To solve this problem, you will need to use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Before we can use the ideal gas law, we need to convert the volume from liters to cubic meters, the pressure from mmHg to atm, and the temperature from Celsius to Kelvin.
1. Convert volume: 8.73 L = 0.00873 m^3 (since 1 L = 0.001 m^3)
2. Convert pressure: 755 mmHg = 1 atm (since 1 atm = 760 mmHg)
3. Convert temperature: 24.0°C = 24.0 + 273.15 = 297.15 K
Now we have all the values we need to use the ideal gas law equation:
PV = nRT
Solving for n (number of moles):
n = (PV) / (RT)
Substituting the values into the equation:
n = (1 atm) x (0.00873 m^3) / [(0.0821 L x atm/mol x K) x (297.15 K)]
Calculating this expression gives the number of moles of Cl2 gas in the sample.
Finally, to find the mass of Cl2 gas in grams, we need to use the molar mass of Cl2, which is approximately 70.91 g/mol.
1 mole of Cl2 gas weighs 70.91 grams.
So, multiply the number of moles by the molar mass to get the mass in grams:
Mass (g) = (n moles) x (70.91 g/mol)
Now you can plug in the value of n (number of moles) that you calculated earlier into this expression to find the mass of Cl2 gas in grams.