How to Find Density at a Certain Temperature
Finding the density of a substance at a specific temperature depends on the substance's state (solid, liquid, or gas).
For gases, we can use the ideal gas law. A modified version allows us to directly calculate density: PM = dRT, where:
- P is pressure (in atm)
- M is molar mass (g/mol)
- d is density (g/L)
- R is the ideal gas constant (0.0821 atm·L/mol·K)
- T is temperature (in Kelvin)
To find density (d), rearrange the formula: d = PM/RT. Remember to convert temperature to Kelvin (add 273.15 to Celsius).
Example: Find the density of oxygen (O₂ molar mass = 32 g/mol) at 25°C and 1 atm.
- Convert temperature: 25°C + 273.15 = 298.15 K
- Apply the formula: d = (1 atm 32 g/mol) / (0.0821 atm·L/mol·K 298.15 K) ≈ 1.31 g/L
Density of Liquids and Solids
For liquids and solids, the process differs slightly. Density is typically temperature-dependent and often presented in tables or equations.
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Tables: Many resources provide density values at various temperatures for common substances (e.g., water). Simply look up the density at your desired temperature. ACS lesson on water density
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Empirical Equations: Some substances have density expressed as a function of temperature using an empirical equation. This equation often incorporates a coefficient that accounts for the thermal expansion of the material. For example, ρ = ρr[1 + b(T − Tr)], where ρ is density at temperature T, ρr is density at reference temperature Tr, and b is the volumetric temperature expansion coefficient. Physics StackExchange discussion
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Experimental Measurement: The most direct way is through experimental measurement. Measure the mass and volume of a sample at the desired temperature; density is mass divided by volume. Ensure accurate temperature control during measurement.
Remember that the density of water is unique, showing unusual behavior around 4°C.
