In the following reaction, how many liters of oxygen produce 560 liters of carbon dioxide in the oxidation of methane, given that both gases are at STP?
CH4 + 2O2 d CO2 + 2H2O
Here is a worked example of a stoichiometry problem.
http://www.jiskha.com/science/chemistry/stoichiometry.html
To determine the number of liters of oxygen required to produce 560 liters of carbon dioxide in the given reaction, we need to understand the stoichiometry of the balanced equation.
Given the balanced equation:
CH4 + 2O2 -> CO2 + 2H2O
From the equation, we can see that 1 mole of methane (CH4) reacts with 2 moles of oxygen (O2) to produce 1 mole of carbon dioxide (CO2).
Step 1: Convert liters of carbon dioxide to moles of carbon dioxide.
To do this, we need to use the ideal gas law equation:
PV = nRT
At STP (Standard Temperature and Pressure), the values are:
Pressure (P) = 1 atm
Temperature (T) = 273 K
Gas constant (R) = 0.0821 L·atm/(mol·K)
The volume (V) at STP can be directly converted to moles by dividing by the molar volume. The molar volume at STP is approximately 22.4 L/mol.
Let's calculate the number of moles of CO2:
Number of moles of CO2 = (560 L) / (22.4 L/mol) = 25 mol
Step 2: Apply stoichiometry to determine the number of moles of oxygen.
From the balanced equation, it is clear that 1 mole of methane reacts with 2 moles of oxygen to produce 1 mole of carbon dioxide.
Since the ratio is 1:2, we can conclude that:
Number of moles of oxygen = 2 x Number of moles of CO2 = 2 x 25 mol = 50 mol
Step 3: Convert moles of oxygen to liters of oxygen.
Again, using the ideal gas law equation, we need to calculate the volume of oxygen at STP.
Number of liters of oxygen = Number of moles of oxygen x Molar volume
Number of liters of oxygen = 50 mol x 22.4 L/mol = 1120 L
Therefore, to produce 560 liters of carbon dioxide in the given reaction, you would need 1120 liters of oxygen at STP.