To compute the density of a gas using the ideal gas law, we can use the formula:
Density = (Molar mass * Pressure) / (Gas constant * Temperature)
Given:
Molar mass of H₂S (M) = 34.1 kg/kmol
Pressure (P) = 2.00 atm
Temperature (T) = 27°C = 27 + 273.15 = 300.15 K (converted to Kelvin)
Gas constant (R) = 0.0821 atm·L/(mol·K) (ideal gas constant)
Now, let's calculate the density:
Density = (M * P) / (R * T)
= (34.1 kg/kmol * 2.00 atm) / (0.0821 atm·L/(mol·K) * 300.15 K)
First, we need to convert the molar mass from kg/kmol to g/mol:
Molar mass (M) = 34.1 kg/kmol * 1000 g/kg = 34100 g/kmol
Now, let's substitute the values and calculate the density:
Density = (34100 g/kmol * 2.00 atm) / (0.0821 atm·L/(mol·K) * 300.15 K)
= 68100 g·atm / (24.963 g·L/(mol·K))
Simplifying further:
Density ≈ 2730 g/L
Therefore, the density of H₂S gas at 27°C and 2.00 atm, assuming it to be ideal, is approximately 2730 g/L.