Which of the following measurements correctly represents the pressure of a gas?

Introduction / Context:
Gas properties are often described by variables such as pressure, temperature, and density. Each property has its own appropriate units. Being able to recognise which units correspond to which physical quantity is crucial when working with gas laws like Boyle law and Charles law. This question asks you to identify which of the given measurements represents the pressure of a gas, as opposed to its temperature or density.

Given Data / Assumptions:

• We are considering standard physical quantities: pressure, temperature, and density.
• Units given include millimetres of mercury (mm Hg), kelvin (K), and grams per cubic centimetre (g/cm^3).
• We assume familiarity with common units used in gas law problems.
• We look for the unit that is traditionally used for pressure.

Concept / Approach:
Pressure is defined as force per unit area and in the context of gases is often measured in units such as pascals (Pa), atmospheres (atm), bar, or millimetres of mercury (mm Hg). Temperature is measured in degrees Celsius or kelvin (K), and density is measured as mass per unit volume, for example in g/cm^3 or kg/m^3. Therefore, among the given units, mm Hg is the one that corresponds to pressure, K to temperature, and g/cm^3 to density. The correct measurement for gas pressure among the options is the one expressed in mm Hg.

Step-by-Step Solution:
Step 1: Recall that pressure in gas law problems is often given in atmospheres, kilopascals, or millimetres of mercury. Step 2: Recognise that 1 atmosphere is equal to 760 mm Hg at standard conditions, establishing mm Hg as a pressure unit. Step 3: Identify that kelvin (K) is the SI unit of absolute temperature, not pressure. Step 4: Recognise that grams per cubic centimetre (g/cm^3) measures mass per unit volume, which is density, not pressure. Step 5: Therefore, the measurement 450 mm Hg represents gas pressure, while the other values represent different physical quantities.

Verification / Alternative check:
Practical examples include blood pressure readings, which are often given in mm Hg (for example, 120/80 mm Hg), and barometer readings reporting atmospheric pressure in mm Hg. Gas law calculations in chemistry often convert between atm and mm Hg using the relation 1 atm = 760 mm Hg. Temperature in kelvin appears in the ideal gas law PV = nRT, but here K clearly labels temperature. Density units like g/cm^3 are used in discussions of mass and volume relationships, confirming that these units do not represent pressure.

Why Other Options Are Wrong:
315 K: Kelvin is a unit of temperature and is used to measure how hot or cold a gas is, not how much force it exerts per unit area. 251 g/cm^3: Grams per cubic centimetre is a unit of density, describing how much mass is contained in a given volume. None of the above: This would be correct only if none of the choices represented pressure, but 450 mm Hg clearly does, so this option is wrong.

Common Pitfalls:
Students may sometimes rely on the magnitude of the number rather than the unit, thinking a large number always indicates pressure or energy. Always focus on the units, not just the numerical value. Another common confusion is between atmosphere as a physical environment and atmosphere as a unit of pressure. Remember that millimetres of mercury were historically used in barometers to measure atmospheric pressure, which helps connect the unit mm Hg with the concept of gas pressure.

Final Answer:
The measurement that describes the pressure of a gas is 450 mm Hg.