Chemical analysis of a gas shows that it contains one carbon atom for every one hydrogen atom. The densiry ofthis gas is 1.161 g/l at STP. What is the minimus oxygen volume needed at STP for the complete combustion of .500 mol of this gas?
density of 1.161 g/L x 22.4 L/mol@ATP = 26 for the mass of 1 mole or the molar mass of 26. The molecular formula must be C2H2.
2C2H2 + 5O2 ==> 4CO2 + 2H2O
0.5 mol C2H2 x (5 moles O2/2 moles C2H2) = ?? moles oxygen needed.
At STP, each mole oxygen occupies 22.4 L.
To determine the minimum oxygen volume needed for the complete combustion of a given amount of gas, we need to calculate the stoichiometric ratio between the gas and oxygen.
First, let's identify the chemical formula for the gas. Since the gas contains one carbon atom for every one hydrogen atom, it can be determined that the gas is methane (CH4).
Now, let's write and balance the chemical equation for the combustion of methane:
CH4 + 2O2 -> CO2 + 2H2O
From the balanced equation, we can see that it requires 2 moles of oxygen gas (O2) to react with 1 mole of methane (CH4) to produce 1 mole of carbon dioxide (CO2) and 2 moles of water (H2O).
Given that the amount of gas is 0.500 mol, we can multiply this value by the stoichiometric ratio of oxygen to methane to find the required amount of oxygen gas:
0.500 mol CH4 * (2 mol O2 / 1 mol CH4) = 1.000 mol O2
So, we need 1.000 mol of oxygen gas to completely combust 0.500 mol of methane.
Next, to calculate the volume of oxygen gas at STP (Standard Temperature and Pressure), we need to use the ideal gas law, which states:
PV = nRT
Where:
P = pressure
V = volume
n = amount of gas (in moles)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
At STP, the temperature is 273.15 K. The pressure is 1 atmosphere.
Let's plug in the values into the ideal gas law to solve for the volume (V) of oxygen gas:
V = (n * R * T) / P
V = (1.000 mol * 0.0821 L·atm/mol·K * 273.15 K) / 1 atm
V = 22.41 L
Therefore, the minimum volume of oxygen gas needed at STP for the complete combustion of 0.500 mol of methane is 22.41 liters.