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 Moles
Density (ρ) is mass (m) per unit volume (V):
ρ = m/V
We can also express mass (m) as the product of moles (n) and molar mass (M):
m = nM
Substituting this into the density equation:
ρ = (nM)/V
3. Combine the Equations
Now, rearrange the ideal gas law to solve for n/V:
n/V = P/RT
Substitute this into the density equation:
ρ = (P/RT) * M
4. Plug in the Values
* P = 0.97 atm
* R = 0.0821 L·atm/mol·K (ideal gas constant)
* T = 35 °C = 308 K (convert to Kelvin by adding 273.15)
* M = 46.01 g/mol (molar mass of NO2)
5. Calculate the Density
ρ = (0.97 atm / (0.0821 L·atm/mol·K * 308 K)) * 46.01 g/mol
ρ ≈ 1.77 g/L
Therefore, the density of NO2 gas at 0.97 atm and 35 °C is approximately 1.77 g/L.
