Problem 81 - Chemistry: Atoms First

Question

As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. The only container readily available is a 150-mL Erlenmeyer flask. Is it large enough to contain the acid, whose density is 1.83 g/mL?

Step-by-Step Solution

Answer

Yes, the Erlenmeyer flask is large enough to contain the acid, as it can hold 150 mL, whereas only 122.95 mL is needed for 225 g of phosphoric acid (density = 1.83 g/mL).

Step 1: Calculate the volume of phosphoric acid needed

To find the volume of phosphoric acid, use the density formula: Density = mass/volume. Rearrange it to find the volume, so the volume = mass/density. Insert the given values, volume = 225 g / 1.83 g/mL.

Step 2: Perform the calculation

Divide the given mass of the phosphoric acid by its density to calculate the volume in mL. So, volume = 225 g / 1.83 g/mL = 122.95 mL.

Step 3: Compare the volume with flask capacity

Now compare the calculated volume of phosphoric acid (122.95 mL) with the volume capacity of the Erlenmeyer flask (150 mL). If the calculated volume is less than the flask capacity, the flask is large enough to contain the acid.

Key Concepts

Chemical Density

Understanding the concept of chemical density is crucial in various fields of chemistry, especially when mixing substances or determining their purity. Density is defined as the mass of a substance divided by its volume. It is usually expressed in grams per milliliter (\( g/mL \) for liquids) or grams per cubic centimeter (\( g/cm^3 \) for solids). High-density substances are generally heavier for their size, whereas low-density substances are lighter. For instance, when you need to determine if a container can hold a certain chemical without overflowing, knowing the density of the chemical is critical. In the exercise, the instructor uses the density of phosphoric acid to decide whether a 150-mL Erlenmeyer flask can hold 225 g of the substance without pouring over.

Erlenmeyer Flask Volume

In chemistry labs, Erlenmeyer flasks are commonly used due to their conical shape and flat bottom, which make them stable and suitable for mixing contents by swirling without the risk of spillage. The capacity or volume of an Erlenmeyer flask is typically marked on the container, representing the maximum volume of liquid the flask can hold.When working with such equipment, it's essential to understand their volume capacity to avoid overfilling, which can lead to inaccurate measurements or messy spills. For the given problem, knowing that the Erlenmeyer flask can hold up to 150 mL provides the information needed to decide if it's large enough for the 225 g of phosphoric acid, as determined by the chemical's density and the necessary mass-to-volume conversion.

Mass to Volume Conversion

Mass to volume conversion in chemistry is an essential skill that allows chemists to convert between the weight of a substance and the space it occupies, using density as the conversion factor. Since density is mass per unit volume, by rearranging the equation, you can easily calculate the volume of a mass of substance, provided its density is known.In our exercise, the instructor uses mass to volume conversion to find out the volume that 225 g of phosphoric acid would occupy. By dividing the mass of the acid by its density (\( \frac{mass}{density} \) = volume), the instructor can then compare this volume to the volume of the Erlenmeyer flask. This is a practical application of the conversion that ensures accuracy and safety in the lab.