Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is 70. cm3. If the combustion of this mixture releases 885 J of energy, to what volume will the gases expand against a constant pressure of 645 torr if all the energy of combustion is converted into work to push back the piston?

To find the final volume of the gases, we need to use the ideal gas law. The ideal gas law equation can be stated as:

PV = nRT

Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant
- T is the temperature of the gas

In this case, we have a constant pressure and the number of moles of gas is not given. However, we can assume that the number of moles remains constant, so we can use the equation as:

V₁/P₁ = V₂/P₂

Where:
- V₁ is the initial volume of the gas
- P₁ is the initial pressure of the gas
- V₂ is the final volume of the gas
- P₂ is the final pressure of the gas

In this case, the initial volume is given as 70 cm³, and the initial pressure is not provided. The final pressure is given as 645 torr.

Converting units:
1 torr = 1 mmHg
1 atm = 760 mmHg

So, 645 torr = 645/760 atm ≈ 0.849 atm.

Plugging the values into the equation:

70 cm³/P₁ = V₂/0.849 atm

We need to rearrange the equation to solve for V₂:

V₂ = (70 cm³ × 0.849 atm) / P₁

To find P₁, we can use the energy released during combustion.

The energy released during combustion is given as 885 J. This energy is converted into work to push back the piston. Work (W) is defined as:

W = PΔV

Where:
- W is work done
- P is the pressure
- ΔV is the change in volume

Since all the energy of combustion is converted into work to push back the piston, we can equate the work done with the energy released:

P₁ × ΔV = 885 J

Now we have two equations:

70 cm³/P₁ = V₂/0.849 atm
P₁ × ΔV = 885 J

To solve this system of equations, we need to find the value of P₁ first. Then we can use it to calculate V₂.