Problem 46 - Chemistry and Chemical Reactivity

Question

You have a white crystalline solid, known to be one of the potassium compounds listed below. To determine which, you measure the solid's density. You measure out \(18.82 \mathrm{g}\) and transfer it to a graduated cylinder containing kerosene (in which salts will not dissolve). The level of liquid kerosene rises from \(8.5 \mathrm{mL}\) to \(15.3 \mathrm{mL}\). Calculate the density of the solid, and identify the compound from the following list. (a) \(\mathrm{KF}, d=2.48 \mathrm{g} / \mathrm{cm}^{3} \quad\) (c) \(\mathrm{KBr}, d=2.75 \mathrm{g} / \mathrm{cm}^{3}\) (b) \(\mathrm{KCl}, d=1.98 \mathrm{g} / \mathrm{cm}^{3} \quad\) (d) \(\mathrm{KI}, d=3.13 \mathrm{g} / \mathrm{cm}^{3}\)

Step-by-Step Solution

Answer

The compound is KBr.

Step 1: Calculate Volume of Displaced Liquid

The volume of kerosene displaced by the solid indicates the volume of the solid. It can be calculated as the difference in the kerosene levels: \[ \text{Volume of solid} = 15.3 \, \mathrm{mL} - 8.5 \, \mathrm{mL} = 6.8 \, \mathrm{mL}. \]

Step 2: Calculate the Density of the Solid

Density is calculated using the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). We know the mass is \(18.82\, \mathrm{g}\) and the volume is \(6.8\, \mathrm{cm}^3\) (since \(1 \mathrm{mL} = 1 \mathrm{cm}^3\)). Thus, \[ \text{Density of the solid} = \frac{18.82 \, \mathrm{g}}{6.8 \, \mathrm{cm}^3} \approx 2.77 \, \mathrm{g/cm}^3. \]

Step 3: Identify the Compound

Compare the calculated density with the densities provided for each compound:- KF: \(2.48 \, \mathrm{g/cm}^3\)- KCl: \(1.98 \, \mathrm{g/cm}^3\)- KBr: \(2.75 \, \mathrm{g/cm}^3\)- KI: \(3.13 \, \mathrm{g/cm}^3\)The calculated density, \(2.77 \, \mathrm{g/cm}^3\), is closest to the density of \(\mathrm{KBr}\).

Key Concepts

Potassium Compounds

Potassium compounds encompass a variety of chemical substances that contain potassium as a principal component. They are known for their diverse uses, such as in fertilizers, food additives, and water softeners. In our density calculation exercise, the compounds considered are:

• Potassium Fluoride ( KF)
• Potassium Chloride ( KCl)
• Potassium Bromide ( KBr)
• Potassium Iodide ( KI)

These compounds appear as white crystalline solids. Each has a distinct density, which is the ratio of its mass to its volume. Thus, measuring the density of an unknown potassium compound helps in identifying it. Knowing the properties of each compound allows us to match the experimentally determined density to the correct compound in the provided list.

Volume Displacement

Volume displacement is a helpful method in determining the volume of an irregular object. This approach involves submerging the object in a fluid and observing how much the fluid level rises.

Here's why this method is effective:

• It does not depend on the shape of the object.
• It allows for the calculation of volume using a simple subtraction of fluid levels.

In our example, a white crystalline solid is submerged in kerosene, causing the kerosene level to rise from 8.5 mL to 15.3 mL, indicating that the volume of the solid is indeed 6.8 mL. This volumetric measurement is essential for the next step, which is density calculation.

Kerosene

Kerosene is a clear liquid commonly used as a fuel, but it also serves as an exceptional medium for certain experimental purposes in the lab. One key reason kerosene is chosen for this experiment is that it does not dissolve ionic salts, such as those formed by potassium compounds.

This feature ensures that the mass and form of the solid remain unchanged during the experiment. Additionally, kerosene's own density has little effect in altering the results of volume displacement. Consequently, it accurately reflects the solid's volume, serving as an inert medium that maintains the integrity of the solid being tested.

Identification of Compounds

Identification of compounds through density is a practical technique in chemistry. Density serves as a physical property that is unique to each compound, providing a clear basis for comparison.

• First, calculate the density of the unknown solid using \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\).
• Next, compare the computed density with standard reference densities of known substances.

The precision of the density calculation stems from accurate mass and volume measurements. In the exercise, by calculating the density as \(2.77 \, \text{g/cm}^3\), we deduce that the compound is potassium bromide (KBr), since its density of \(2.75 \, \text{g/cm}^3\) closely matches the calculated value.