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 \(1.7 \times 10^{-6} \mathrm{~atm} .\) (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 treat small quantities of spilled mercury is to spray sulfur powder over the metal. Suggest a physical and a chemical reason for this action.

The ideal gas law is a cornerstone of chemical and physical sciences that relates pressurized gases to their volume, temperature, and the amount of gas present. A common formula representing this relationship is \( PV = nRT \), where \(P\) stands for pressure, \(V\) is volume, \(n\) signifies the number of moles of gas, \(R\) is the universal gas constant, and \(T\) is the absolute temperature in Kelvin.
When dealing with a mercury spill in a lab, as described in our exercise, the ideal gas law is utilized to calculate the mass of mercury vapor in the air. By substituting and rearranging the ideal gas law equation, we can find the mass \(m\) of the vapor as it relates to other measurable quantities: \(m = PMV / RT\).
Practical application of this law is essential not only in academic exercises but also in industries and laboratories, to ensure that conditions remain safe and controlled.

Vapor pressure is a term that describes the pressure exerted by a vapor in equilibrium with its solid or liquid phase at a given temperature. It is an indication of a liquid's evaporation rate and an important factor when calculating the saturation level of a vapor in an environment, such as in closed spaces like the lab scenario presented.
For mercury, which is the subject of our example, the vapor pressure at \(20^\circ C\) is given as \(1.7 \times 10^{-6} atm\), a relatively low pressure reflecting that mercury does not easily evaporate into the air at room temperature. However, any significant level of mercury vapor in the air poses a health hazard, reinforcing the need for accurate calculations as part of safety protocols.

Air quality regulations are guidelines established to protect the health and safety of the public by limiting the concentration of pollutants in the air we breathe. In our exercise, the regulation in question limits the mercury vapor concentration to \(0.050 mg/m^3\). Understanding and applying this standard is crucial, as it dictates whether the conditions post-spill are hazardous.
By using the mercury mass calculated through the ideal gas law, and then determining the concentration, we can assess the safety of the air in the lab. Professionals in fields such as environmental health, industrial hygiene, and chemical manufacturing must be adept at such calculations to ensure compliance with these critical safety regulations.

The treatment of chemical spills, such as mercury, requires both immediate and carefully planned actions to mitigate risks. In the scenario presented, sulfur powder is suggested as a remedy. This method physically separates mercury from the environment, reducing its availability to react with the air or be inhaled. It is an efficient way to tackle small spills, making them less volatile and easier to clean.
The choice of sulfur among other possible agents is primarily due to its chemical reactivity with mercury. A practitioner faced with a spill must have a deep understanding of such reactive properties to select the most effective treatment method.

The reaction between mercury and sulfur is both a physical and chemical process, as indicated in the exercise. Physically, applying sulfur powder increases the contact area, enabling a faster reaction with the spilled mercury. Chemically, the combination of sulfur and mercury forms mercury(II) sulfide, which is solid and non-volatile, minimizing further vaporization of mercury.
This reaction not only contains the spill but also facilitates the conversion of a toxic vapor into a more stable compound, which is safer to handle and dispose of. Those working with mercury must be informed about this remediation strategy to effectively address accidental releases.