1. Understand the Ideal Gas Law
The ideal gas law relates pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T):
PV = nRT
2. Relate Density to the Ideal Gas Law
* Density (ρ) = mass (m) / volume (V)
* Molar mass (M) = mass (m) / moles (n)
We can rearrange the ideal gas law to solve for density:
* n/V = P/RT
* (m/M) / V = P/RT
* ρ/M = P/RT
* ρ = (PM) / (RT)
3. Convert Units
* Pressure (P): 0.970 atm
* Temperature (T): 36°C + 273.15 = 309.15 K
* Molar mass (M) of NO₂: 14.01 g/mol (N) + 2 * 16.00 g/mol (O) = 46.01 g/mol
* Ideal gas constant (R): 0.0821 L·atm/(mol·K)
4. Calculate the Density
ρ = (PM) / (RT)
ρ = (0.970 atm * 46.01 g/mol) / (0.0821 L·atm/(mol·K) * 309.15 K)
ρ ≈ 1.76 g/L
Therefore, the density of NO₂ gas at 0.970 atm and 36°C is approximately 1.76 g/L.
