Stoichiometry

Gas Calculations: Molar Volume and the Ideal Gas Equation

5th Year · 6th Year (Leaving Cert)

✓By the end of this lesson students will be able to define molar volume and state its value at Standard Temperature and Pressure (STP).
✓By the end of this lesson students will be able to perform calculations involving molar volume at STP to determine the volume, moles, or mass of a gas.
✓By the end of this lesson students will be able to state the Ideal Gas Equation (PV=nRT) and identify the correct units for each variable.
✓By the end of this lesson students will be able to perform calculations using the Ideal Gas Equation to find pressure, volume, temperature, or moles of a gas (Higher Level).
✓By the end of this lesson students will be able to convert between different units of pressure and temperature for gas calculations.

Key concepts

Molar Volume

The molar volume of a gas is the volume occupied by one mole of any gas. At Standard Temperature and Pressure (STP), the molar volume of any ideal gas is 22.4 litres (dm³). This value is constant for all ideal gases under these specific conditions, regardless of the gas's identity.

Standard Temperature and Pressure (STP)

STP is a set of standard reference conditions used for comparing properties of gases. It is defined as a temperature of 0 °C (which is 273 K when converted to the absolute Kelvin scale) and a pressure of 1 atmosphere (101,325 Pascals or 101.3 kPa).

Ideal Gas

An ideal gas is a theoretical gas composed of randomly moving point particles that do not interact with each other except for elastic collisions. While no real gas is perfectly ideal, many gases behave approximately ideally under ordinary conditions of temperature and pressure. The Ideal Gas Equation describes the behaviour of an ideal gas.

Ideal Gas Equation (PV=nRT)

The Ideal Gas Equation relates the pressure, volume, temperature, and number of moles of an ideal gas. It is given by the formula PV = nRT, where: P = Pressure (usually in Pascals, Pa, or atmospheres, atm) V = Volume (usually in cubic metres, m³, or litres, dm³) n = Number of moles (mol) R = The Ideal Gas Constant (8.31 J K⁻¹ mol⁻¹ when P is in Pa and V is in m³, or 0.0821 L atm K⁻¹ mol⁻¹ when P is in atm and V is in L) T = Absolute Temperature (always in Kelvin, K). This equation is typically examined at Higher Level.

PV = nRT

Key facts to remember

1The molar volume of any ideal gas at STP is 22.4 L (dm³).
2STP (Standard Temperature and Pressure) is defined as 0 °C (273 K) and 1 atmosphere (101.3 kPa).
3The Ideal Gas Equation is PV = nRT.
4In the Ideal Gas Equation, P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the absolute temperature.
5Temperature (T) must always be in Kelvin (K) for gas calculations (T(K) = T(°C) + 273).
6Common values for the ideal gas constant R are 8.31 J K⁻¹ mol⁻¹ (when P is in Pa, V in m³) or 0.0821 L atm K⁻¹ mol⁻¹ (when P is in atm, V in L).
7Useful conversions: 1 atmosphere (atm) = 101,325 Pascals (Pa) = 101.3 kPa; 1 L = 1 dm³ = 10⁻³ m³.

Worked examples

Example 1

Calculate the volume occupied by 0.5 moles of oxygen gas at STP.

I1. Identify the given information: n = 0.5 mol, conditions are STP.

II2. Recall the molar volume at STP: 1 mole of any gas occupies 22.4 L at STP.

III3. Use the relationship: Volume = moles × molar volume.

IV4. Substitute the values: Volume = 0.5 mol × 22.4 L/mol.

Answer

11.2 L

Example 2

What mass of carbon dioxide gas (CO₂) would occupy a volume of 5.6 L at STP? (Relative atomic masses: C=12, O=16)

I1. Identify the given information: Volume = 5.6 L, conditions are STP.

II2. Recall the molar volume at STP: 1 mole of any gas occupies 22.4 L at STP.

III3. Calculate the number of moles: moles = Volume / molar volume.

IV4. Substitute the values: moles = 5.6 L / 22.4 L/mol = 0.25 mol.

V5. Calculate the molar mass of CO₂: Mᵣ(CO₂) = 12 + (2 × 16) = 44 g/mol.

VI6. Calculate the mass: Mass = moles × molar mass.

VII7. Substitute the values: Mass = 0.25 mol × 44 g/mol.

Answer

11 g

Remember to convert volume to moles first, then moles to mass.

Example 3

A sample of nitrogen gas has a volume of 10.0 L at a pressure of 2.0 atm and a temperature of 27 °C. Calculate the number of moles of nitrogen gas in the sample. (R = 0.0821 L atm K⁻¹ mol⁻¹)

I1. Identify the given information: V = 10.0 L, P = 2.0 atm, T = 27 °C.

II2. Convert temperature to Kelvin: T(K) = T(°C) + 273.15 = 27 + 273.15 = 300.15 K.

III3. State the Ideal Gas Equation: PV = nRT.

IV4. Rearrange the equation to solve for n: n = PV / RT.

V5. Substitute the values, ensuring units match the given R value: n = (2.0 atm × 10.0 L) / (0.0821 L atm K⁻¹ mol⁻¹ × 300.15 K).

Answer

0.812 mol (to 3 significant figures)

Always convert temperature to Kelvin before using the Ideal Gas Equation. Choose the value of R that matches the units of pressure and volume provided in the question.

Common mistakes

✗Forgetting to convert temperature from Celsius to Kelvin when using the Ideal Gas Equation.
✗Using inconsistent units for pressure and volume with the chosen value of the ideal gas constant (R).
✗Confusing STP conditions (0 °C, 1 atm) with other standard conditions (e.g., SATP, which is 25 °C, 1 bar).
✗Incorrectly rearranging the Ideal Gas Equation (PV=nRT) to solve for a specific variable.
✗Not converting mass to moles (or vice-versa) when required in molar volume calculations.

Exam tips

★Always write down the known values and the unknown variable before starting any calculation to help organise your thoughts.
★Pay close attention to the units given in the question and ensure they are consistent with the gas constant (R) you choose, or convert them accordingly.
★For PV=nRT calculations, the very first step should always be to convert any temperature given in Celsius to Kelvin.
★Show all your working steps clearly, as marks are often awarded for correct method even if the final answer has a minor arithmetic error.

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