Total Pressure, Partial Pressure, and Real vs. Ideal Gases

Comprehensive practice flashcards covering total pressure, partial pressure, Dalton's law, gas collection over water, ideal vs. real gas behavior, the compressibility factor, and the Van der Waals equation of state.

What happens when multiple non-reacting gases are placed together inside a single container?

Each gas diffuses to occupy the entire volume of the container, and its particles move in continuous random motion, colliding with the container walls almost independently.

Why are non-reacting gases in a mixture able to act independently as if each were alone in the container?

Because of the absence of attractive or repulsive forces between the particles, and the fact that they do not react chemically with each other.

What is the definition of total pressure ($P_{\text{Total}}$) of a gas mixture?

The sum of the partial pressures of all non-reacting gases in the mixture, representing the total force exerted by gas particle collisions on the container walls.

What is the definition of partial pressure ($P_i$) of a component gas in a mixture?

The pressure each component gas would exert if it alone occupied the same volume as the mixture.

What does Dalton's law of partial pressures state?

Under constant volume and temperature, the total pressure of a gas mixture is equal to the sum of the partial pressures of its component gases: $P = P_1 + P_2 + P_3 + \dots$

Why is the idea that 'the largest gas molecule creates the highest pressure' a misconception?

Gas pressure depends mainly on the number of gas particles (molecules), not on the size of the molecules.

Why does a scuba diver breathe a mixture of oxygen and nitrogen instead of pure oxygen?

Oxygen is necessary for life, while nitrogen affects the total pressure; changing the ratio of gases alters the pressure effects exerted on the diver's body (lungs).

What is mole fraction ($X_i$) and how is it defined mathematically for gas A in a mixture with gas B?

The ratio of the amount of substance ($n$) of a component gas to the total amount of substance of the mixture: $X_A = \frac{n_A}{n_A + n_B}$.

Why is mole fraction unitless, and why is its value always less than $1$ in a gas mixture?

It is unitless because it is a ratio between two quantities of the same type ($\text{mol}$). It is less than $1$ because it represents a part-to-whole ratio, meaning the value of the part is less than one integer.

What is the sum of the mole fractions of all gases present in any gas mixture?

The sum of all mole fractions in a mixture is always equal to $1$.

How is the partial pressure ($P_i$) of a component gas calculated from total pressure ($P_{\text{Total}}$) and mole fraction ($X_i$)?

$$P_i = P_{\text{Total}} \times X_i$$

Based on this relationship triangle, what are the three algebraic formulas connecting partial pressure ($P_i$), mole fraction ($X_i$), and total pressure ($P_{\text{Total}}$)?

$P_i = X_i \times P_{\text{Total}}$, $X_i = \frac{P_i}{P_{\text{Total}}}$, and $P_{\text{Total}} = \frac{P_i}{X_i}$.

At constant temperature and volume, what is the mathematical relationship between the partial pressures and amounts of substance of two component gases?

$$\frac{n_A}{n_B} = \frac{P_A}{P_B}$$

At constant temperature and pressure, what is the relationship between the individual volumes and amounts of substance of two extracted component gases?

$$\frac{n_A}{n_B} = \frac{V_A}{V_B}$$

Under identical conditions of volume and temperature, which of these containers contains the gas with the highest pressure, and why?

Container (C), because it contains the largest number of molecules ($P \propto n$), and pressure depends on the number of particles rather than molecule size.

What is the formula used to calculate the average relative molecular mass ($M_r$) of a gas mixture?

$$M_r(\text{mixture}) = (X_1 \times M_1) + (X_2 \times M_2) + (X_3 \times M_3) + \dots$$

How is the partial pressure of each gas determined after opening a stopcock connecting two rigid containers at constant temperature?

By applying Boyle's law to each gas individually using the combined total volume: $P_1 V_1 = P_2 V_{\text{Total}}$, where $V_{\text{Total}} = V_1 + V_2$.

When collecting a gas over water, why must the vapour pressure of water be subtracted from the total pressure to find the pressure of the pure gas?

Because the trapped gas mixture contains both the collected gas and water vapour; thus, $P_{\text{gas}} = P_{\text{Total}} - P_{H_2O}$.

What condition must be met for the total pressure of gas collected in an inverted measuring cylinder over water to equal atmospheric pressure ($P_{\text{atm}}$)?

The water levels inside and outside the collection container must be equalized ($P_{\text{atm}} = P_{\text{Total}}$).

What happens to the total pressure and to the partial pressures of existing gases when a new gas is introduced into a rigid container at constant temperature?

The total pressure increases, while the partial pressures of the remaining original gases stay unaffected.

How can the partial pressure of a gas be calculated from its percentage in a mixture and the total pressure?

$$P_i = \left(\frac{\text{Percentage (\%)}}{100}\right) \times P_{\text{Total}}$$

What are the core assumptions that define an ideal gas?

1. Molecular volume is negligible relative to the container volume. 2. No intermolecular attractive or repulsive forces exist. 3. Molecules move in continuous random motion. 4. Molecular collisions are completely elastic (no kinetic energy lost). 5. It strictly obeys $PV = nRT$.

Under what two conditions do real gases behave most like an ideal gas?

At very low pressure and high temperature.

What are the two main reasons real gases deviate from ideal gas behaviour?

1. Intermolecular attractive and repulsive forces exist between real molecules. 2. Real gas molecules possess a finite, non-negligible molecular volume.

How is the compressibility factor ($Z$) defined mathematically, and what is its value for an ideal gas?

$Z = \frac{PV}{nRT} = \frac{V_{\text{Real}}}{V_{\text{Ideal}}}$. For an ideal gas, $Z = 1$.

Why does the compressibility factor become less than $1$ ($Z < 1$) at moderate pressure and low temperature?

Intermolecular attractive forces become significant, drawing molecules together and reducing the frequency and force of their collisions with the container walls; thus, observed pressure decreases and $PV < nRT$.

Why does the compressibility factor become greater than $1$ ($Z > 1$) at very high pressure?

Molecules are forced close together so that the physical volume occupied by the gas molecules themselves can no longer be neglected, making $V_{\text{Real}} > V_{\text{Ideal}}$ and $PV > nRT$.

What key trend regarding pressure and ideality is illustrated in this compressibility factor graph?

Real gases behave more ideally ($Z \rightarrow 1$) at lower pressures, and deviate increasingly from ideal behavior as pressure rises.

What relationship between temperature ($T$) and intermolecular attractive forces is illustrated by this curve?

An inversely proportional relationship; as temperature increases, molecular kinetic energy increases, which minimizes the effect of intermolecular attractive forces.

State the Van der Waals equation of state and specify what constants $a$ and $b$ correct for.

$\left(P + \frac{n^2 a}{V^2}\right)(V - nb) = nRT$, where $a$ corrects for intermolecular attractive forces and $b$ corrects for the finite volume of gas molecules.

What does a horizontal line on a plot of the product $PV$ versus pressure ($P$) indicate for an ideal gas at constant temperature?

It shows that the product of pressure and volume remains constant ($PV = \text{constant}$) regardless of pressure changes, obeying Boyle's law.