Final answer:
The work done by a chemical reaction when the volume increases from 3.1 L to 3.4 L against a constant pressure of 3.9 atm is -120 J, using the formula W = - P ∆V and converting units appropriately.
Step-by-step explanation:
To calculate the work done by a chemical reaction where the volume of a gas increases from 3.1 L to 3.4 L against a constant external pressure of 3.9 atm, we use the formula:
W = - P ∆V
where W is the work done on the system (in joules), P is the pressure (in atmospheres), and ∆V is the change in volume (in liters).
First, convert the pressure from atmospheres to pascals (1 atm = 101325 Pa), and then multiply by the change in volume.
The change in volume (∆V) is 3.4 L - 3.1 L = 0.3 L,
which we need to convert to cubic meters (1 L = 0.001 m³), so ∆V = 0.0003 m³.
The work done is then calculated as follows:
W = - P ∆V
W = - (3.9 atm × 101325 Pa/atm) × 0.0003 m³
W = - (394567.5 Pa) × 0.0003 m³
W = -118.37 J
We express this value using two significant figures:
Work done = -120 J
The negative sign indicates that work is done by the system (expanding against the external pressure).