Chlorine is widely used to treat municipal water supplies and swimming pools. If the volume of a sample of Cl2 gas is 8.73L at 755mmHg and 24.0C, how many grams of Cl2 gas are in this sample?
This is one of those multi step problems that I get lost....I need to to know how to derive at an answer here....I think I have to convert units here or at least pay attention to the units somewhere...but I am getting lost with the calculation...Help!
You must pay attention to units no matter what problem you are working.
Here, use PV = nRT and solve for n
P must be in atm and 755/760 = ? atm.
V in L
n = number of mols. Solve for this.
R = 0.08205 L*atm/mol*K
T = 24C + 273 = ?K. T must be in kelvin.
Then n = mols = grams/molar mass
You know molar mass Cl2 (about 71) and you know mols from PV = nRT, solve for grams.
n=PV/RT
n=(755/760)(8.73)÷24.37182
n=0.357mol
Mass=molar mass *number of moles
Mass=71g*0.357
=25.3g
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.