The density of a gas of unknown molar mass was measured as a function of pressure at 0 C, as in the table that follows. (b) Why is d>P not a constant as a function of pressure?

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Step 1: Observe the graph provided, which shows the relationship between d/P (density divided by pressure) and pressure (P) for a gas at 0°C.

Step 2: Note that the y-axis represents d/P in units of g/(atm·L) and the x-axis represents pressure (P) in units of atm.

Step 3: Identify that the graph shows a non-linear relationship, indicating that d/P is not constant as pressure increases.

Step 4: Understand that according to the ideal gas law (PV = nRT), for an ideal gas, the density (d) should be directly proportional to pressure (P) at constant temperature, making d/P a constant value.

Step 5: Conclude that the deviation from a constant d/P value suggests that the gas does not behave ideally at higher pressures, likely due to intermolecular forces and the finite volume of gas molecules.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law (PV=nRT) relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas. It assumes that gas particles do not interact and occupy no volume, which is a good approximation under many conditions. Understanding this law is crucial for analyzing gas behavior, especially when considering how density changes with pressure.

Density and Molar Mass Relationship

Density (d) is defined as mass per unit volume (d = m/V). For gases, density can also be expressed in terms of molar mass (M) and the Ideal Gas Law. The relationship shows that density is directly proportional to molar mass and inversely proportional to temperature and pressure, which is essential for understanding why d/P varies with pressure.

Real Gas Behavior

Real gases deviate from ideal behavior at high pressures and low temperatures due to intermolecular forces and the volume occupied by gas particles. This deviation can lead to non-constant relationships between density and pressure, as seen in the provided graph. Recognizing these deviations is important for interpreting experimental data and understanding gas properties under varying conditions.

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Textbook Question

The density of a gas of unknown molar mass was measured as a function of pressure at 0 C, as in the table that follows. (a) Determine a precise molar mass for the gas. [Hint: Graph d>P versus P.]

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