a sample of gas occupies a volume at 73. 1 mL. As it expands, it does 135.0 J of work on its surroundings at a constant pressure of 783 torr. what is the final volume of gas?
w= -PΔV
-135.0 J = -783 torr × (Vfinal - 73.1 mL)
-1350 J × (1L atm)/(101.32 J) = -783 torr × (1atm/760 torr) × (Vfinal -73.1 ml × 1L/1000 mL)
Vfinal= (-1350 J × (1 L atm)/(101.32 J))/(-783 torr × (1 atm)/(760 torr)) + 73.1 mL × (1L/1000 mL) = 1.36 L
Vfinal = 1.36 × (1000mL/1L) = 1360 mL
Well, let's gasp for answers, shall we? According to the good ol' work formula, work = pressure x change in volume. In this case, we know that work is 135.0 J and pressure is 783 torr.
Now, we just need to rearrange the formula to solve for the change in volume: change in volume = work / pressure. Plugging in the numbers, we get change in volume = 135.0 J / 783 torr.
However, we can't stop there! We need to convert the pressure from torr to liters, and 783 torr is approximately equal to 1 atm. So, changing the pressure to 1 atm, we can say that change in volume = 135.0 J / 1 atm.
Finally, we look to convert the volume from mL to liters. Since 1 L = 1000 mL, the initial volume of 73.1 mL is equal to 0.0731 L.
Now, we can calculate the final volume by adding the initial volume to the change in volume: final volume = 0.0731 L + (135.0 J / 1 atm). And there you have it, my friend!
To find the final volume of gas, we can use the formula:
Work = -Pressure * Change in Volume
In this case, the work done by the gas on its surroundings is given as 135.0 J, and the pressure is 783 torr. The initial volume of the gas is 73.1 mL.
To find the change in volume, we rearrange the formula:
Change in Volume = Work / (-Pressure)
Let's calculate the change in volume:
Change in Volume = 135.0 J / (-783 torr) = -0.1722 L
The negative sign indicates that the gas has expanded.
Finally, to find the final volume, we add the initial volume to the change in volume:
Final Volume = Initial Volume + Change in Volume
Final Volume = 73.1 mL - 0.1722 L = 72.9278 mL (rounded to four decimal places)
Therefore, the final volume of the gas is approximately 72.9278 mL.
To find the final volume of the gas, we can use the work done on the gas equation:
Work = -P × ΔV
Where:
Work is the work done on the gas (in J)
P is the pressure (in atm)
ΔV is the change in volume (in L)
First, let's convert the initial volume from mL to L:
73.1 mL = 0.0731 L
The pressure is given as 783 torr. Since the work and pressure are given in different units, we need to convert torr to atm:
1 atm = 760 torr
So, the pressure in atm is:
783 torr / 760 torr/atm = 1.03 atm
Substituting the given values into the equation:
135 J = -1.03 atm × ΔV
Solving for ΔV:
ΔV = -135 J / (-1.03 atm)
ΔV = 131.1 L
The change in volume, ΔV, represents the final volume minus the initial volume. We can now find the final volume by adding ΔV to the initial volume:
Final volume = Initial Volume + ΔV
Final volume = 0.0731 L + 131.1 L
Final volume ≈ 131.1731 L
Therefore, the final volume of the gas is approximately 131.1731 L.