From the following gases, choose the one with the lowest density at 25 C and 5 atm:
H2S, CO2, C2H2, C2H6, C2H4
The answer is C2H2, but I am not sure why. Can you explain this? Thank you very much.
density (g/L) = molar mass/22.4
To determine the gas with the lowest density at a given temperature and pressure, you need to compare their molar masses and apply the ideal gas law.
First, let's calculate the molar masses of each gas:
- H2S (Hydrogen sulfide): Molar mass = 2(g/mol) + 32(g/mol) = 34(g/mol)
- CO2 (Carbon dioxide): Molar mass = 12(g/mol) + 2 * 16(g/mol) = 44(g/mol)
- C2H2 (Acetylene): Molar mass = 2 * 12(g/mol) + 2 * 1(g/mol) = 26(g/mol)
- C2H6 (Ethane): Molar mass = 2 * 12(g/mol) + 6 * 1(g/mol) = 30(g/mol)
- C2H4 (Ethene): Molar mass = 2 * 12(g/mol) + 4 * 1(g/mol) = 28(g/mol)
Next, let's apply the ideal gas law to compare their densities:
Density (d) = (molar mass * pressure)/(0.0821 * temperature)
Since all gases are at the same temperature (25°C or 298K) and pressure (5 atm), we can simplify the equation as:
Density (d) ∝ molar mass
From the calculated molar masses, we can see that C2H2 (Acetylene) has the lowest molar mass (26 g/mol). Therefore, it will have the lowest density among the given gases at 25°C and 5 atm.
Hence, C2H2 (Acetylene) is the gas with the lowest density at these conditions.