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Gas density calculation using the ideal gas law is straightforward, with this calculator providing density as the output instead of volume. Contrary to a common misconception, the density of ideal gases varies widely—hydrogen has a density as low as 0.07927 kg/m³, while butane reaches 2.281 kg/m³, making butane approximately 29 times denser than hydrogen! This diversity arises from differences in molar mass and specific gas constants.
This tool simplifies the process, but understanding the underlying equations enhances comprehension. Let’s explore how density is derived from the ideal gas law.
The ideal gas law is given by:
\( P \nu = R T \)
Where:
Specific volume (\( \nu \)) is the inverse of density (\( \rho \)): \( \nu = \frac{1}{\rho} \). Substituting this into the ideal gas law:
\( \frac{P}{\rho} = R T \)
Solving for \( \rho \):
\( \rho = \frac{P}{R T} \)
Alternatively, using the universal gas constant (\( \bar{R} = 8.3144626 \, \text{J/(mol·K)} \)) and molar mass (\( M \) in kg/mol):
\( \rho = \frac{M P}{\bar{R} T} \)
This equation allows density calculation based on gas-specific properties.
Let’s calculate the density of air, a common gas, using the ideal gas law. For air, the specific gas constant is \( R = 287 \, \text{J/(kg·K)} \). Suppose conditions are \( T = 15 \, \text{°C} = 288.15 \, \text{K} \) and \( P = 101325 \, \text{Pa} \):
\( \rho = \frac{P}{R T} = \frac{101325}{287 \cdot 288.15} \approx 1.225 \, \text{kg/m³} \)
This matches the widely accepted air density at these conditions, confirming the calculator’s accuracy.
When using the ideal gas law to find density, keep these points in mind:
Gas density is the mass of a gas per unit volume, typically in kg/m³. It varies with temperature, pressure, and gas type. Lower temperatures and higher pressures increase density, while the specific gas constant (tied to molar mass) affects the value. This calculator supports various gases, including dry air, and allows custom input.
Dry air, primarily nitrogen and oxygen, features molecules moving at high speeds—e.g., a nitrogen molecule (mass 14 u) travels ~670 m/s at room temperature, twice the speed of sound. Higher temperatures accelerate molecules, expanding volume and reducing density (per the ideal gas law), while increased pressure compresses the gas, raising density.
Altitude impacts density: as altitude rises, pressure and temperature drop, lowering air (and oxygen) per unit volume. Climbers at high altitudes need oxygen cylinders, while airplane cabins maintain sea-level density via pressurization. See the dry air density table below (U.S. Standard Atmosphere, 1976):
| Altitude [ft (m)] | Temperature [°F (°C)] | Pressure [psi (hPa)] | Air Density [lb/cu ft (kg/m³)] |
|---|---|---|---|
| Sea level | 59 (15) | 14.7 (1013.25) | 0.077 (1.23) |
| 2,000 (610) | 51.9 (11.1) | 13.7 (941.7) | 0.072 (1.16) |
| 4,000 (1,219) | 44.7 (7.1) | 12.7 (873.3) | 0.068 (1.09) |
| 6,000 (1,829) | 37.6 (3.1) | 11.7 (808.2) | 0.064 (1.02) |
| 8,000 (2,438) | 30.5 (-0.8) | 10.8 (746.2) | 0.06 (0.95) |
| 10,000 (3,048) | 23.3 (-4.8) | 10 (687.3) | 0.056 (0.9) |
| 12,000 (3,658) | 16.2 (-8.8) | 9.2 (631.6) | 0.052 (0.84) |
| 14,000 (4,267) | 9.1 (-12.8) | 8.4 (579) | 0.048 (0.77) |
| 16,000 (4,877) | 1.9 (-16.7) | 7.7 (530.9) | 0.045 (0.72) |
At 16,000 ft (~5 km), dry air density is nearly half that at sea level, underscoring altitude’s effect.
The SI unit for density is kilogram per cubic meter (kg/m³). Other useful units include:
Imperial units include:
The calculator displays density in multiple units for flexibility.
Gas density depends on temperature and pressure, so standard conditions are defined:
Standard dry air densities are approximately: STP (1.2754 kg/m³), NIST (1.2923 kg/m³), ICAO (1.225 kg/m³), EPA (1.204 kg/m³), SATP (1.1684 kg/m³). Use “Dry air” for standard calculations.
Gas pressure is the force exerted by gas molecules on their surroundings. In a closed container, molecules (e.g., nitrogen, oxygen) move rapidly, colliding with walls. With ~10²³ molecules (Avogadro’s constant order), these collisions produce measurable pressure. Higher temperatures increase molecular speed, raising pressure if volume is constant, while higher pressure compresses the gas, increasing density.
Relative humidity (RH) is the ratio of water vapor partial pressure to equilibrium vapor pressure at a given temperature (0% to 100%). Partial pressure is one gas component’s pressure alone at the same volume and temperature. Total pressure is:
\( p_{\text{total}} = p_{\text{N}_2} + p_{\text{O}_2} + p_{\text{Ar}} + p_{\text{H}_2\text{O}} + \ldots \)
Equilibrium vapor pressure increases with temperature, reflecting evaporation tendency. At RH = 0%, air is dry; at RH = 100%, it’s saturated, leading to condensation if cooled further.
The dew point is the temperature at which water vapor saturates, causing condensation (dew) upon further cooling. It’s tied to humidity. The formula is:
DP = \(\frac{243.12 \cdot a}{17.62 - a}\)
Where \( a = \ln\left(\frac{\text{RH}}{100}\right) + \frac{17.62 \cdot T}{243.12 + T} \).
Dew point cannot exceed air temperature (RH ≤ 100%). Low dew points (dry air) may irritate skin, while high dew points (humid air) hinder sweat evaporation, affecting comfort. Wind enhances evaporation, providing cooling.
Is steam an ideal gas?
At pressures below 10 kPa, steam behaves as an ideal gas regardless of temperature. Errors increase at higher pressures, especially near the critical point (100% error at ~7.39 MPa, 31.05 °C).
Is CO2 an ideal gas?
CO2 acts as an ideal gas when far from its critical pressure (7.39 MPa) or below its critical temperature (31.05 °C). Reduced pressure and temperature gauge this distance.
How to determine which gas behaves most ideally?
Compare gases by:
Is the density of all ideal gases the same?
No, density varies due to different molar masses. Use this calculator to explore densities—e.g., hydrogen at 0.07927 kg/m³ vs. butane at 2.281 kg/m³!