Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is 40. cm^3. If the combustion of this mixture releases 950. J of energy, to what volume will the gas expand against a constant pressure of 650. torr if all the energy of combustion is converted into work to push back the piston.
To find the final volume of the gas, we can use the ideal gas law, which states:
PV = nRT
Where:
P = pressure (in torr)
V = volume (in cm^3)
n = number of moles
R = gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
First, we need to convert the pressure from torr to atm. Since 1 atm = 760 torr, we can divide the given pressure of 650 torr by 760 to get the pressure in atm:
Pressure (in atm) = 650 torr / 760 torr/atm = 0.855 atm
Next, we need to convert the original volume from cm^3 to L (liters) since the gas constant is usually given in terms of liters. Since 1 L = 1000 cm^3, we divide the given volume of 40 cm^3 by 1000 to get the volume in liters:
Volume (in L) = 40 cm^3 / 1000 cm^3/L = 0.04 L
Now we can rearrange the ideal gas law equation to solve for the final volume:
Vf = Vi * (Pi / Pf)
Where:
Vf = final volume
Vi = initial volume
Pi = initial pressure
Pf = final pressure
In this case, we are given the initial volume (Vi = 0.04 L), the initial pressure (Pi = 0.855 atm), and the final pressure (Pf = 0.855 atm).
Plugging these values into the equation, we get:
Vf = 0.04 L * (0.855 atm / 0.855 atm)
Since the initial pressure is the same as the final pressure, the equation simplifies to:
Vf = 0.04 L
Therefore, the final volume of the gas will remain the same as the initial volume, which is 0.04 L (or 40 cm^3).