1. Convert Units
* Pressure: Convert millimeters of mercury (mmHg) to atmospheres (atm):
475 mmHg * (1 atm / 760 mmHg) = 0.625 atm
* Temperature: Convert Celsius (°C) to Kelvin (K):
58.5 °C + 273.15 = 331.65 K
2. Use the Ideal Gas Law
The ideal gas law is: PV = nRT
Where:
* P = pressure (atm)
* V = volume (L)
* n = number of moles
* R = ideal gas constant (0.0821 L·atm/mol·K)
* T = temperature (K)
We can rearrange this equation to solve for density (ρ), which is mass (m) per unit volume (V):
ρ = m/V = (n * M) / V
Where M is the molar mass of SO2 (64.06 g/mol).
Substitute the ideal gas law into the density equation:
ρ = (P * M) / (R * T)
3. Plug in the Values
ρ = (0.625 atm * 64.06 g/mol) / (0.0821 L·atm/mol·K * 331.65 K)
4. Calculate the Density
ρ ≈ 1.46 g/L
Therefore, the density of sulfur dioxide gas at 475 mmHg and 58.5 °C is approximately 1.46 g/L.
