Effect of drug Piper nigrum on magnesium chloride at varying concentration and temperature through ultrasonic method: A thermoacoustic study

Figures & data

Table 1. Comparison of experimental ultrasonic velocity (U), density (ρ), and viscosity (η) of pure liquids with literature values at 303.15 K

Liquid	U (ms^−1)		ρ (kg/m^3)		η (×10^−3 N s/m^2)
	Expt.	Lit. (Ref.)	Expt.	Lit. (Ref.)	Expt.	Lit. (Ref.)
Ethanol	1,130	1,131.5 (51)	776.2	779.15 (51)	0.9126	0.9122 (51)
MgCl2 in ethanol	1,655	1,656 (52)	1,060	1059 (52)	1.6396	1.6398 (52)
P. nigrum (drug)	1,152	–	776.8	–	5.3405	–

Table 2. Ultrasonic velocities (U), densities (ρ), and viscosities (η) for MgCl₂ + P. nigrum system at 303.15, 308.15, 313.15, and 318.15 K

Temperature (T) (K)	Number of moles (n)	U (ms^−1)	ρ (kg/m^3)	η (×10^−3 N Sm^−2)
303.15	0.7009	1,674	893.2	6.197
	1.4018	1,679	891.6	6.580
	2.1027	1,689	889.1	6.999
	2.8036	1,698	886.5	7.327
	3.5045	1,710	887.3	6.656
308.15	0.7009	1663	890.3	5.722
	1.4018	1,672	887.9	6.005
	2.1027	1,682	885.1	6.397
	2.8036	1,688	881.2	6.667
	3.5045	1,701	883.2	6.219
313.15	0.7009	1,646	885.8	5.283
	1.4018	1,656	882.5	5.548
	2.1027	1,666	880.1	5.813
	2.8036	1,670	877.4	6.076
	3.5045	1,683	879.1	5.665
318.15	0.7009	1,627	880.4	4.755
	1.4018	1,636	878.2	5.062
	2.1027	1,641	876.3	5.265
	2.8036	1,652	872.7	5.585
	3.5045	1,667	875.1	5.228

Figure 1. Variation in (a) ultrasonic velocity (U), (b) density (ρ), and (c) viscosity (η) of MgCl₂ + P. nigrum (n) system at 303.15, 308.15, 313.15, and 318.15 K.

Table 3. Adiabatic compressibility (β) (×10⁻¹⁰ kg⁻¹ ms²), intermolecular free lengths (L_f) (×10⁻¹¹ m), specific acoustic impedance (Z) (×10⁵ Kgm⁻² s⁻¹), relaxation amplitude (α/f²) (×10⁻¹⁴ Npm⁻¹ s²), relaxation time (τ) (×10⁻¹²) for MgCl₂ + P. nigrum system at 303.15, 308.15, 313.15 and 318.15 K

Number of moles (n)	Temperature (T) (K)
	303.15	308.15	313.15	318.15
	β (×10^−10 kg^−1 ms^2)
0.7009	3.995	4.061	4.166	4.290
1.4018	3.978	4.028	4.132	4.255
2.1027	3.943	3.993	4.093	4.239
2.8036	3.912	3.982	4.086	4.198
3.5045	3.854	3.913	4.016	4.112
	Lf (×10^−11 m)
0.7009	4.148	4.223	4.318	4.423
1.4018	4.139	4.206	4.300	4.405
2.1027	4.121	4.187	4.280	4.396
2.8036	4.105	4.181	4.276	4.375
3.5045	4.074	4.145	4.239	4.330
	Z (×10^5 kgm^−2 s^−1)
0.7009	14.95	14.80	14.58	14.32
1.4018	14.96	14.84	14.61	14.36
2.1027	15.01	14.88	14.66	14.37
2.8036	15.05	14.87	14.65	14.41
3.5045	15.17	15.02	14.79	14.58
	α/f^2 (×10^−14 npm^−1 s^2)
0.7009	3.888	3.674	3.516	3.297
1.4018	4.099	3.804	3.640	3.462
2.1027	4.296	3.993	3.755	3.576
2.8036	4.439	4.136	3.909	3.732
3.5045	3.944	3.761	3.554	3.391
	τ (×10^−12)
0.7009	3.301	3.099	2.935	2.720
1.4018	3.490	3.225	3.057	2.872
2.1027	3.680	3.406	3.173	2.976
2.8036	3.822	3.540	3.310	3.126
3.5045	3.420	3.244	3.033	2.866

Figure 2. Variation in (a) adiabatic compressibility (β), (b) intermolecular free length (L_f), (c) specific acoustic impedance (Z), (d) relaxation amplitude (α/f²), and (e) relaxation time (τ) of MgCl₂ + P. nigrum (n) system at 303.15, 308.15, 313.15 and 318.15 K.

Table 4. Excess values of ultrasonic velocity ($U^E$), excess density (${\mathit{\rho }}^E$) and excess viscosity (${\mathit{\eta }}^E$) for MgCl₂ + P. nigrum (n) at 303.15, 308.15, 313.15, and 318.15 K

Temperature (T) (K)	Number of moles (n)	$U^E$ (ms^−1)	${\mathit{\rho }}^E$ (kg/m^3)	${\mathit{\eta }}^E$ (×10^−3 NSm^−2)
303.15	0.7009	517.028	0.1152	3.7411
	1.4018	524.552	0.1134	3.4948
	2.1027	534.380	0.1116	3.5039
	2.8036	543.993	0.1092	3.5507
	3.5045	556.421	0.1110	2.6719
308.15	0.7009	526.494	0.1180	3.4905
	1.4018	535.382	0.1161	3.1953
	2.1027	545.717	0.1139	3.2112
	2.8036	553.596	0.1111	3.2230
	3.5045	565.733	0.1134	2.5848
313.15	0.7009	516.177	0.1194	3.2925
	1.4018	526.871	0.1175	3.0657
	2.1027	537.336	0.1152	3.0097
	2.8036	541.683	0.1128	3.0525
	3.5045	555.032	0.1148	2.4803
318.15	0.7009	508.420	0.1210	2.8752
	1.4018	517.195	0.1193	2.6925
	2.1027	522.488	0.1171	2.5768
	2.8036	533.630	0.1150	2.6777
	3.5045	548.534	0.1164	2.1598

Figure 3. (a) Variation in excess ultrasonic velocity(U^E), (b) excess density (ρ^E), and (c) excess viscosity (η^E) of MgCl₂ + P. nigrum (n) system at 303.15, 308.15, 313.15 and 318.15 K.

Table 5. Excess values of adiabatic compressibility (${\mathit{\beta }}^E$) (×10⁻¹⁰ kg⁻¹ ms²), excess intermolecular free length ($L_f^E$) (×10⁻¹¹ m), specific acoustic impedance ($Z^E$) (×10⁵ Kgm⁻² s⁻¹), relaxation amplitude ($\frac{{\mathit{\alpha }}^E}{f^2}$) (×10⁻¹⁴ Npm⁻¹ s²) and relaxation time (${\mathit{\tau }}^E$) (×10⁻¹²) for MgCl₂ + P. nigrum (n) system at 303.15, 308.15, 313.15 and 318.15 K

Number of moles (n)	Temperature (T) (K)
	303.15	308.15	313.15	318.15
	${\mathit{\beta }}^E$ (×10^−10 kg^−1 ms^2)
0.7009	−4.3053	−5.0040	−5.6373	−6.3927
1.4018	−4.6329	−5.2653	−5.7848	−6.4032
2.1027	−4.8684	−5.4476	−5.8961	−6.4043
2.8036	−5.0375	−5.5603	−5.9537	−6.4343
3.5045	−5.1977	−5.7049	−6.0613	−6.5128
	$L_f^E$ (×10^−11 m)
0.7009	−1.8129	−2.0690	−2.2888	−2.5370
1.4018	−1.9316	−2.1656	−2.3469	−2.5501
2.1027	−2.0232	−2.2376	−2.3953	−2.5580
2.8036	−2.0889	−2.2795	−2.4177	−2.5776
3.5045	−2.1562	−2.3429	−2.4687	−2.6218
	$Z^E$ (×10^5 kgm^−2 s^−1)
0.7009	6.0258	5.9815	5.8958	5.8027
1.4018	6.0586	6.0104	5.9574	5.8693
2.1027	6.0760	6.0162	5.9582	5.8802
2.8036	6.1552	6.1027	6.0104	5.9275
3.5045	6.2440	6.1976	6.1571	6.1027
	$\frac{{\mathit{\alpha }}^E}{f^2}$ (×10^−14 npm^−1 s^2)
0.7009	−1.2107	−4.9246	−4.4989	−4.4241
1.4018	−2.4852	−6.3525	−5.7570	−5.7025
2.1027	−3.2380	−7.2666	−6.5628	−6.5211
2.8036	−3.7542	−7.9003	−7.1213	−7.0885
3.5045	−4.7337	−8.3665	−7.5321	−7.5059
	${\mathit{\tau }}^E$ (×10^−12 Sec)
0.7009	0.4899	0.3801	0.4139	0.2021
1.4018	−0.2230	−0.3400	−0.1941	−0.3697
2.1027	−0.6133	−0.7032	−0.5466	−0.7305
2.8036	−0.8718	−0.9454	−0.7332	−0.9014
3.5045	−1.5689	−1.5179	−1.2488	−1.3977

Figure 4. (a) Variation in excess adiabatic compressibility (β^E), (b) excess intermolecular free length ($L_f^E$), (c) excess specific acoustic impedance (Z^E), (d) excess relaxation amplitude ($\frac{{\mathit{\alpha }}^E}{f^2}$), and (e) excess relaxation time (τ^E) of MgCl₂ + P. nigrum (n) system at 303.15, 308.15, 313.15 and 318.15 K.