A gas is confined to a cylinder under constant atmospheric pressure, as illustrated in the following figure. When the gas undergoes a particular chemical reaction, it absorbs 827 J of heat from its surroundings and has 0.66 kJ of P−V work done on it by its surroundings. Calculate Delta H and Delta E.

You just convert the absorption of heat into kJ

So 827 J of heat absorbed = .827 kJ

^ that is for delta H

Delta E is going to be kJ of heat absorbed plus kJ of work
So in this case it is .827 kJ + .66 kJ = 1.49 kJ

Well, let's start by clarifying what ΔH and ΔE represent.

ΔH stands for the change in enthalpy, which is the heat flow in or out of a system at constant pressure. ΔE represents the change in internal energy of a system, which takes into account the system's heat and work.

Now, to calculate ΔH, we know that the gas absorbs 827 J of heat from its surroundings. So, ΔH = +827 J (because it is gaining heat from the surroundings).

Moving on to ΔE, we need to consider the work done on the system. The work done on the gas is given as 0.66 kJ. However, we need to convert this value to joules to match the unit of heat.

1 kJ = 1000 J

So, 0.66 kJ = 0.66 * 1000 J = 660 J.

Since the work is done on the system, ΔE = -660 J (negative because the system is losing energy).

So, to summarize:
ΔH = +827 J
ΔE = -660 J

But hey, at least the gas is absorbing some heat and not feeling left out. You could say it's a hot topic!

To calculate Delta H (change in enthalpy) and Delta E (change in internal energy), we need to understand their definitions and the relationship between them.

1. Delta H: Delta H represents the change in enthalpy, which is the heat absorbed or released during a chemical reaction at constant pressure.

The formula to calculate Delta H is:
Delta H = q (heat energy) + PΔV (pressure-volume work)

In this case, we know:
q = 827 J (heat absorbed by the gas)
PΔV = 0.66 kJ = 0.66 * 1000 J (P-V work done on the gas)

2. Delta E: Delta E represents the change in internal energy, which is the total energy of the system. It includes both the heat exchange and work done on or by the system.

The formula to calculate Delta E is:
Delta E = q (heat energy) + W (work done on or by the system)

In this case, we already have the values for q and W.

Now let's calculate Delta H and Delta E:

Delta H = q + PΔV
Delta H = 827 J + 0.66 * 1000 J
Delta H = 827 J + 660 J
Delta H = 1487 J

Therefore, the change in enthalpy (Delta H) is 1487 J.

Delta E = q + W
Delta E = 827 J + 0.66 * 1000 J
Delta E = 827 J + 660 J
Delta E = 1487 J

Therefore, the change in internal energy (Delta E) is also 1487 J.

Note: It's important to convert the units consistently throughout the calculation. In this case, we converted kJ to J by multiplying by 1000.

delta H = q = 827 J and since it absorbs heat the sign is +.

delta E = q + work
work = PdV = 0.66 kJ
Since work is done ON IT, the sign of work is +.
Substitute and solve.

827.66