A balloon filled with 22.3 mol helium has a volume of 500. L at 0.0°C and 1.00 atm pressure. The temperature of the balloon is increased to 38.0°C as it expands to a volume of 570. L, the pressure remaining constant. Calculate q, w, and E for the helium in the balloon. (The molar heat capacity for helium gas is 20.8 J/°C·mol.)

q = mass He x specific heat He x (Tf - Ti) where Tf is final T and Ti is initial T. mass He is 22.3 mol and Cp is 20.8 J/mol*c. Solve for q.

work = -p(delta V) = -p(V2 - V1)
V2, V1, and p are given. Solve for work. Work will be in L*atm so multiply what you get by 101.3 J/1 atm to convert to Joules.

Delta E = q + w.

Post your work if you get stuck.

for q i got 70538.931

for w i got 7091
and for the change i got 77629.931

the last one was worng, are they all wrong?

To calculate q, w, and E for the helium in the balloon, we need to use the first law of thermodynamics, which states that the change in internal energy (ΔE) of a system is equal to the heat (q) added to the system minus the work (w) done by the system:

ΔE = q - w

Let's go step by step to calculate q, w, and E:

Step 1: Calculate the change in temperature (ΔT)
ΔT = T₂ - T₁ = 38.0°C - 0.0°C = 38.0°C

Step 2: Calculate the change in volume (ΔV)
ΔV = V₂ - V₁ = 570 L - 500 L = 70 L

Step 3: Calculate the heat added to the system (q)
q = nCΔT
where n is the number of moles of helium and C is the molar heat capacity for helium gas.

Given:
n = 22.3 mol
C = 20.8 J/°C·mol
ΔT = 38.0°C

q = 22.3 mol × 20.8 J/°C·mol × 38.0°C
q = 18,707 J

Therefore, q = 18,707 J

Step 4: Calculate the work done by the system (w)
Since the pressure remains constant, the work done is given by the equation:
w = -PΔV
where P is the pressure in atm and ΔV is the change in volume in liters.

Given:
P = 1.00 atm
ΔV = 70 L

w = -1.00 atm × 70 L
w = -70 atm·L

Since we need the work done in Joules, we will convert atm·L to J using the conversion factor 1 atm·L = 101.3 J:

w = -70 atm·L × 101.3 J/atm·L
w = -7071 J

Therefore, w = -7071 J

Step 5: Calculate the change in internal energy (ΔE)
ΔE = q - w

ΔE = 18,707 J - (-7071 J)
ΔE = 18,707 J + 7071 J
ΔE = 25,778 J

Therefore, ΔE = 25,778 J

In summary:
q = 18,707 J
w = -7071 J
ΔE = 25,778 J