A gas at \(25.0{ }^{\circ} \mathrm{C}\) occupies a volume of \(5.00\) gallons and exerts a pressure of \(755 \mathrm{~mm} \mathrm{Hg}\). Express (a) the temperature of the gas in Kelvin, (b) the volume of the gas in liters, and (c) the pressure of the gas in atmospheres.

Grasping the Kelvin temperature conversion is a fundamental aspect of gas-related calculations in chemistry. To convert Celsius to Kelvin, the process is straightforward: add 273.15 to the Celsius temperature. This is because the Kelvin scale is an absolute scale based on theoretical absolute zero, which is -273.15°C.

This means for our example, converting a temperature of 25.0°C entails the following calculation:
\[T_K = 25.0\,^\circ C + 273.15 = 298.15\,K\]
Understanding this conversion allows students to work with the ideal gas law and other thermodynamic equations that require temperature in Kelvin units.

When dealing with gas volume, converting between gallons and liters is a frequent task. It is essential to remember that volume conversions rely on a fixed conversion factor: 1 gallon is equivalent to 3.78541 liters. Therefore, to convert the volume from gallons to liters, multiply the number of gallons by 3.78541.

Here's the application of this conversion:
\[V_L = 5.00\,\text{gallons} \times 3.78541 = 18.92705\,\text{liters}\]
The precision of your conversion may vary depending on the required significant figures or the precision of the measurement tools you're using. However, for most educational purposes, rounding the converted volume to the nearest hundredth is often sufficient, resulting in approximately 18.93 liters in this case.

Pressure conversion is a crucial skill in various scientific fields, especially chemistry, where pressure plays a role in gas laws and equilibria. The conversion factor between millimeters of mercury (mmHg) and atmospheres (atm) is 760 mmHg to 1 atm, which represents the standard atmospheric pressure at sea level.

In our exercise, converting 755 mmHg to atmospheres is performed as follows:
\[P_{atm} = \frac{755\,\text{mmHg}}{760} = 0.99342\,\text{atm}\]
This simple division allows the transformation of pressure values, commonly measured in mmHg by instruments such as the mercury barometer, into the atmospheres unit often used in scientific equations. However, remember that while we often round pressure to two decimals for ease of use, precise calculations in laboratory settings may require more significant figures for accuracy.