Question

An organic solvent has density \(1.31 \mathrm{g} / \mathrm{mL}\). What volume is occupied by \(50.0 \mathrm{g}\) of the liquid?

Short answer

The volume occupied by the \(50.0\,\mathrm{g}\) of organic solvent with a density of \(1.31 \mathrm{g/mL}\) can be calculated using the formula \(Volume = \frac{Mass}{Density}\). Plugging in the given values, we get \(Volume = \frac{50.0\,\mathrm{g}}{1.31\,\mathrm{g/mL}} \approx 38.17\,\mathrm{mL}\).

Step-by-step solution

Write down the density formula and rearrange for volume.

The formula for density is: \[Density = \frac{Mass}{Volume}\] To find the volume, we need to rearrange the equation as follows: \[Volume = \frac{Mass}{Density}\] In this problem, we have the mass and density of the organic solvent, so we can use this formula to find the volume.

Identify the given values.

We're given the following values in the exercise: - Density of the organic solvent = \(1.31 \mathrm{g/mL}\) - Mass of the liquid = \(50.0 \mathrm{g}\)

Calculate the volume using the given values.

Now, we can plug these values into the rearranged formula to calculate the volume: \[Volume = \frac{Mass}{Density} = \frac{50.0\,\mathrm{g}}{1.31\,\mathrm{g/mL}}\] Next, carry out the division: \[Volume = 38.17\,\mathrm{mL}\] So, the volume occupied by \(50.0\,\mathrm{g}\) of the organic solvent is approximately \(38.17\,\mathrm{mL}\).

Key concepts

Understanding Organic Solvents

Organic solvents are fascinating substances used in a wide range of applications from industrial processes to household cleaning. They are composed of organic compounds, which means they contain carbon atoms. This unique composition is what gives many organic solvents their characteristic properties such as volatility and ability to dissolve other organic substances.

Often, organic solvents are used because they do not react with solutes, making them ideal for use in chemical reactions and extractions. Common everyday organic solvents include acetone, alcohols, and benzene. It's important to be mindful of their flammability and potential health impacts during handling. Always ensure proper ventilation and protective equipment when using these solvents to avoid exposure.

In our specific exercise, understanding the solvent is crucial as its density is a key factor in determining the volume when a specific mass is given. The density of the organic solvent in question here is used directly in the density formula, establishing how mass relates to volume.

Mass and Volume Relationship

The relationship between mass and volume is foundational in understanding density. Density is essentially a measure of how much mass is contained in a given volume. When we look at objects or substances, their mass and volume determine their density, connecting these two fundamental properties.

Consider this:

• Mass is how much material there is in an object or substance, typically measured in grams (g) or kilograms (kg).
• Volume is the space that substance occupies, usually measured in milliliters (mL) or liters (L).

Different substances have different densities because they pack their mass into volume differently depending on their physical state and composition.

In our exercise, we're provided with a mass of 50.0 grams and tasked to determine the volume using a given density. By understanding how mass relates to volume through the lens of density, we see how volume can be determined for any mass when density is given. This principle is widely used in practical applications, from cooking to chemistry, making it crucial to grasp.

The Density Formula in Action

The density formula is a handy tool for converting between mass and volume. It reads:\[Density = \frac{Mass}{Volume}\]This can also be rearranged to find either mass or volume when two of the three variables are known. To find the volume, as we needed in the exercise, the formula becomes:\[Volume = \frac{Mass}{Density}\]By substituting the mass and density into this formula, we not only solve our exercise but appreciate how this equation finds utility in various scientific and real-world scenarios.

For instance, in our problem, the density of the organic solvent is given as 1.31 g/mL, and the mass is 50.0 g.Plugging these values into our rearranged formula gives:\[Volume = \frac{50.0\, \mathrm{g}}{1.31\, \mathrm{g/mL}} = 38.17\, \mathrm{mL}\]This means that 50 grams of this organic solvent will occupy a volume of approximately 38.17 milliliters. The density formula is versatile and is used not just in chemistry, but in any field that requires the understanding of how materials are stacked in space, like pharmacology and engineering.