1. Convert Pressure to Atmospheres:
* 1 atm = 760 torr
* 7.50 x 10² torr * (1 atm / 760 torr) = 0.987 atm
2. Convert Temperature to Kelvin:
* K = °C + 273.15
* 25.0 °C + 273.15 = 298.15 K
3. Use 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
To find density (ρ), we need to rearrange the equation to solve for mass (m) over volume (V):
* ρ = m/V
We can relate mass to moles using the molar mass (M) of chlorine gas (Cl₂):
* m = nM
Now, substitute these relationships into the ideal gas law:
* P(V) = (m/M)RT
* PV = (ρV)RT / M
* ρ = (PM) / (RT)
4. Plug in the Values and Calculate:
* P = 0.987 atm
* M = 70.90 g/mol (molar mass of Cl₂)
* R = 0.0821 L·atm/mol·K
* T = 298.15 K
ρ = (0.987 atm * 70.90 g/mol) / (0.0821 L·atm/mol·K * 298.15 K)
ρ ≈ 2.85 g/L
Therefore, the density of chlorine gas at 7.50 x 10² torr and 25.0 °C is approximately 2.85 g/L.
