The Russian Mir space station used a chemical oxygen generator system to make oxygen for the crew. The system ignited a tube of solid lithium perchlorate (LiClO4) to make oxygen and lithium chloride (LiCl):
LiClO4 (s) ---> 2O2 (g) + LiCl (s)
If you have 500 g of LiClO4, then how many liters of oxygen will the system make at the station’s standard operating conditions, a pressure of 101.5 kPa and a temperature of 21°C? (Show the steps involved in your work.)
To calculate the volume of oxygen gas produced, we can 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.
Given:
Pressure, P = 101.5 kPa
Temperature, T = 21°C = 294 K
First, let's calculate the number of moles of oxygen produced by reacting 500 g of LiClO4 using stoichiometry.
1. Calculate the molar mass of LiClO4:
Molar mass of Li = 6.94 g/mol
Molar mass of Cl = 35.45 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of LiClO4 = (6.94 + 35.45 + (16.00 * 4)) g/mol = 117.37 g/mol
2. Calculate the number of moles of LiClO4:
Moles of LiClO4 = Mass of LiClO4 / Molar mass of LiClO4
= 500 g / 117.37 g/mol
= 4.26 mol
3. According to the balanced chemical equation, 1 mole of LiClO4 yields 2 moles of O2. Therefore, the number of moles of O2 produced is twice the moles of LiClO4 used.
Moles of O2 = 2 * Moles of LiClO4
= 2 * 4.26 mol
= 8.52 mol
Now, let's calculate the volume of oxygen gas produced using the ideal gas law equation:
4. Convert the pressure from kPa to atm:
Pressure = 101.3 kPa * 1 atm / 101.3 kPa
= 1 atm
5. Calculate the volume of oxygen gas:
V = nRT / P
= (8.52 mol) * (0.0821 L∙atm/mol∙K) * (294 K) / (1 atm)
≈ 218 L
Therefore, approximately 218 liters of oxygen gas will be produced at the station's standard operating conditions.
To determine the number of liters of oxygen produced by the chemical oxygen generator system, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atmospheres (101.5 kPa = 0.999 atm)
V = volume in liters (what we are trying to find)
n = number of moles of oxygen gas produced (what we need to calculate)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin (21°C = 294 K)
First, let's calculate the number of moles of oxygen gas produced using the stoichiometric coefficients from the balanced chemical equation:
1 mol LiClO4 produces 2 mol O2
To convert grams of LiClO4 to moles, we need the molar mass of LiClO4 which is:
Molar mass of Li = 6.941 g/mol
Molar mass of Cl = 35.453 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of LiClO4 = (6.941 + 35.453 + (4 * 16.00)) g/mol = 150.91 g/mol
Now, let's calculate the number of moles of LiClO4:
Moles of LiClO4 = 500 g / 150.91 g/mol = 3.31 mol
Since 1 mol of LiClO4 produces 2 mol of O2, the number of moles of O2 produced is:
Moles of O2 = 3.31 mol LiClO4 * (2 mol O2 / 1 mol LiClO4) = 6.62 mol O2
Now, let's solve the ideal gas law equation for V (volume):
PV = nRT
V = (nRT) / P
V = (6.62 mol * 0.0821 L·atm/mol·K * 294 K) / 0.999 atm
V ≈ 158.48 L
Therefore, the system will produce approximately 158.48 liters of oxygen at the given standard operating conditions.
mols LiClO4 = grams/molar mass = ?
Use the coefficients in the balanced equation to convert mols LiClO4 to mols O2.
Now convert mols O2 to L at the conditions listed. Use PV = nRT for that. Beware of units. If you use P in kPa, you must use R = 8.314. If you use P in atmospheres, you must use R = 0.08206