Respuesta :
Answer:
6.21 × 10²² Carbon Atoms
Solution:
Data Given:
Mass of Butane (C₄H₁₀) = 1.50 g
M.Mass of Butane = 58.1 g.mol⁻¹
Step 1: Calculate Moles of Butane as,
Moles = Mass ÷ M.Mass
Putting values,
Moles = 1.50 g ÷ 58.1 g.mol⁻¹
Moles = 0.0258 mol
Step 2: Calculate number of Butane Molecules;
As 1 mole of any substance contains 6.022 × 10²³ particles (Avogadro's Number) then the relation for Moles and Number of Butane Molecules can be written as,
Moles = Number of C₄H₁₀ Molecules ÷ 6.022 × 10²³ Molecules.mol⁻¹
Solving for Number of Butane molecules,
Number of C₄H₁₀ Molecules = Moles × 6.022 × 10²³ Molecules.mol⁻¹
Putting value of moles,
Number of C₄H₁₀ Molecules = 0.0258 mol × 6.022 × 10²³ Molecules.mol⁻¹
Number of C₄H₁₀ Molecules = 1.55 × 10²² C₄H₁₀ Molecules
Step 3: Calculate Number of Carbon Atoms:
As,
1 Molecule of C₄H₁₀ contains = 4 Atoms of Carbon
So,
1.55 × 10²² C₄H₁₀ Molecules will contain = X Atoms of Carbon
Solving for X,
X = (1.55 × 10²² C₄H₁₀ Molecules × 4 Atoms of Carbon) ÷ 1 Molecule of C₄H₁₀
X = 6.21 × 10²² Atoms of Carbon
[tex]\boxed{6.216 \times {\text{1}}{{\text{0}}^{{\text{22}}}}{\text{ atoms}}}[/tex] of carbon is present in 1.50 g of butane.
Further Explanation:
Avogadro’s number indicates how many atoms or molecules a mole can have in it. In other words, it provides information about the number of units that are present in one mole of the substance. It is numerically equal to [tex]{\text{6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}\;{\text{units}}[/tex]. These units can be atoms or molecules.
The formula to calculate the moles of [tex]{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}[/tex] is as follows:
[tex]{\text{Moles of }}{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}} = \dfrac{{{\text{Given mass of }}{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}}}{{{\text{Molar mass of }}{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}}}[/tex] …… (1)
Substitute 1.50 g for the given mass and 58.1 g/mol for the molar mass of [tex]{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}[/tex] in equation (1).
[tex]\begin{aligned}{\text{Moles of }}{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}} &= \left( {{\text{1}}{\text{.50 g}}} \right)\left( {\frac{{{\text{1 mol}}}}{{{\text{58}}{\text{.1 g}}}}} \right)\\&= {\text{0}}{\text{.0258 mol}}\\\end{aligned}[/tex]
Since one mole of [tex]{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}[/tex] has [tex]{\text{6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}\;{\text{molecules}}[/tex] of [tex]{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}[/tex]. Therefore the formula to calculate the molecules of butane is as follows:
[tex]{\text{Molecules of }}{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}} = \left( {{\text{Moles of }}{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}} \right)\left( {{\text{Avogadro's Number}}} \right)[/tex] …… (2)
Substitute 0.0258 mol for the moles of [tex]{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}[/tex] and [tex]{\text{6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}\;{\text{molecules}}[/tex] for Avogadro’s number in equation (2).
[tex]\begin{aligned}{\text{Molecules of }}{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}{\mathbf{}}&=\left( {0.0258{\text{ mol}}} \right)\left( {\frac{{{\text{6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}{\text{ molecules}}}}{{{\text{1 mol}}}}} \right)\\&= 1.554 \times {\text{1}}{{\text{0}}^{{\text{22}}}}{\text{ molecules}} \\\end{aligned}[/tex]
The chemical formula of butane is [tex]{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}[/tex]. This indicates one molecule of butane has four atoms of carbon. Therefore the number of carbon atoms can be calculated as follows:
[tex]\begin{aligned}{\text{Atoms of carbon}} &= \left( {1.554 \times {\text{1}}{{\text{0}}^{{\text{22}}}}{\text{ molecules}}} \right)\left( {\frac{{{\text{4 C atoms}}}}{{{\text{1 molecule of }}{{\text{C}}_{\text{4}}}{{\text{H}}_{{\text{10}}}}}}} \right)\\&= 6.216 \times {\text{1}}{{\text{0}}^{{\text{22}}}}{\text{ C atoms}} \\\end{aligned}[/tex]
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: 1.50 g, 58.1 g/mol, butane, C4H10, Avogadro’s number, [tex]6.216*10^22[/tex] C atoms, [tex]1.554*10^22[/tex]molecules, moles, one mole, chemical formula, carbon atoms, molar mass of C4H10, given mass of C4H10.
