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 930. J of energy, to what volume will the gases expand against a constant pressure of 670. torr if all the energy of combustion is converted into work to push back the piston?

I try to use the Work = =P * Delta V with Delta E = q +w But I end up with two variables. And I am to confused as to what 930 J Stands for as it says energy, not heat so i pluged it in for Delta E.

To solve this problem, we can use the ideal gas law and the concept of work done by a gas. Let's break down the steps:

1. Determine the number of moles of gasoline vapor: We need to convert the given volume from cm³ to L since the pressure is given in torr. Using the conversion factor 1 L = 1000 cm³, the volume becomes 0.07 L. Next, we use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Assuming the temperature remains constant, we can rearrange the equation as n = PV / RT.

2. Calculate the number of moles of air: Since the mixture is a combination of air and gasoline vapor, we need to subtract the moles of gasoline vapor from the total moles. The number of moles of air can be calculated using the same ideal gas law equation but with the initial volume of 70 cm³.

3. Calculate the total number of moles: Add the moles of gasoline vapor to the moles of air to find the total number of moles in the cylinder.

4. Calculate the final volume of the gases: To find the final volume, we can use the equation Vf = Vi * (ni / nf), where Vf is the final volume, Vi is the initial volume, ni is the initial number of moles, and nf is the final number of moles.

5. Calculate the work done: The work done by the gases can be calculated using the equation W = P * ΔV, where W is the work, P is the pressure, and ΔV is the change in volume (final volume minus initial volume).

Let's put it all together:

Step 1: Calculate the number of moles of gasoline vapor
n_gasoline = (P * V_gasoline) / (R * T)

Step 2: Calculate the number of moles of air
n_air = (P * V_air) / (R * T)

Step 3: Calculate the total number of moles
n_total = n_gasoline + n_air

Step 4: Calculate the final volume of the gases
V_final = V_initial * (n_initial / n_total)

Step 5: Calculate the work done
W = P * (V_final - V_initial)

Now you can plug in the values into the respective equations to find the answer.