Final answer:
To calculate the density of chlorine gas (Cl₂) at a specific temperature and pressure, the Ideal Gas Law can be rearranged in terms of density and the given values substituted to find the answer.
Step-by-step explanation:
To find the density of chlorine gas (Cl₂) at a given temperature and pressure, we can use the Ideal Gas Law, which is PV = nRT. However, to find the density, we need to rearrange the formula to solve for mass (ρ) over volume (V), since density is mass per unit volume. First, we convert the temperature to Kelvin by adding 273.15 to the Celsius temperature, and then we use the ideal gas constant in the units that match the pressure in atm (0.0821 L·atm/(mol·K)).
The molar mass of Cl₂ is given by the conversion factor, which is 1 mole Cl₂ over 70.90 grams Cl₂. By rearranging the Ideal Gas Law to solve for m (mass), and knowing that n (number of moles) is mass (m) divided by molar mass (M), we get the formula ρ = (P × M) / (R × T), where ρ is the density, P is the pressure, M is the molar mass, R is the ideal gas constant, and T is the temperature in Kelvin.
Substitute the given values into the formula:
ρ = ρ = (1.21 atm × 70.90 g/mol) / (0.0821 L·atm/(mol·K) × (34.9°C + 273.15K)) = density of Cl₂.