30cm3 of ethane were mixed with 100cm3of oxygen and the mixture was sparked to complete reaction. If all the volume were measured at a pressure of one atmosphere and a temperature of 25 degrees Celsius,calculate the volume of the residual gas under. State condition
To calculate the volume of the residual gas, we need to determine the stoichiometry of the reaction between ethane (C2H6) and oxygen (O2). The balanced equation for the complete combustion of ethane is:
C2H6 + 7/2 O2 → 2 CO2 + 3 H2O
From the balanced equation, we can see that 1 mole of ethane reacts with 7/2 moles of oxygen to produce 2 moles of carbon dioxide and 3 moles of water. Since we have the volume of ethane and oxygen in cm3, we need to convert them to moles using the ideal gas law.
The molar volume of an ideal gas at STP (standard temperature and pressure) is 22.4 L or 22,400 cm3/mol.
1) Volume of ethane (C2H6):
30 cm3 x (1 mol / 22,400 cm3) = 0.0013393 mol
2) Volume of oxygen (O2):
100 cm3 x (1 mol / 22,400 cm3) = 0.0044643 mol
Since the stoichiometry ratio is 1:7/2 (ethane to oxygen), the limiting reactant is ethane. This means that all the ethane will react completely and determine the volume of the residual gas.
Now, let's calculate the volume of the residual gas (CO2 and H2O):
Volume of CO2:
0.0013393 mol ethane x (2 mol CO2 / 1 mol ethane) x (22,400 cm3 / 1 mol CO2) = 59.9512 cm3
Volume of H2O:
0.0013393 mol ethane x (3 mol H2O / 1 mol ethane) x (22,400 cm3 / 1 mol H2O) = 100.034 cm3
The total volume of the residual gas is the sum of the volume of CO2 and H2O:
Total volume of residual gas = Volume of CO2 + Volume of H2O
= 59.9512 cm3 + 100.034 cm3
= 159.9852 cm3
Therefore, the volume of the residual gas is approximately 159.9852 cm3 under the given conditions of 1 atmosphere pressure and 25 degrees Celsius temperature.