To determine the volume of the gas mixture, we can use the ideal gas law equation:
PV = nRT
Where: P = Pressure (in atm) V = Volume (in liters) n = Number of moles of gas R = Ideal gas constant (0.0821 L·atm/(mol·K)) T = Temperature (in Kelvin)
To calculate the number of moles of each gas, we'll use their respective molar masses:
Molar mass of O2 (oxygen gas) = 32 g/mol Molar mass of Cl2 (chlorine gas) = 70.91 g/mol
First, let's calculate the number of moles of O2: n(O2) = mass/molar mass = 7 g / 32 g/mol = 0.21875 mol (approximately)
Next, let's calculate the number of moles of Cl2: n(Cl2) = mass/molar mass = 1.5 g / 70.91 g/mol = 0.02115 mol (approximately)
The total number of moles of gas (n) in the mixture is the sum of the moles of O2 and Cl2: n(total) = n(O2) + n(Cl2) = 0.21875 mol + 0.02115 mol = 0.2399 mol (approximately)
Now, let's convert the temperature from Celsius to Kelvin: T(K) = T(°C) + 273.15 = 22 + 273.15 = 295.15 K
Now we can substitute the known values into the ideal gas law equation to find the volume:
PV = nRT
V = (nRT)/P = (0.2399 mol * 0.0821 L·atm/(mol·K) * 295.15 K) / 482 atm ≈ 0.03806 L
To convert the volume to milliliters (ml), we multiply by 1000: V(ml) = 0.03806 L * 1000 ml/L ≈ 38.06 ml
Therefore, when 7g of O2 and 1.5g of Cl2 are mixed in a container with a pressure of 482 atm and at a temperature of 22⁰C, the volume of the gas mixture is approximately 38.06 ml.