Convert the following temperatures to degrees Celsius: (a) \(77 \mathrm{~K}\), the boiling point of liguid nitrogen, (b) \(4.2 \mathrm{~K},\) the boiling point of liquid helium, (c) \(601 \mathrm{~K},\) the melting point of lead.

Understanding how to switch between Kelvin (K) and Celsius (°C) is crucial in chemistry, as it allows scientists and students to navigate between these scales which are used for different purposes. The Kelvin scale is an absolute thermodynamic temperature scale that starts at absolute zero, which is the theoretical absence of all thermal energy, and is widely used in scientific contexts. The Celsius scale, however, is typically used in everyday life and it is related with degrees that are more palpable for day-to-day temperatures.

The formula for converting Kelvin to Celsius is quite straightforward: \( C = K - 273.15 \). When using this formula, keep in mind that you're subtracting the numerical value of absolute zero in Celsius from the Kelvin temperature. So, for example, converting 77 K to Celsius would involve computing \( 77 K - 273.15 \), which results in an equivalent temperature on the Celsius scale.

Always ensure your calculations are accurate and consider using a calculator for the subtraction to avoid errors. This conversion helps in understanding temperature comparisons in chemistry, such as assessing the boiling or melting points of substances.

The boiling point of an element is a fundamental physical property that signifies the temperature at which the substance transitions from liquid to gas. It's a critical parameter in many applications including distillation processes, material science, and understanding the environmental behavior of chemicals.

Different elements have widely varying boiling points, which are influenced by molecular structure and intermolecular forces. For instance, liquid nitrogen boils at 77 K, which after conversion to the Celsius scale showcases as a very cold temperature, reflecting nitrogen's significant use in cryogenics and refrigeration. Comparatively, liquid helium has a much lower boiling point at just 4.2 K, indicative of its status as a liquid only at extremely low temperatures and its importance in supercooling applications, such as in MRI machines.

Knowing an element's boiling point is essential for safe and efficient chemical handling and storage. It also helps in designing experimental setups where temperature control is paramount. In advanced studies, boiling points can be used to infer molecular characteristics and the strength of intermolecular attractions in different substances.

The melting point is yet another critical physical property of elements and compounds, indicating the temperature at which a solid becomes a liquid. For lead (Pb), this temperature is important to note because of its usage in batteries, solder, and radiation shielding, among various other applications.

The melting point of lead is 601 K, which shows it is relatively low compared to other metals. This is one of the reasons lead was historically used in pipes and is easily moldable for various applications. When we convert this Kelvin temperature into Celsius, we use the same formula as before, \( C = K - 273.15 \) leading us to find that lead melts at about 327.85 °C.

Understanding lead's melting point helps in metallurgy and material science, as it impacts how lead and its alloys are processed and used. Additionally, this knowledge is necessary when considering the safety precautions required when working with lead as it relates to smelting and casting processes.