Boyles law: PV=K, P1V1=P2V2

Boyles law

• Boyle’s law states that the pressure of an ideal gas increases as its container volume decreases.
• The volume of an ideal gas is inversely proportional to its absolute pressure at a constant temperature.

Equation

PV = K

Where

P = pressure

V = Volume

K Is the constant

To find pressure or volume, the equation becomes

Pi Vi = Pf Vf

Pi = initial pressure of the gas

Vi = initial volume of the gas

Pf = Final pressure

Vf = Final volume

Example. 1

A tank of volume 250 L, is evacuated and connected to a 50 L  bulb filled with air. When the two are joined, the air pressure inside the bulb drops to 2.20 atm, while the temperature remains the same. Find the initial pressure In the 50L bulb

Solution

In this sample question, we are provided with the initial volume of the bulb, final volume, and final pressure.

Pi Vi = Pf Vf

P initial = ?

V initial = 50 L

P final = 2.20 atm

V final = (50L +250L) = 300 L

We can make P initial the subject of the formula as follows

Pi * 50 = (2.2 * 300)

Pi = (2.2 *300) / 50

Pi = 13.2 atm

The initial pressure of the 50 L bulb is 13.2 atm

Gas Laws and Formulas

Boyle’s Law

Formula: The formula for Boyle’s Law is P₁V₁ = P₂V₂.

Units of Temperature

Three units of temperature are Kelvin (K), Celsius (°C), and Fahrenheit (°F).

Problem-Solving with Gas Laws (GUESS)

GUESS Steps:

• Given: Identify what is given in the problem.
• Unknown: Determine what the problem is asking for.
• Equation: Select the appropriate gas law equation.
• Setup: Rearrange the equation and plug in the values.
• Solve: Perform the calculations to find the unknown.

Temperature Symbol

The symbol for temperature is “T.”

Direct and Inverse Proportions

• Direct Proportions: When one variable increases, the other increases.
• Inverse Proportions: When one variable increases, the other decreases.

Charles’ Law

Formula: The formula for Charles’ Law is V₁/T₁ = V₂/T₂.

Constant in Boyle’s Law

In Boyle’s Law, temperature (T) is constant.

Real Gas Law

Another name for the real gas law is Van der Waal’s equation.

Combined Gas Law

Formula: The formula for the combined gas law is P₁V₁/T₁ = P₂V₂/T₂.

Number of Moles Symbol

The symbol for the number of moles is “n.”

Ideal Gas Law Constant Change

The ideal gas law constant (R) can change if the units for pressure or volume change.

Dalton’s Law

Formula: The formula for Dalton’s Law is Pt = P₁ + P₂ + P₃ + … (the total pressure of a gas is the sum of the partial pressures of each gas in the mixture).

Diffusion and Example

Definition: Diffusion is the spreading of molecules from a high concentration to a low concentration. Example: The scent of air freshener or perfume spreading across a room.

Moles of Gas at STP

There are 22.4 liters in a mole of gas at Standard Temperature and Pressure (STP).

Combined Gas Law Constant Factor

In a combined gas law problem, one factor (pressure, temperature, volume, or amount) is held constant.

Use of STP in Gas Law Problems

STP is used when givens are estimated for a gas.

Ideal Gases in Gas Law Problems

Ideal gases are used to simplify gas law calculations, negating molecular attraction and molecular volume effects.

Solution Definition

A solution is a homogeneous mixture of substances.

Dalton’s Law in Gas Mixtures

Relevance: Dalton’s Law states that the total pressure exerted by a gas is equal to the sum of the partial pressures of each gas in the mixture.

Water Vapor in Gas Law Calculations

Nature: Water vapor is a gas formed by water particles in the air. Consideration: It is considered when determining the pressure of a “dry” gas using Dalton’s Law.

Van der Waals Equation

Purpose: Van der Waal’s equation account for deviations from ideal behavior in real gases.

Ideal Gas Formula Units

When working with the ideal gas formula, volume should be in liters (L), and temperature should be in Kelvin (K).