We have 1 mol of N2 gas that is heated at constant pressure from 300K to 5770K on the surface of the sun.

i) Find H and S given that P for nitrogen is (25.7 + 0.0130T) J/mol-K.
ii) Now, redo your calculation assuming that the second T-dependent term in the P expression is negligible (i.e. P does not depend on T)
iii) What is the percent error if we assume that P is not temperature dependent?

To find ΔH and ΔS given the equation P = (25.7 + 0.0130T) J/mol-K, we need to integrate this equation with respect to T.

i) Find ΔH and ΔS assuming T-dependent P:

To find ΔH, we need to integrate the equation P with respect to T, and then multiply the result by the change in temperature (ΔT). Since we have a temperature-dependent pressure, the integration equation becomes:

ΔH = ∫P dT

Integrating the given equation:
ΔH = ∫(25.7 + 0.0130T) dT

Evaluating the integral:
ΔH = 25.7T + 0.0065T^2 + C

To find the constant C, we need boundary conditions. Here, C represents the value of ΔH at T = 300K. Let's assume C = 0. Substitute the values:

0 = 25.7(300) + 0.0065(300)^2
0 = 7710 + 5850
0 = 13,560

Since this equation doesn't hold true, let's assume a different value for C. Let's set C = -13,560 to satisfy the equation at T = 300K:

ΔH = 25.7T + 0.0065T^2 - 13,560

To find ΔS, we use the equation ΔS = ∫(ΔH/T) dT:

ΔS = ∫[(25.7T + 0.0065T^2 - 13,560)/T] dT

Evaluating the integral:
ΔS = 25.7ln(T) + 0.0065(T^2)/2 - 13,560ln(T) + C

Assuming C = 0:
ΔS = 12.7ln(T) + 0.00325T^2

Now, we can substitute the final temperatures into these formulas to calculate ΔH and ΔS.

ii) Find ΔH and ΔS when assuming negligible T-dependent P:

Since the second T-dependent term in the P expression is negligible, we can consider P to be constant. Let's assume P = P0.

ΔH = P0ΔT
ΔS = (ΔH/T) + Rln(P0/P1)

R is the ideal gas constant, which is 8.314 J/(mol·K), and P1 is the initial pressure.

iii) Calculate percent error if we assume P is not temperature dependent:

To calculate the percent error, we need the actual value of ΔH and ΔS and the values obtained when assuming P is not temperature dependent. We can calculate the percent error using the following formula:

Percent Error = ((Actual Value - Assumed Value) / Actual Value) * 100