To determine the volume of carbon dioxide (CO2) produced when 95 g of methane (CH4) and 102 g of oxygen (O2) undergo complete combustion at STP (Standard Temperature and Pressure), we need to set up a balanced chemical equation for the combustion of methane.
The balanced equation for the combustion of methane is:
CH4 + 2O2 -> CO2 + 2H2O
From the balanced equation, we can see that one molecule of methane reacts with two molecules of oxygen to produce one molecule of carbon dioxide and two molecules of water.
To calculate the volume of carbon dioxide produced, we need to use the ideal gas law, which states:
PV = nRT
Where: P = Pressure (in this case, it's STP, so it's 1 atm) V = Volume (unknown) n = Number of moles R = Ideal gas constant (0.0821 L·atm/(mol·K)) T = Temperature (in this case, it's STP, so it's 273 K)
First, we need to determine the number of moles of methane and oxygen:
Number of moles of methane (CH4): molar mass of methane (CH4) = 12.01 g/mol (carbon) + 4(1.01 g/mol) (hydrogen) = 16.05 g/mol moles of methane = mass of methane / molar mass of methane = 95 g / 16.05 g/mol
Number of moles of oxygen (O2): molar mass of oxygen (O2) = 2(16.00 g/mol) = 32.00 g/mol moles of oxygen = mass of oxygen / molar mass of oxygen = 102 g / 32.00 g/mol
According to the balanced equation, the ratio of methane to carbon dioxide is 1:1. Therefore, the moles of carbon dioxide produced will be the same as the moles of methane.
Now, we can calculate the volume of carbon dioxide using the ideal gas law:
n(CO2) = moles of methane = moles of carbon dioxide V(CO2) = Volume of carbon dioxide (unknown) R = 0.0821 L·atm/(mol·K) T = 273 K
PV = nRT V(CO2) = n(CO2)RT/P
Substituting the values into the equation:
V(CO2) = (moles of methane)(R)(T)/P
Calculate the moles of methane and oxygen:
moles of methane = 95 g / 16.05 g/mol moles of oxygen = 102 g / 32.00 g/mol
Since the stoichiometric ratio between methane and carbon dioxide is 1:1, the moles of carbon dioxide will be the same as the moles of methane.
Now, we can calculate the volume of carbon dioxide:
V(CO2) = (moles of methane)(R)(T)/P = (moles of methane)(0.0821 L·atm/(mol·K))(273 K) / (1 atm)
Substituting the values:
V(CO2) = (95 g / 16.05 g/mol)(0.0821 L·atm/(mol·K))(273 K) / (1 atm)
Calculating this expression will give you the volume of carbon dioxide produced in liters.