Question

Ethanol is the substance commonly called alcohol. The density of liquid alcohol is \(0.8 \mathrm{~g} / \mathrm{ml}\) at \(293 \mathrm{~K}\). If \(1.2\) moles of ethanol is needed for a particular experiment, what volume of ethanol should be measured out? (a) \(55.2 \mathrm{ml}\) (b) \(57.5 \mathrm{ml}\) (c) \(69 \mathrm{ml}\) (d) \(47.9 \mathrm{ml}\)

Short answer

69 ml

Step-by-step solution

Identify the molar mass of ethanol

Use the periodic table to find the atomic masses of carbon (C), hydrogen (H), and oxygen (O) and calculate the molar mass of ethanol (C2H5OH). The molar mass is given by 2(C) + 6(H) + 1(O). For carbon, the atomic mass is approximately 12.01 g/mol, for hydrogen it is about 1.01 g/mol, and for oxygen, it is approximately 16.00 g/mol. Hence, the molar mass of ethanol is 2(12.01) + 6(1.01) + 16.00 = 46.07 g/mol.

Calculate the mass of ethanol needed

To find the mass of ethanol required for 1.2 moles, use the formula: Mass = Molar mass * Number of moles. That is, the mass of ethanol = 46.07 g/mol * 1.2 mol = 55.284 g.

Calculate the volume of ethanol required

Use the density formula Density = Mass/Volume to calculate the volume. Rearrange the formula to solve for volume: Volume = Mass/Density. The volume of ethanol required = 55.284 g / (0.8 g/ml) = 69.105 ml.

Key concepts

Stoichiometry

Stoichiometry is the heart of chemistry as it quantifies the relationships between reactants and products in a chemical reaction. Understanding stoichiometry involves mastering the mole concept and the ability to convert between moles, mass, volume, and particles using the molar mass and Avogadro's number. It's key to identify what you know and what you need to find out in a problem—here it's the volume of ethanol based on moles of reactants.

Let's take the exercise as an example. With the known molar mass of ethanol and the amount of moles needed, stoichiometry allows you to calculate the mass of ethanol required for the reaction. Once the mass is known, stoichiometry also enables you to convert this mass into volume, using the substance's density. This is the very essence of stoichiometry—the ability to predict and measure quantities needed or produced in a chemical process.

Density

Density is the mass per unit volume of a substance and is crucial in calculating the volume of a substance when its mass is known. The density formula goes hand in hand with stoichiometry, as seen in our exercise where mass and volume interchange depending on the calculation requirements.

For ethanol in the example, a density of 0.8 g/ml signifies that each milliliter of ethanol weighs 0.8 grams. By rearranging the density formula Density = Mass/Volume to Volume = Mass/Density, we can find out the volume once we know the mass. It's like solving a puzzle; knowing how densely packed ethanol molecules are in a given space helps us measure the right volume of ethanol for the experiment.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic world we live in. It allows us to count particles by weighing them. One mole corresponds to Avogadro's number (6.022 \( \times \) 10²³) of particles (atoms, molecules, ions, etc.).

In our exercise, 1.2 moles of ethanol translates to a specific number of ethanol molecules needed for the experiment. The exercise requires us to understand that these moles can be converted to mass using the molar mass of ethanol, and this mass can then be converted to a practical volume that can be measured and used in the lab. The mole concept is foundational since all stoichiometric conversions begin and end with moles.

Molar Volume

Molar volume is the volume occupied by one mole of a substance at a given temperature and pressure. In the case of gases at standard temperature and pressure (STP), the molar volume is 22.4 liters. However, the concept can extend to liquids and solids with different values depending on the density.

In the context of the exercise, we use the concept of molar volume indirectly when we relate moles of ethanol to its volume through its density. Ethanol is a liquid, and it doesn't have a fixed molar volume like a gas would at STP, but knowing its density gives us the tool needed to convert the calculated mass (from the mole concept) into volume. So, the molar volume here is personalized for ethanol and relies on its specific density.