How many liters of o2(g) measured at 22 degree and 763 Torr are consumed in the complete combustion of 2.55 L of dimethyl ether measured at 25 degree celsius and 748 Torr.
C2H6O + 3O2 ==> 2CO2 + 3H2O
Use PV = nRT and conditions listed to calculate n = number mols of the ether.
Use the coefficients in the balanced equation to convert mols dimethyl ether to mols O2.
Now use PV = nRT, substitute the conditions for O2 and solve for V in liters.
Thanks a lot.
To find out how many liters of O2(g) are consumed in the complete combustion of dimethyl ether, we can use the balanced equation for the combustion reaction of dimethyl ether.
The balanced equation is:
2(CH3)(OCH3) + 5(O2) -> 4(CO2) + 6(H2O)
From this equation, we can see that for every 2 moles of dimethyl ether (CH3OCH3), we need 5 moles of O2 to fully combust the dimethyl ether.
First, let's convert the volume of dimethyl ether from 25 degrees Celsius and 748 Torr to the standard conditions of 22 degrees Celsius and 763 Torr. We can use the ideal gas law equation for this conversion:
PV = nRT
Where:
P = pressure (in Torr)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
Rearranging the equation, we get:
n = PV / RT
Calculating the number of moles of dimethyl ether:
P(Dimethyl ether) = 748 Torr
V(Dimethyl ether) = 2.55 L
T = 25 + 273 = 298 K
n(Dimethyl ether) = (748 Torr * 2.55 L) / (0.0821 L·atm/mol·K * 298 K) = 9.27 moles
Now, using the stoichiometry of the balanced equation, we can calculate the number of moles of O2 required:
1 mole dimethyl ether : 5 moles O2
9.27 moles dimethyl ether : x moles O2
x = (9.27 moles dimethyl ether) * (5 moles O2 / 1 mole dimethyl ether) = 46.35 moles O2
Finally, let's convert the moles of O2 to liters, again using the ideal gas law equation:
n = PV / RT
P(O2) = 763 Torr
V = ?
n(O2) = 46.35 moles
T = 22 + 273 = 295 K
Rearranging the equation, we get:
V = nRT / P
Calculating the volume of O2 in liters:
V(O2) = (46.35 moles * 0.0821 L·atm/mol·K * 295 K) / 763 Torr = 15.12 L
Therefore, approximately 15.12 liters of O2(g) are consumed in the complete combustion of 2.55 L of dimethyl ether, measured at 25 degrees Celsius and 748 Torr.