Problem 71 - Chemistry and Chemical Reactivity

Question

Chlorine dioxide, \(\mathrm{ClO}_{2},\) reacts with fluorine to give a new gas that contains \(\mathrm{Cl}\), \(\mathrm{O}\), and \(\mathrm{F}\). In an experiment, you find that \(0.150 \mathrm{g}\) of this new gas has a pressure of \(17.2 \mathrm{mm}\) Hg in a \(1850-\mathrm{mL}\). flask at \(21^{\circ} \mathrm{C} .\) What is the identity of the unknown gas?

Step-by-Step Solution

Answer

The unknown gas is likely \(\mathrm{ClO}_2\mathrm{F}_2\) (dichlorine dioxide difluoride).

Step 1: Convert Pressure to Atmospheres

To solve this problem, first, convert the pressure from mm Hg to atmospheres. We know that 1 atm = 760 mm Hg. Therefore, \(17.2\) mm Hg can be converted to atm by dividing by 760: \[\text{Pressure in atm} = \frac{17.2}{760} \approx 0.0226 \, \text{atm}.\]

Step 2: Convert Volume to Liters

Next, convert the volume from mL to liters. Since 1 L = 1000 mL, divide the volume by 1000: \[\text{Volume in L} = \frac{1850}{1000} = 1.85 \, \text{L}.\]

Step 3: Convert Temperature to Kelvin

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \[\text{Temperature in K} = 21 + 273.15 = 294.15 \, \text{K}.\]

Step 4: Use the Ideal Gas Law

Apply the ideal gas law to find the molar mass of the gas. The ideal gas law is \(PV = nRT\), where \(n\) is the number of moles. Rearrange to solve for \(n\): \[n = \frac{PV}{RT}.\] Use \(R = 0.0821 \, \text{L} \, \text{atm/mol} \, \text{K}\). Substitute the values: \[n = \frac{0.0226 \, \text{atm} \times 1.85 \, \text{L}}{0.0821 \, \text{L} \, \text{atm/mol} \, \text{K} \times 294.15 \, \text{K}} \approx 0.00173 \, \text{mol}.\]

Step 5: Calculate Molar Mass

Knowing the mass and the number of moles of the gas, calculate its molar mass: \[\text{Molar Mass} = \frac{\text{Mass}}{n} = \frac{0.150 \, \text{g}}{0.00173 \, \text{mol}} \approx 86.71 \, \text{g/mol}.\]

Step 6: Identify the Gas

The molar mass of the unknown gas is approximately 86.71 g/mol. Based on the composition \((\mathrm{ClO}_2 \, \text{and} \, \mathrm{F}\)) and known molar masses, the gas is likely \(\mathrm{ClO}_2\mathrm{F}_2\) (dichlorine dioxide difluoride), which has a molar mass of approximately 86.45 g/mol.

Key Concepts

Chlorine Dioxide

Chlorine dioxide, represented as \( \text{ClO}_2 \), is a chemical compound composed of one chlorine atom and two oxygen atoms. It's a yellow to reddish-yellow gas that is known for its bleaching and disinfecting properties. Chlorine dioxide is not naturally occurring, meaning it is generally created through chemical reactions.

• Stable compound that acts as an oxidizing agent.
• Used in water treatment and as a disinfectant.

Its unique properties make it a valuable compound in many industries, but care must be taken due to its reactive nature, especially with other chemicals. Understanding its chemical behavior is crucial when manipulating chlorine dioxide, as its reactions can lead to different substances with varied properties, such as its potential to react with elements like fluorine.

Molar Mass Calculation

Calculating the molar mass of a compound is an essential part of chemistry, helping to identify and understand the composition of various substances. The molar mass is quantified as the sum of the average atomic masses of all atoms in a molecule, expressed in grams per mole (g/mol).

• To calculate, add up the atomic weights of all constituent atoms.
• Atomic weights can be found on the periodic table.

For example, to find the molar mass of \( \text{ClO}_2 \), you would add the atomic masses of two oxygen atoms and one chlorine atom. These calculations are critical, as they allow chemists to weigh accurate amounts of substances for reactions. In exercises dealing with gasses, like our example, knowing the molar mass is integral to using the Ideal Gas Law correctly. This assists in situations where identification of an unknown substance is required, as demonstrated when dichlorine dioxide difluoride was identified in the exercise.

Chemical Reactions with Fluorine

Fluorine, a highly reactive halogen, often engages in energetic reactions, especially with other halogens or compounds like chlorine dioxide. Understanding how fluorine reacts is vital for predicting the outcomes and potential products of such interactions.

• Fluorine is the most reactive and electronegative element.
• It forms compounds by gaining electrons from other elements.

When chlorine dioxide reacts with fluorine, the small, reactive fluorine atoms can form bonds with both chlorine and oxygen, producing new compounds such as dichlorine dioxide difluoride. Such products often display unique properties different from their components. Recognizing the potential reactions with fluorine can enlighten the comprehension of chemical behavior and synthesis of new materials, reinforcing the knowledge you'll apply in identifying substances through experiments like those outlined in our exercise.