Chemistry, 06.07.2019 21:30 peachyparty

How many molecules of ethanol (c2h5oh) (the alcohol in alcoholic beverages) are present in 140 ml of ethanol? the density of ethanol is 0.789 g/cm3?

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An mL is also equivalent to cm³, signifying that 140 mL is equivalent to 140 cm³. The mass of ethanol is calculated by multiplying the density by the volume.

mass = (140 cm³)(0.789 g/cm³)
mass = 110.46 g

Then, calculate the number of moles of ethanol by dividing the mass by the molar mass of ethanol equal to 46.07 g/mol.
number of moles = (110.46 g/ 46.07 g/mol) = 2.4 mol

Then, multiply the number of moles by the Avogadro's number.
2.4 mol (6.022 x 10²³)
number of molecules = 1.445 x 10²⁴

Answer from: kromer6797

Taking into account the definition of density and Avogadro's number, 1.44×10²⁴ molecules of ethanol are present in 140 ml of ethanol.

Definition of density

Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space.

In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance. Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:

$density=\frac{mass}{volume}$

Avogadro's Number

Avogadro's Number or Avogadro's Constant is called the number of particles that make up a substance (usually atoms or molecules) and that can be found in the amount of one mole of said substance. Its value is 6.023×10²³ particles per mole. Avogadro's number applies to any substance.

Amount of molecules of ethanol

In this case, you know that:

Density= 0.789 $\frac{g}{cm^{3} }$ Volume= 140 mL= 140 cm³

Replacing in the definition of density:

$0.789\frac{g}{cm^{3} } =\frac{mass}{140cm^{3} }$

Solving:

mass= 0.789 $\frac{g}{cm^{3} }$ ×140 cm³

mass= 110.46 g

The molar mass of ethanol, that is, the amount of mass present in one mole of the compound, is 46 $\frac{g}{mol}$ . Then the number of moles that 110.46 g of ethanol contain is calculated by:

110.46 g× $\frac{1 mol}{46 g}$ = 2.40 moles

Finally, you can apply the following rule of three: If by definition of Avogadro's number 1 mole of ethanol contains 6.023×10²³ molecules, 2.40 moles contains how many molecules?

amount of molecules= (2.40 moles× 6.023×10²³ molecules)÷ 1 mole

amount of molecules= 1.44×10²⁴ moles

In summary, 1.44×10²⁴ molecules of ethanol are present in 140 ml of ethanol.

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