In a certain chemical reaction, 20.40kJ of heat are evolved. The volume of the reaction is 36.8dm^3 and that of the product is 9.6dm^3. Calculate the change in internal energy for the reaction. Assume the reaction is at ATM pressure.?

But what is atm pressure? It could be anything. I assume you meant normal or standard atm pressure.

dE = q + w
q = -20.40 kJ. Negative because heat is released
w = p*dV.
p = 1 atm
dV = 36.8 - 9.6 = 27.2
Volume decreases meaning that work is done on the system so w is positive. Also the 27.2 is dm^3 * atm. Convert to kJ. Multiply by 101.325
dE = -20.40 + (101.325 x 27.2) = ? kJ.
Check this carefully.

To calculate the change in internal energy (ΔU) for the reaction, we need to use the equation:

ΔU = q + w

where:
ΔU is the change in internal energy
q is the heat transferred
w is the work done

In this case, we are given that 20.40 kJ of heat (q) is evolved in the reaction. However, we are not given any information about the work done (w). Therefore, we cannot directly calculate the change in internal energy using the given information.

To calculate the work done, we need to know the pressure of the reaction. Since the question states that the reaction is at "ATM" pressure, we can assume that the pressure is standard atmospheric pressure, which is approximately 1 atmosphere (atm).

The work done in a chemical reaction can be calculated using the equation:

w = -PΔV

where:
w is the work done
P is the pressure
ΔV is the change in volume

In this case, the change in volume (ΔV) can be calculated by subtracting the initial volume (36.8 dm^3) from the final volume (9.6 dm^3):

ΔV = 9.6 dm^3 - 36.8 dm^3 = -27.2 dm^3

Since the reaction is at atmospheric pressure, we can substitute the values into the equation:

w = -(1 atm) * (-27.2 dm^3) = 27.2 atm·dm^3

Now, we can calculate the change in internal energy (ΔU) using the equation:

ΔU = q + w

ΔU = 20.40 kJ + 27.2 atm·dm^3

However, we need to convert the units of work (27.2 atm·dm^3) to kilojoules (kJ) so that the units are consistent:

1 atm·dm^3 = 101.325 J
1 kJ = 1000 J

Therefore, to convert atm·dm^3 to kJ:

27.2 atm·dm^3 * (101.325 J / 1 atm·dm^3) * (1 kJ / 1000 J) ≈ 2.75 kJ

Now we can substitute the values into the equation:

ΔU = 20.40 kJ + 2.75 kJ ≈ 23.15 kJ

Therefore, the change in internal energy for the reaction is approximately 23.15 kJ.