Pressure and Its Measurement

Definition and SI Unit

Pressure is defined as the force exerted per unit area by gas molecules as they collide with the surfaces of their container. The SI unit for pressure is the pascal (Pa), named after the French mathematician Blaise Pascal.

• Pressure Formula: $P = \frac{F}{A}$, where $F$ is force (in newtons) and $A$ is area (in square meters).

• Other common units: atmosphere (atm), millimeters of mercury (mmHg), and torr.

Example: If the same amount of gas is transferred from a 5.0 L container to a 10.0 L container, the pressure will decrease (assuming temperature and amount of gas are constant).

Pressure Unit Conversions

Pressure can be measured in several units. Common conversions include:

Example: Convert 24.9 inHg to mmHg and atm.

The Ideal Gas Law

Formula and Variables

The Ideal Gas Law relates the pressure, volume, temperature, and amount of gas:

$PV = nRT$

• $P$ = pressure (atm or Pa)

• $V$ = volume (L or m3)

• $n$ = amount of gas (mol)

• $R$ = gas constant

• $T$ = temperature (K)

Example: Calculate the number of moles of NH3 in a 25.0 L tank at 190°C and 5.20 atm.

Gas Constant (R)

The value of the gas constant $R$ depends on the units used:

Use the appropriate value of $R$ based on the units in your calculation.

Applications of the Ideal Gas Law

Direct and Inverse Relationships

By rearranging the Ideal Gas Law, we can establish relationships between variables:

• $P$ and $V$ are inversely proportional (Boyle's Law)

• $V$ and $T$ are directly proportional (Charles's Law)

• $P$ and $T$ are directly proportional (Gay-Lussac's Law)

• $V$ and $n$ are directly proportional (Avogadro's Law)

Example: If the number of moles is tripled at constant pressure, the volume will triple.

Chemistry Gas Laws

Boyle's Law

At constant temperature and amount of gas, the pressure and volume of a gas are inversely proportional:

$P_1V_1 = P_2V_2$

• As volume increases, pressure decreases, and vice versa.

Charles's Law

At constant pressure and amount of gas, the volume and temperature of a gas are directly proportional:

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Temperature must be in Kelvin.

Gay-Lussac's Law

At constant volume and amount of gas, the pressure and temperature of a gas are directly proportional:

$\frac{P_1}{T_1} = \frac{P_2}{T_2}$

Avogadro's Law

At constant temperature and pressure, the volume and amount (moles) of gas are directly proportional:

$\frac{V_1}{n_1} = \frac{V_2}{n_2}$

Combined Gas Law

The Combined Gas Law combines Boyle's, Charles's, and Gay-Lussac's Laws:

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

This law is useful when more than one variable changes.

Mole Fraction and Partial Pressure

Mole Fraction (X)

The mole fraction is the ratio of the moles of a component to the total moles in a mixture:

$X = \frac{n_{component}}{n_{total}}$

Example: Calculate the mole fraction of dichloromethane in a solution.

Law of Partial Pressures (Dalton's Law)

The total pressure of a mixture of gases is the sum of the partial pressures of each gas:

$P_{total} = P_{gas1} + P_{gas2} + P_{gas3} + \ldots$

Partial pressure can also be calculated using the Ideal Gas Law:

$P_{gas} = \frac{nRT}{V}$

Practice Problems and Applications

• Calculating the mass of a gas using the Ideal Gas Law.

• Determining the volume of a gas at different conditions using the Combined Gas Law.

• Converting between pressure units (atm, mmHg, torr, kPa, psi).

• Finding the partial pressure of a gas in a mixture.

• Using mole fraction to determine the composition of a gas mixture.

Summary Table: Gas Laws and Their Relationships

Additional info: These notes are based on standard General Chemistry curriculum and include both conceptual explanations and practical calculation strategies for gas laws and properties of gases.