Final answer:
To find the final volume of a gas that expands at a constant pressure and does work on its surroundings, the work equation W = -PΔV can be used. After converting the given pressure from Torr to Pa and the work done from joules to L·atm, we calculate the change in volume and add it to the initial volume, obtaining the final volume as 1314.2 mL.
Step-by-step explanation:
The question involves the expansion of a gas doing work on its surroundings, which is a concept in thermodynamics, a branch of Chemistry. To find the final volume of the gas after it does work on its surroundings at a constant pressure, we can use the work formula
W = -PΔV,
where W is the work done by the gas, P is the pressure, and ΔV is the change in volume. Since we know the initial volume (59.2 mL), the work done (131.4 J), and the constant pressure (783 Torr), we can rearrange this formula to solve for the change in volume and thus find the final volume.
First, note that 1 Torr = 1 mmHg and to use the work equation correctly, we need to convert Torr to the SI unit of pressure, pascal (Pa), where 1 atm = 101325 Pa and 1 atm = 760 mmHg.
The conversion from Torr to Pa is as follows:
783 Torr * (1 atm / 760 mmHg) * (101325 Pa / 1 atm) = 104850 Pa (rounded to the nearest whole number).
Also, we need to convert the work done from joules to liter·atmospheres because 1 J = 1 Pa·m³, and since we are dealing in mL and L for volume, we use 1 L·atm = 101.325 J to get the work in the correct units.
Applying the conversion:
131.4 J * (1 L·atm / 101.325 J) = 1.297 L·atm (rounded to three decimals).
Now we calculate the change in volume using the pressure in Pa and the work in L·atm:
ΔV = -W / P = -1.297 L·atm / (104850 Pa * (1 L / 101325 Pa)) = -0.001255 m³.
Converting this to mL (since 1 m³ = 1,000,000 mL):
ΔV = -0.001255 m³ * 1,000,000 mL/m³ = -1255 mL.
The negative sign indicates that the gas does work on the surroundings and therefore expands, so the absolute value is taken. Adding this change in volume to the initial volume gives the final volume:
Final volume = 59.2 mL + 1255 mL = 1314.2 mL.