Question

A sample of gas occupies a volume of 74.7 mL. As it expands, it does 123.3 J of work on its surroundings at a constant pressure of 783 torr. What is the final volume of the gas?

Answer 1

Are you familiar with the gas laws?

Answer 2

I am not too strong with them

Answer 3

work= -PΔV
-123.3 J = -783 torr × (Vfinal - 74.7 mL)

Answer 4

So,
\[.157 = (Vfinal - 74.6 mL)\]

Answer 5

\[Vfinal = 74.757\] ?

Answer 6

We have to make some conversions. Torr is not an SI unit.

Answer 7

What would we convert it to?

Answer 8

Right!

Answer 9

we need the units on the left to match the units on the right.
so we can convert Joules to L atm.

Answer 10

work= -PΔV
-123.3 J = -783 torr × (Vfinal - 74.7 mL)
-123.3 × (1L atm)/(101.32 J) = -783 torr × (1atm/760 torr) × (Vfinal -74.7 ml × 1L/1000 mL)

Answer 11

\[1.21694 = -1.03(Vfinal - .0747)\]

Answer 12

Sorry, the first one is negative

Answer 13

\[-1.21694=−1.03(Vfinal−.0747)\]

Answer 14

\[10.89 = (Vfinal - .0747)\]
\[Vfinal = 10.965\]

Answer 15

But then we have to convert back to mL, so would it be 10965 mL?

Answer 16

doing this on paper, one minute

Answer 17

You should not round intermediate calculations.
Ideally put it in one equation.

-123.3 /101.3 = -783 / 760 ( v - 74.7/1000)

Answer 18

I did too when I did it the second time. I put 12.1694 by accident into my calculator

Answer 19

Gotcha, that way it is more accurate

Answer 20

I got 1.255889902 L or 1255.889902 mL
which is about 1255.9 mL

Answer 21

Thank you for your help. I'm looking at another problem and it actually makes sense now!

Answer 22

Great :)

Answer 23

Again, thank you for teaching

Answer 24

your welcome