Effect of Hydration and Base Contaminants on Sulfuric Acid Diffusion Measurement: A Computational Study

Figures & data

Table 1 Clusters included in the systems studied using the B3LYP/CBSB7//RICC2/aug-cc-pV(T+d)Z cluster energies. The number of water molecules in the cluster is indicated in parenthesis. Additional clusters, that were included only in the simulations where the system was extended to clusters containing up to two H₂SO₄ and two base molecules, are marked with an asterisk; otherwise only clusters containing up to one H₂SO₄ and one base molecule were included

	0 base molecules	1 base molecule	2 base molecules
0 H2SO4 molecules		DMA ( = 0–1) NH3 ( = 0–4) MMA ( = 0–2) TMA ( = 0–1)	DMA ( = 0)*
H2SO4	( = 0–5)	DMA ( = 0–5) NH3 ( = 0–5) MMA ( = 0–3) TMA ( = 0–2)	DMA ( = 0)*
(H2SO4)2	( = 0–5)*	DMA ( = 0–5)*	DMA ( = 0–5)*

Figure 1 Flowchart of the procedure and methods implemented in this study.

Figure 2 Effective diffusion coefficient as a function of RH for the system containing only single sulfuric acid molecules and its hydrates H₂SO₄•(H₂O)_n, with n = 0−2 and n = 0−n_max, calculated using (a) B3LYP/CBSB7//RICC2/aug-cc-pV(T+d)Z (n_max = 5; plus signs and circles), (b) MP2/aug-cc-pV(D+d)Z//ΔE₀,3-step (n_max = 4; x's and squares), and (c) RI-MP2/aug-cc-pVDZ//RI-MP2/CBS (n_max = 6; asterisks and triangles) Gibbs free energies.

Figure 3 Effective diffusion coefficient as a function of RH for the system containing H₂SO₄, base, and H₂SO₄•base species and their hydrates at varying initial RH-independent base concentration when the base is DMA (top panel) and TMA (bottom panel), calculated using the B3LYP/CBSB7//RICC2/aug-cc-pV(T+d)Z Gibbs free energies.

Figure 4 Effective diffusion coefficient as a function of RH for the system containing H₂SO₄, base, and H₂SO₄•base species and their hydrates at RH-dependent base concentration and varying initial H₂SO₄ concentration when the base is DMA (top panel) and TMA (bottom panel), calculated using the B3LYP/CBSB7//RICC2/aug-cc-pV(T+d)Z Gibbs free energies. The shaded (green) area presents the spread of the results for pD_eff as the initial H₂SO₄ concentration varies between 3 × 10⁷ cm⁻³ and 3 × 10⁹ cm⁻³.

Figure 5 Effective diffusion coefficient as a function of RH for the H₂SO₄–DMA system extended to include larger clusters, calculated using the B3LYP/CBSB7//RICC2/aug-cc-pV(T+d)Z Gibbs free energies. The shaded (green) area presents the spread of the results for pD_eff as the initial H₂SO₄ concentration varies between 3 × 10⁷ cm⁻³ and 3 × 10⁹ cm⁻³. The upper limit of the shaded area corresponds to [H₂SO₄]_init = 4 × 10⁸ cm⁻³.

Table 2 Equilibrium constants K₁ and K₂ obtained from the fits (Equation (2)[2] ) to the theoretical effective diffusion coefficients presented in Figures 2–5, and their changes ΔK₁ and ΔK₂ with respect to the actual input values, defined as ΔK_n = (K_n,fit−K_n,input)/K_n,input, for the systems where the changes in the simulation result were significant (note that the constants are not at the standard state of 1 atm). 95% confidence bounds for the absolute values K_n are stated in the parenthesis. N/A indicates that the fit could not be unambiguously applied because the initial acid and base concentrations as a function of RH are not known; K_n corresponding to specific concentrations are given in the square brackets

Studied	Quantum chemical
system	method	K1	ΔK1	K2	ΔK2
H2SO4 hydrated by up	a	0.02506 (actual value)	–	0.006512 (actual value)	–
to 2 waters	b	0.1039 (actual value)	–	0.01517 (actual value)	–
	c	0.03971 (actual value)	–	0.002536 (actual value)	–
	d	0.01467 (actual value)	–	0.04945 (actual value)	–
H2SO4 hydrated by up to nmax waters	a	0.02088 (0.02028, 0.02148)	−17%	0.01085 (0.01054, 0.01116)	67%
	b	0.003249 (0.0, 0.008021)	−97%	0.5877 (0.0, 1.446)	3774%
	c	0.02303 (0.02096, 0.02511)	−42%	0.01449 (0.01335, 0.01563)	471%
	d	0.001134 (0.0, 0.002479)	−92%	0.8650 (0.0, 1.88)	1649%
H2SO4–DMA	a	N/A [0.001467 (0.0, 0.003912)*]	N/A [−94%*]	N/A [0.6030 (0.0, 1.592)*]	N/A [9159%*]
H2SO4–TMA	a	N/A [0.04238 (0.04141, 0.04336)*]	N/A [69%*]	N/A [0.01845 (0.01814, 0.01876)*]	N/A [183%*]
H2SO4–DMA, extended to include larger clusters	a	N/A [0.02043 (0.02000, 0.02085)*]	N/A [−18%*]	N/A [0.005097 (0.004943, 0.005252)*]	N/A [−22%*]

a: B3LYP/CBSB7//RICC2/aug-cc-pV(T+d)Z, n_max = 5.b: MP2/aug-cc-pV(D+d)Z//ΔE₀,3-step, n_max = 4.c: RI-MP2/aug-cc-pVDZ//RI-MP2/CBS, n_max = 6.d: PW91PW91/6-311++G(3df,3pd), n_max = 3.*At [H₂SO₄]_init = 3×10⁸ cm⁻³ and [base]_init = 2.5 × 10⁶ cm⁻³ × RH.