Question

Write the ideal gas equation and also state it in words. Give the units for each term in the equation.

Short answer

The ideal gas equation is \( PV = nRT \). In words, this reads: the product of the pressure and volume of a gas is equal to the number of moles of the gas multiplied by the gas constant multiplied by the temperature. The units are: Pressure(P) in Pascal (Pa), Volume(V) in cubic meters (m³), number of moles (n) in mol, gas constant (R) in J.mol⁻¹.K⁻¹, temperature (T) in Kelvin.

Step-by-step solution

- Write down the ideal gas equation

The ideal gas equation is usually represented by \( PV = nRT \), where:\n P = Pressure,\n V = Volume,\n n = number of moles,\n R = ideal gas constant,\n T = temperature

- Express the equation in words

In words, this equation states: the product of the pressure and volume of an ideal gas is equal to the number of moles of the gas multiplied by the gas constant and the temperature.

- Identify the units for each term

In the International System unit:\n\n- The unit of pressure P is Pascal (Pa),\n- Volume V is typically expressed in cubic meters (m³),\n- Number of moles n is dimensionless but often expressed in moles (mol),\n- The universal gas constant R is given in J.mol⁻¹.K⁻¹ (Joules per mole per Kelvin),\n- The temperature T is expressed in Kelvin (K).

Key concepts

Gas Constants

The ideal gas constant, often denoted by the symbol \( R \), is a key part of the ideal gas law. This constant is universal, meaning it applies to all ideal gases. The value of \( R \) is approximately 8.314 J.mol⁻¹.K⁻¹ in the International System of Units (SI).

Knowing the gas constant enables us to relate various gas properties such as pressure, volume, and temperature. This relationship can be essential in predicting and understanding the behavior of gases under different conditions.

• The gas constant is obtained from the combination of energy units (Joules), amount of substance units (moles), and temperature units (Kelvin).
• It is used in the ideal gas equation \( PV = nRT \) to unite these various physical quantities in one comprehensive formula.

Pressure Units

Pressure in physics is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed. In gas-related calculations, pressure is a significant factor and is often measured in Pascals (Pa), which is the SI unit for pressure.

• 1 Pascal is equivalent to 1 Newton per square meter (N/m²).
• Pressure can also be expressed in other units, such as atmospheres (atm), millimeters of mercury (mmHg), or torr, depending on the context or region.

Choosing the correct units for pressure is crucial, as it directly influences the accuracy of gas law calculations.
In the ideal gas equation \( PV = nRT \), pressure must be in Pascals when using the SI value of \( R \) to ensure unit consistency and correct calculations.

Volume Measurement

Volume is the amount of space that a substance or an object occupies. For gases, the volume is typically measured in cubic meters (m³) when using the SI system, especially in scientific contexts.

The measurement of volume is vital in gas calculations as it helps us understand how much space a gas occupies under given conditions.

• In laboratory settings or other unit systems, volume might be expressed in liters (L), where 1 cubic meter equals 1000 liters.
• Accurate volume measurement is essential for precise gas calculations in the ideal gas equation \( PV = nRT \).

Correctly determining the volume allows us to predict how a gas will react to changes in other factors like pressure and temperature.

Temperature in Kelvin

Temperature is a measure of the thermal energy of a substance. In the context of the ideal gas law, temperature must be measured in Kelvin (K). This is the SI unit for temperature measurement.
Kelvin is an absolute temperature scale, meaning it starts at absolute zero—the theoretical absence of all thermal energy.

• To convert Celsius to Kelvin, simply add 273.15 to the Celsius temperature.
• An absolute measurement of temperature is crucial because it simplifies calculations and aligns with physical laws, which assume no negative temperature values.

In the equation \( PV = nRT \), temperature in Kelvin ensures consistent and accurate calculations across various gas properties.

Moles in Chemistry

A mole is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles. In chemistry, moles help to express amounts of a chemical substance.

• One mole is defined as exactly 6.02214076 × 10²³ particles, an amount known as Avogadro's number.
• In the ideal gas equation \( PV = nRT \), \( n \) represents the number of moles, which indicates how many moles of a gas are present in the reaction.

Understanding moles is essential for making quantitative predictions in chemical reactions and processes. It helps equilibrate substances in terms of the molecules or atoms involved, aligning with the principles of stoichiometry.