Here are some formulas.
#ΔS_"total" = ΔS_"univ" = ΔS_"sys" + ΔS_"surr" = q_"sys"/T_"sys" + q_"surr"/T_"surr"#
where #q# is the heat and #T# is the Kelvin temperature.
Entropy Change for the System
#ΔS_"sys" = ΔS_"rxn" = Sigma(n_pS_"products"^"o") – Sigma(n_rS_"reactants"^"o")#
where #n_p# and #n_r# represent moles of products and reactions.
Entropy Change for the Surroundings
#ΔS_"surr" = q_"surr"/T_"surr"#
#q_"surr" = -q_"sys"#
#ΔS_"surr" = q_"surr"/T_"surr" = -q_"sys"/T_"surr"#
Example 1:
What is #ΔS_"surr"# at 300 K for the reaction
reactants → products; #ΔH# = 75 kJ
Solution:
#ΔS_"sys" = q/T = (75 000" J")/(300" K")# = 250 J/K
#ΔS_"surr" = q_"surr"/T_"surr" = -(ΔH_"sys")/T_"surr" = -(75 000" J")/(300" K")# = -250 J/K
Example 2:
What is #ΔS_"rxn"^"o"# for the following reaction?
4NH₃(g) + 5O₂(g) → 4NO(g) + 6H₂O(g)
The #S^"o"# values are NH₃ = 193 J·K⁻¹mol⁻¹; O₂ = 205 J·K⁻¹mol⁻¹; NO = 211 J·K⁻¹mol⁻¹;
H₂O = 189 J·K⁻¹mol⁻¹
#ΔS_"sys" = Sigma(n_pS_"products"^"o") – Sigma(n_rS_"reactants"^"o")#
#ΔS_"rxn"^"o" = 4S_"NO"^"o" + 6S_"H₂O"^"o" – 4S_"NH₃" - 5S_"O₂"^"o"#
#ΔS_"rxn"^"o" = (4×211 + 6 × 189 - 4 × 193 + 5 × 205 )# J/K⁻¹ = 181 J•K⁻¹
