The density of ethanol varies slightly with temperature, as shown in the table below. Based on this data, how many molecules of ethanol are contained in 30 mL of ethanol at 8 °C? (Note: The molar mass of ethanol is 46.08 g/mol.)

Question

The density of ethanol varies slightly with temperature, as shown in the table below.  Based on this data, how many molecules of ethanol are contained in 30 mL of ethanol at 8 °C?  (Note: The molar mass of ethanol is 46.08 g/mol.)

Quizplus · Accepted Answer

11ecba2d_124d_b575_a3bf_a588c487ec79_MD0008_00 The density ρ of a substance is defined as the mass m it contains per unit of volume V that it occupies. This physical property is expressed mathematically as: 11ecba2d_124d_b576_a3bf_29e9282966ac_MD0008_00 Because materials tend to expand when heated and contract when cooled, the volume that a substance occupies can undergo minute changes with temperature. As a result, the exact density of a substance varies slightly with temperature. When the density of a substance at a given temperature is known, density can be used as a conversion factor to convert between the mass and volume of that substance. For example, 30 mL of ethanol at 8 °C has a density of 0.800 g/mL and a mass of 24 g. 11ecba2d_124d_b577_a3bf_793cc346e31d_MD0008_00 The molar mass of a compound is the amount of mass contained in 1 mole of the compound; it can be used to convert the mass of a compound to the number of moles. As such, dividing the mass of ethanol by its molar mass gives the number of moles of ethanol. 11ecba2d_124d_b578_a3bf_596032ae994e_MD0008_00 A mole is defined as Avogadro's number (N_A = 6.022 × 10²³) of atoms or molecules. Accordingly, the number of molecules of ethanol is found by multiplying the moles of ethanol by N_A. 11ecba2d_124d_b579_a3bf_299e500f36fd_MD0008_00 Therefore, 30 mL of ethanol at 8 °C contains 3.1 × 10²³ molecules of ethanol. (Choice A) 8.6 × 10⁻²⁵ results from dividing rather than multiplying the moles of ethanol by N_A. (Choice C) 4.9 × 10²³ results from dividing rather than multiplying the volume of ethanol by the density. (Choice D) 6.7 × 10²⁶ results from multiplying rather than dividing the mass of ethanol by the molar mass. Educational objective: The density of a substance varies slightly with temperature and is defined as the mass of the substance per unit of volume that it occupies. Avogadro's number (N_A = 6.022 × 10²³) of formula units equals one mole, and the molar mass of a compound is the amount of mass (in grams) contained in 1 mole of formula units (grams/mole).

The Density of Ethanol Varies Slightly with Temperature, as Shown