Question

A student breaks a thermometer and spills most of the mercury (Hg) onto the floor of a laboratory that measures \(15.2 \mathrm{~m}\) long, \(6.6 \mathrm{~m}\) wide, and \(2.4 \mathrm{~m}\) high. (a) Calculate the mass of mercury vapor (in grams) in the room at \(20^{\circ} \mathrm{C}\). The vapor pressure of mercury at \(20^{\circ} \mathrm{C}\) is \(1.7 \times 10^{-6}\) atm. (b) Does the concentration of mercury vapor exceed the air quality regulation of \(0.050 \mathrm{mg} \mathrm{Hg} / \mathrm{m}^{3}\) of air? (c) One way to deal with small quantities of spilled mercury is to spray sulfur powder over the metal. Suggest a physical and a chemical reason for this action.

Short answer

The mass of mercury vapor is 3.4 g; the concentration exceeds safe levels. Sulfur minimizes evaporation and forms stable HgS.

Step-by-step solution

Calculate the volume of the room

The volume of the room is determined by the formula for volume of a rectangular prism: \( V = \, \text{length} \times \text{width} \times \text{height} \). Substituting the given dimensions, \( V = 15.2 \, \text{m} \times 6.6 \, \text{m} \times 2.4 \, \text{m} = 240.768 \, \text{m}^3 \).

Convert volume to liters

Because gases are usually measured in liters when using the ideal gas law, convert the room volume in cubic meters to liters.\( 1 \, \text{m}^3 = 1000 \, \text{L} \), so the volume of the room is \( 240.768 \, \text{m}^3 \times 1000 \, \text{L/m}^3 = 240768 \, \text{L} \).

Apply Ideal Gas Law to find moles of Hg vapor

Using the ideal gas law \( PV = nRT \), rearrange to solve for \( n \), the number of moles: \( n = \frac{PV}{RT} \).Given values: \( P = 1.7 \times 10^{-6} \, \text{atm} \), \( V = 240768 \, \text{L} \), \( R = 0.0821 \, \text{L} \cdot \text{atm} / (\text{K} \cdot \text{mol}) \), and \( T = 293.15 \text{K} \) \((20^\circ C + 273.15)\).Calculate \( n = \frac{(1.7 \times 10^{-6}) \times 240768}{0.0821 \times 293.15} \approx 0.016949 \text{ moles} \).

Convert moles of Hg to grams

The molar mass of Hg is approximately 200.59 g/mol. Thus, the mass is \( 0.016949 \times 200.59 \approx 3.4 \text{ grams} \).

Analyze air quality regulation

Determine the concentration of mercury vapor in the room by converting the mass of mercury from grams to mg: \( 3.4 \, \text{g} \) is equivalent to \( 3400 \, \text{mg} \).Calculate concentration: \( \frac{3400 \, \text{mg}}{240.768 \, \text{m}^3} \approx 14.12 \, \text{mg/m}^3 \). The air quality regulation limit is \( 0.050 \, \text{mg/m}^3 \), so the concentration exceeds the limit.

Physical reason for using sulfur

Sulfur physically coats and covers the mercury droplets, minimizing the evaporation of mercury into the air, thus limiting exposure.

Chemical reason for using sulfur

Chemically, sulfur reacts with mercury to form mercury sulfide (HgS), which is a stable compound, preventing mercury from vaporizing and reducing the hazard.

Key concepts

Ideal Gas Law

The Ideal Gas Law connects pressure, volume, temperature, and amount of a gas in moles. It is represented by the equation \( PV = nRT \), where:

• \( P \) is the pressure of the gas.
• \( V \) is the volume the gas occupies.
• \( n \) is the number of moles of the gas.
• \( R \) is the universal gas constant \( (0.0821 \, \text{L} \cdot \text{atm} / \text{K} \cdot \text{mol}) \).
• \( T \) is the temperature in Kelvin.

For this specific exercise, the Ideal Gas Law helps determine the number of moles of mercury vapor in a laboratory room. By calculating the moles, we can further convert it into mass. This highlights its critical role in evaluating the concentration and understanding how gases behave under different conditions in enclosed spaces.
It demonstrates the versatility of the Ideal Gas Law in practical scenarios like assessing air quality.

Vapor Pressure

Vapor pressure describes the pressure exerted by the vapor above a liquid in a closed system at equilibrium.

• It indicates how volatile a substance is. The higher the vapor pressure, the more volatile the substance.
• In the case of mercury, its vapor pressure at \(20^{\circ} \text{C}\) is \(1.7 \times 10^{-6} \) atm.

This means even at room temperature, some mercury turns into gas and exerts pressure in the air. Understanding vapor pressure is essential in assessing how much of a liquid can transition into vapor,
as this impacts both environmental and health considerations. It's especially vital with mercury due to its toxic nature, as even small amounts in vapor form can pose significant health risks.

Air Quality Regulation

Air quality regulations exist to protect human health by setting limits on pollutants, including mercury vapor. In our exercise,

• The permissible limit for mercury vapor concentration is \(0.050 \, \text{mg/m}^3\).
• After calculations, the concentration in the room was \(14.12 \, \text{mg/m}^3\).

This value significantly exceeds the limit, indicating a serious safety hazard. Such concentrations can lead to mercury poisoning, affecting the brain and kidneys. These regulations help minimize the risk of exposure, emphasizing the importance of proper containment and clean-up procedures in laboratory incidents.
Understanding these limits guides education on safe handling of materials like mercury.

Mercury Sulfide

Mercury sulfide (HgS) formation is a crucial safety measure when dealing with mercury spills. It is achieved by using sulfur:

• Physical Reason: Sulfur covers mercury droplets, reducing their surface area and preventing them from evaporating further.
• Chemical Reason: Sulfur chemically reacts with mercury to form mercury sulfide. This compound is both stable and insoluble, significantly reducing the amount of harmful mercury vapor in the air.

This approach not only decreases immediate health risks but also simplifies the cleanup process. Mercury sulfide effectively immobilizes mercury, making it a preferred method in reducing toxic exposure.
Both the physical and chemical properties of sulfur provide a comprehensive solution to mercury spills, ensuring safer environments in laboratories.