To calculate pressure using the Ideal Gas Law Calculator:

1. Select the "Solve for Pressure" tab at the top of the calculator.
2. Enter the volume value and select its unit (L, mL, m³, ft³, or gal).
3. Enter the number of moles and select its unit (mol, mmol, or kmol).
4. Enter the temperature value and select its unit (K, °C, °F, or °R).
5. Click "Calculate Pressure" to see your results.

The calculator will display:

• Pressure in the selected unit
• The appropriate gas constant R used
• Step-by-step solution showing unit conversions

Example: For V = 2.5 L, n = 0.1 mol, T = 25°C, the pressure P = 0.997 atm.

The calculator supports multiple units for each variable:

Pressure (P):

• atm - atmospheres (standard)
• Pa - pascals
• kPa - kilopascals
• bar - bars
• psi - pounds per square inch
• torr - torr (mmHg)

Volume (V):

• L - liters (standard)
• mL - milliliters
• m³ - cubic meters
• ft³ - cubic feet
• gal - gallons (US)

Amount (n):

• mol - moles (standard)
• mmol - millimoles
• kmol - kilomoles

Temperature (T):

• K - Kelvin (standard)
• °C - Celsius
• °F - Fahrenheit
• °R - Rankine

The calculator automatically selects the appropriate R constant based on your unit choices.

The ideal gas law equation is:

PV = nRT

Where:

• P = Pressure of the gas
• V = Volume occupied by the gas
• n = Number of moles of gas
• R = Universal gas constant
• T = Absolute temperature (must be in Kelvin or Rankine)

Important relationships:

• At constant T and n: P₁V₁ = P₂V₂ (Boyle's Law)
• At constant P and n: V₁/T₁ = V₂/T₂ (Charles's Law)
• At constant V and n: P₁/T₁ = P₂/T₂ (Gay-Lussac's Law)
• At constant P and T: V₁/n₁ = V₂/n₂ (Avogadro's Law)

The gas constant R value depends on your unit system. Common values include:

Note: The calculator automatically selects the correct R value based on your chosen units. You don't need to memorize these values!

The ideal gas law is an approximation that works best under certain conditions:

Most accurate when:

• High temperature (well above boiling point)
• Low pressure (< 10 atm)
• Small, non-polar molecules (He, H₂, N₂)

Less accurate when:

• Near condensation conditions
• High pressure (> 50 atm)
• Large, polar molecules
• Low temperatures

Typical deviations:

• < 1 atm: Usually < 1% error
• 1-10 atm: 1-5% error
• 10-50 atm: 5-10% error
• > 50 atm: > 10% error

For more accurate results with real gases, use the van der Waals equation or other real gas equations of state.

STP (Standard Temperature and Pressure) is a reference condition for gas calculations.

Modern STP (IUPAC):

• Temperature: 273.15 K (0°C)
• Pressure: 100 kPa (0.98692 atm)
• Molar volume: 22.711 L/mol

Old STP (still commonly used):

• Temperature: 273.15 K (0°C)
• Pressure: 1 atm (101.325 kPa)
• Molar volume: 22.414 L/mol

Using STP in calculations:

Example: What volume does 2.5 mol of gas occupy at STP?

• Using old STP: V = n × 22.414 = 2.5 × 22.414 = 56.035 L
• Using IUPAC STP: V = n × 22.711 = 2.5 × 22.711 = 56.778 L

Always check which STP definition your problem uses!

Yes, you can use the calculator for gas mixtures with some considerations:

For ideal gas mixtures:

• Use total moles (n_total = n₁ + n₂ + ... + nᵢ)
• Use total pressure or calculate partial pressures
• Each gas follows PV = nRT independently

Dalton's Law of Partial Pressures:

• P_total = P₁ + P₂ + ... + Pᵢ
• Pᵢ = (nᵢ/n_total) × P_total = Xᵢ × P_total
• Where Xᵢ is the mole fraction

Example calculation:

A 5.0 L container at 25°C contains 0.1 mol N₂ and 0.2 mol O₂:

• n_total = 0.1 + 0.2 = 0.3 mol
• P_total = (0.3 × 0.08206 × 298.15) / 5.0 = 1.47 atm
• P(N₂) = (0.1/0.3) × 1.47 = 0.49 atm
• P(O₂) = (0.2/0.3) × 1.47 = 0.98 atm

Temperature must be in absolute units (Kelvin or Rankine) for the ideal gas law because:

1. Mathematical requirement:

• The ideal gas law requires T to be proportional to kinetic energy
• Absolute zero (0 K) means zero kinetic energy
• Celsius and Fahrenheit have arbitrary zero points

2. What happens with Celsius?

• At 0°C, PV ≠ 0 (gas still has pressure and volume)
• Negative Celsius values would give negative pressure (impossible!)

3. Conversion formulas:

• Celsius to Kelvin: K = °C + 273.15
• Fahrenheit to Kelvin: K = (°F + 459.67) × 5/9
• Fahrenheit to Rankine: °R = °F + 459.67

Remember: The calculator handles these conversions automatically when you select temperature units!

Avoid these common errors:

1. Temperature units:

• ❌ Using Celsius or Fahrenheit directly
• ✅ Converting to Kelvin or Rankine first

2. Unit mismatch:

• ❌ Mixing units without proper R value
• ✅ Using consistent units with correct R

3. Significant figures:

• ❌ Using R = 0.082 (too few digits)
• ✅ Using R = 0.08206 for better accuracy

4. Real gas assumptions:

• ❌ Using for steam near 100°C at 1 atm
• ✅ Recognizing when ideal behavior fails

5. Gauge vs absolute pressure:

• ❌ Using gauge pressure readings directly
• ✅ Adding atmospheric pressure: P_abs = P_gauge + P_atm

6. Standard conditions:

• ❌ Assuming STP means 25°C
• ✅ Remember STP is 0°C (273.15 K)

You can determine molar mass (M) by modifying the ideal gas law:

The relationship:

Since n = mass/M, we can write:

PV = (mass/M)RT

Rearranging:

M = (mass × R × T) / (P × V)

Or using density (ρ = mass/V):

M = (ρ × R × T) / P

Example calculation:

A 2.5 L flask at 25°C and 0.95 atm contains 3.2 g of unknown gas:

• T = 25°C + 273.15 = 298.15 K
• M = (3.2 × 0.08206 × 298.15) / (0.95 × 2.5)
• M = 78.3 / 2.375 = 33.0 g/mol

This could be O₂ (32.0 g/mol) with experimental error.

Real gases deviate from ideal behavior due to:

1. Molecular volume:

• Ideal gases assume point particles (no volume)
• Real molecules occupy space
• At high pressure, molecular volume matters

2. Intermolecular forces:

• Ideal gases assume no attractions/repulsions
• Real molecules have van der Waals forces
• Stronger for polar/large molecules

3. Compressibility factor (Z):

Z = PV/(nRT)

• Ideal gas: Z = 1 always
• Real gas: Z ≠ 1
• Z < 1: attractive forces dominate
• Z > 1: repulsive forces dominate

4. van der Waals equation:

[P + a(n/V)²][V - nb] = nRT

• a: attraction parameter
• b: volume parameter

Use ideal gas law for quick estimates; use real gas equations for high accuracy at extreme conditions.

The combined gas law relates initial and final states:

(P₁V₁)/T₁ = (P₂V₂)/T₂

(when n is constant)

Steps to solve:

1. Identify what stays constant (usually n)
2. List initial conditions (P₁, V₁, T₁)
3. List final conditions (with one unknown)
4. Convert temperatures to Kelvin
5. Ensure pressure units match
6. Solve for the unknown

Example problem:

A balloon at 20°C and 1.0 atm has volume 2.5 L. What's its volume at 35°C and 0.95 atm?

• T₁ = 293.15 K, T₂ = 308.15 K
• V₂ = V₁ × (P₁/P₂) × (T₂/T₁)
• V₂ = 2.5 × (1.0/0.95) × (308.15/293.15)
• V₂ = 2.5 × 1.053 × 1.051 = 2.77 L

The ideal gas law has numerous practical applications:

1. Weather and meteorology:

• Predicting air pressure changes
• Understanding weather balloon expansion
• Calculating air density at altitude

2. Scuba diving:

• Tank pressure calculations
• Decompression planning
• Air consumption rates

3. Automotive:

• Tire pressure vs temperature
• Engine compression ratios
• Airbag deployment calculations

4. Chemical industry:

• Reactor design and scaling
• Gas storage requirements
• Process control and monitoring

5. Medical applications:

• Anesthesia gas delivery
• Oxygen tank duration
• Respiratory volume measurements

6. Everyday examples:

• Hot air balloon operation
• Pressure cooker function
• Aerosol can warnings

Common pressure unit conversions:

Starting with 1 atm:

• 1 atm = 101,325 Pa
• 1 atm = 101.325 kPa
• 1 atm = 1.01325 bar
• 1 atm = 14.696 psi
• 1 atm = 760 torr
• 1 atm = 760 mmHg

Quick conversion factors:

Memory tips:

• 1 bar ≈ 1 atm (actually 0.987)
• 1 psi ≈ 7 kPa
• 760 torr = 760 mmHg = 1 atm

Temperature extremes significantly affect gas behavior:

At very high temperatures:

• Better ideal behavior - molecules move too fast for attractions
• Dissociation - molecules may break apart (N₂ → 2N)
• Ionization - electrons stripped (plasma formation)
• Radiation effects - significant energy loss

At very low temperatures:

• Non-ideal behavior increases - attractions dominate
• Condensation - gas → liquid transition
• Critical temperature - above which gas won't liquefy
• Quantum effects - for H₂ and He near 0 K

Practical implications:

• Cryogenics: Special equations needed for liquid N₂, He
• Combustion: Account for dissociation at high T
• Space applications: Extreme T ranges require careful modeling

Rule of thumb: Ideal gas law works best when T >> boiling point of the substance.