How many molecules of ethanol (C₂H₅OH) (the alcohol in alcoholic beverages) are present in 145 mL of ethanol? The density of ethanol is 0.789 g/cm³.

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Calculate the mass of ethanol using its volume and density. Use the formula: mass = density × volume. Remember to convert the volume from mL to cm³ (1 mL = 1 cm³).

Convert the mass of ethanol from grams to moles using the molar mass of ethanol. The molar mass of ethanol (C2H5OH) is approximately 46.07 g/mol.

Calculate the number of molecules in the moles of ethanol obtained. Use Avogadro's number, which is approximately 6.022 × 10²³ molecules/mol.

Multiply the number of moles by Avogadro's number to find the total number of ethanol molecules.

Ensure all units are consistent throughout the calculations and check your calculations for accuracy.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as mass per unit volume and is typically expressed in grams per cubic centimeter (g/cm³) or kilograms per liter (kg/L). In this question, the density of ethanol is given as 0.789 g/cm³, which means that each cubic centimeter of ethanol has a mass of 0.789 grams. Understanding density is crucial for converting volume measurements into mass, which is a necessary step in determining the number of molecules present.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance, expressed in grams per mole (g/mol). For ethanol (C2H5OH), the molar mass can be calculated by summing the atomic masses of its constituent atoms: carbon (C), hydrogen (H), and oxygen (O). Knowing the molar mass allows us to convert the mass of ethanol obtained from the density calculation into moles, which is essential for finding the number of molecules.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of atoms, ions, or molecules in one mole of a substance. This constant is fundamental in chemistry for converting between moles and the actual number of particles. Once the number of moles of ethanol is determined from the mass, Avogadro's number can be used to calculate the total number of ethanol molecules present in the given volume.