A propane gas (C3H8) heater burns propane at a rate of 500 grams per hour.
a) What is the oxygen consumption rate? (in g O2/hr.)
b) If the heater uses a blower to provide outside air (0°C, 1 atm) for combustion, what is the minimum air flow rate the blower must provide? (in L/min)
start with the balanced chem equation
C3H8 + 5O2 >>3CO2 + 4H2O
so the ratio of moles is 5O2/1C3H8
and the ratio of mass is 5*32gO2/44g propane
so for every 500 g propane/perhour, one used 500*(44g) O2/hour
Outside air is only 27 percent Oxygen, one needs air flow rate
airflowrate=500*44gO2*22.4liters/32gO2 * 1/.27= ...
To determine the oxygen consumption rate and the minimum air flow rate, we need to understand the stoichiometry of the combustion reaction of propane.
The balanced chemical equation for the combustion of propane can be written as:
C3H8 + 5O2 -> 3CO2 + 4H2O
From this equation, we can see that every mole of propane (C3H8) requires five moles of oxygen (O2) for complete combustion. We can use the molar mass of propane (C3H8) to calculate the number of moles of propane consumed.
a) To find the oxygen consumption rate in grams per hour, we need to calculate the amount of propane consumed in moles per hour, and then convert it to moles of O2, and finally convert it back to grams per hour.
Step 1: Calculate the moles of propane consumed per hour.
Given: Propane consumption rate = 500 g/hr
Molar mass of propane (C3H8) = 44.1 g/mol (sum of the atomic masses of carbon and hydrogen)
Using the molar mass of propane, we can calculate the moles of propane consumed per hour:
Moles of propane consumed per hour = Propane consumption rate / Molar mass of propane
Moles of propane consumed per hour = 500 g/hr / 44.1 g/mol
Step 2: Convert moles of propane consumed to moles of O2.
Since the balanced equation shows a 5:1 ratio of moles of propane to moles of O2, we can multiply the moles of propane consumed by 5 to determine the moles of O2 consumed per hour.
Moles of O2 consumed per hour = Moles of propane consumed per hour * 5
Step 3: Convert moles of O2 to grams of O2.
To get the mass of oxygen consumed, we multiply the moles of O2 consumed per hour by the molar mass of O2 (32.0 g/mol).
Mass of O2 consumed per hour = Moles of O2 consumed per hour * Molar mass of O2
b) To find the minimum air flow rate, we need to first calculate the volume of oxygen required for complete combustion of the propane, and then convert it to the volume of air (mixture of gases) needed.
Step 4: Calculate the volume of O2 consumed per hour.
Using the Ideal Gas Law, we can calculate the volume of O2 required.
PV = nRT
We know the pressure (1 atm), temperature (0°C = 273 K), and the number of moles of O2 consumed per hour from Step 2. We can assume the volume (V) is in liters.
Step 5: Convert the volume of O2 to the volume of air.
Since air is approximately 21% oxygen and 79% nitrogen, we need to consider the partial pressures of oxygen and nitrogen in the air. The minimum air flow rate is determined by the amount of oxygen required for combustion.
Given the mole ratio of O2 to N2 in air is 1:4, we can use this ratio to calculate the volume of air required.
Minimum air flow rate = Volume of O2 consumed per hour / (Fraction of O2 in air)
To convert the minimum air flow rate to L/min, divide by 60.
Remember to use correct units and ensure the conversions are consistent throughout the calculations.
By following these steps, you should be able to calculate both the oxygen consumption rate and the minimum air flow rate for the propane gas heater.