
Substitute 0.002823 mol for the moles of aspirin and 180.114 g/mol for the molar mass of aspirin in equation (2).
[tex]\begin{aligned}{\text{Mass of aspirin}}&= \left( {{\text{0}}{\text{.002823 mol}}} \right)\left( {\frac{{{\text{180}}{\text{.114 g}}}}{{1{\text{ mol}}}}} \right)\\&= 0.508{\text{ g}}\\\end{aligned}[/tex]
Therefore the mass of aspirin is 0.508 g.
Learn more:
- Calculate the moles of chlorine in 8 moles of carbon tetrachloride: https://brainly.com/question/3064603
- Calculate the moles of ions in the solution: https://brainly.com/question/5950133
Answer details:
Grade: Senior School
Chapter: Mole concept
Subject: Chemistry
Keywords: aspirin, molar mass, atomic mass, C, H, O, C9H8O4, Avogadro’s number, 0.508 g, 15.99 g, 12.01 g, 1.008 g.
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Rewritten by : Jeany
The answer is 0.508gram
The molecular mass for aspirin (C9H8O4) should be 180g/mol. One mol is composed of 6.02* 10^23 molecule. So, the mass of 1.70×1021 molecules of aspirin would be: (1.70×10^21 molecules) * (1 mol /6.02* 10^23 molecule) * 180g/mol= 0.508 gram
The molecular mass for aspirin (C9H8O4) should be 180g/mol. One mol is composed of 6.02* 10^23 molecule. So, the mass of 1.70×1021 molecules of aspirin would be: (1.70×10^21 molecules) * (1 mol /6.02* 10^23 molecule) * 180g/mol= 0.508 gram
