This question involves analyzing multiple statements about gas behavior and identifying which one is correct. The images likely depict different gas law relationships or graphical representations. Since the exact images cannot be displayed here, the core concept revolves around understanding the fundamental gas laws and their graphical interpretations.

Core Concept: Graphical Representation of Gas Laws

The behavior of an ideal gas is described by several laws, each showing a relationship between two variables while keeping others constant. These relationships are often represented graphically.

Boyle's Law

At constant temperature (T) and amount of gas (n), the pressure (P) of a gas is inversely proportional to its volume (V).

Equation: $P \propto \frac{1}{V}$ or $P V = k$ (constant)

Graph: A plot of P vs. V is a hyperbola. A plot of P vs. 1/V is a straight line passing through the origin.

Charles's Law

At constant pressure (P) and amount of gas (n), the volume (V) of a gas is directly proportional to its absolute temperature (T).

Equation: $V \propto T$ or $\frac{V}{T} = k$ (constant)

Graph: A plot of V vs. T (°C) is a straight line that intersects the temperature axis at -273.15 °C. A plot of V vs. T (K) is a straight line passing through the origin.

Gay-Lussac's Law (Pressure-Temperature Law)

At constant volume (V) and amount of gas (n), the pressure (P) of a gas is directly proportional to its absolute temperature (T).

Equation: $P \propto T$ or $\frac{P}{T} = k$ (constant)

Graph: A plot of P vs. T (°C) is a straight line that intersects the temperature axis at -273.15 °C. A plot of P vs. T (K) is a straight line passing through the origin.

Avogadro's Law

At constant temperature (T) and pressure (P), the volume (V) of a gas is directly proportional to the number of moles (n).

Equation: $V \propto n$ or $\frac{V}{n} = k$ (constant)

Graph: A plot of V vs. n is a straight line passing through the origin.

Combined and Ideal Gas Law

These individual laws combine to form the ideal gas equation.

Equation: $P V = n R T$

This equation can be rearranged to show how any one variable depends on the others. For example, a plot of P vs. T at constant V and n should be a straight line.

How to Approach This Question

To identify the correct statement from the images:

Step 1: Examine each graph carefully. Identify the variables on the x-axis and y-axis.

Step 2: Recall the expected shape of the graph for that particular relationship between the two variables, assuming ideal gas behavior.

Step 3: Check if the graph matches the theoretical prediction. For instance, a P vs. V graph must be hyperbolic, not linear. A V vs. T graph in Kelvin must be a straight line through the origin.

Step 4: The correct statement will be the one where the graph accurately represents a valid gas law.

Step 5: Be cautious of graphs that use Celsius instead of Kelvin for temperature-dependent laws, as they will not pass through the origin.

Related Topics & Formulae

Ideal Gas Equation: $P V = n R T$

Density of a Gas: $ρ = \frac{P M}{R T}$ , where M is the molar mass.

Dalton's Law of Partial Pressures: $P_{total} = P_{1} + P_{2} + P_{3} + \dots$

Graham's Law of Effusion: $\frac{r_{1}}{r_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}$