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2305-2308
Thus, NaCl, CaCl2, MgSO4 are known as 1-1, 2-1 and 2-2 electrolytes respectively All electrolytes of a particular type have the same value for ‘A’ Fig 2
1
2306-2309
All electrolytes of a particular type have the same value for ‘A’ Fig 2 6: Molar conductivity versus c½ for acetic acid (weak electrolyte) and potassium chloride (strong electrolyte) in aqueous solutions
1
2307-2310
Fig 2 6: Molar conductivity versus c½ for acetic acid (weak electrolyte) and potassium chloride (strong electrolyte) in aqueous solutions Rationalised 2023-24 48 Chemistry The molar conductivity of KCl solutions at different concentrations at 298 K are given below: c/mol L–1 LLLLLm/S cm2 mol–1 0
1
2308-2311
2 6: Molar conductivity versus c½ for acetic acid (weak electrolyte) and potassium chloride (strong electrolyte) in aqueous solutions Rationalised 2023-24 48 Chemistry The molar conductivity of KCl solutions at different concentrations at 298 K are given below: c/mol L–1 LLLLLm/S cm2 mol–1 0 000198 148
1
2309-2312
6: Molar conductivity versus c½ for acetic acid (weak electrolyte) and potassium chloride (strong electrolyte) in aqueous solutions Rationalised 2023-24 48 Chemistry The molar conductivity of KCl solutions at different concentrations at 298 K are given below: c/mol L–1 LLLLLm/S cm2 mol–1 0 000198 148 61 0
1
2310-2313
Rationalised 2023-24 48 Chemistry The molar conductivity of KCl solutions at different concentrations at 298 K are given below: c/mol L–1 LLLLLm/S cm2 mol–1 0 000198 148 61 0 000309 148
1
2311-2314
000198 148 61 0 000309 148 29 0
1
2312-2315
61 0 000309 148 29 0 000521 147
1
2313-2316
000309 148 29 0 000521 147 81 0
1
2314-2317
29 0 000521 147 81 0 000989 147
1
2315-2318
000521 147 81 0 000989 147 09 Show that a plot between Lm and c1/2 is a straight line
1
2316-2319
81 0 000989 147 09 Show that a plot between Lm and c1/2 is a straight line Determine the values of L°m and A for KCl
1
2317-2320
000989 147 09 Show that a plot between Lm and c1/2 is a straight line Determine the values of L°m and A for KCl Taking the square root of concentration we obtain: c1/2/(mol L–1 )1/2 LLLLLm/S cm2mol–1 0
1
2318-2321
09 Show that a plot between Lm and c1/2 is a straight line Determine the values of L°m and A for KCl Taking the square root of concentration we obtain: c1/2/(mol L–1 )1/2 LLLLLm/S cm2mol–1 0 01407 148
1
2319-2322
Determine the values of L°m and A for KCl Taking the square root of concentration we obtain: c1/2/(mol L–1 )1/2 LLLLLm/S cm2mol–1 0 01407 148 61 0
1
2320-2323
Taking the square root of concentration we obtain: c1/2/(mol L–1 )1/2 LLLLLm/S cm2mol–1 0 01407 148 61 0 01758 148
1
2321-2324
01407 148 61 0 01758 148 29 0
1
2322-2325
61 0 01758 148 29 0 02283 147
1
2323-2326
01758 148 29 0 02283 147 81 0
1
2324-2327
29 0 02283 147 81 0 03145 147
1
2325-2328
02283 147 81 0 03145 147 09 A plot of Lm ( y-axis) and c1/2 (x-axis) is shown in (Fig
1
2326-2329
81 0 03145 147 09 A plot of Lm ( y-axis) and c1/2 (x-axis) is shown in (Fig 3
1
2327-2330
03145 147 09 A plot of Lm ( y-axis) and c1/2 (x-axis) is shown in (Fig 3 7)
1
2328-2331
09 A plot of Lm ( y-axis) and c1/2 (x-axis) is shown in (Fig 3 7) It can be seen that it is nearly a straight line
1
2329-2332
3 7) It can be seen that it is nearly a straight line From the intercept (c1/2 = 0), we find that L°m = 150
1
2330-2333
7) It can be seen that it is nearly a straight line From the intercept (c1/2 = 0), we find that L°m = 150 0 S cm2 mol–1 and A = – slope = 87
1
2331-2334
It can be seen that it is nearly a straight line From the intercept (c1/2 = 0), we find that L°m = 150 0 S cm2 mol–1 and A = – slope = 87 46 S cm2 mol–1/(mol/L–1)1/2
1
2332-2335
From the intercept (c1/2 = 0), we find that L°m = 150 0 S cm2 mol–1 and A = – slope = 87 46 S cm2 mol–1/(mol/L–1)1/2 Example 2
1
2333-2336
0 S cm2 mol–1 and A = – slope = 87 46 S cm2 mol–1/(mol/L–1)1/2 Example 2 6 Example 2
1
2334-2337
46 S cm2 mol–1/(mol/L–1)1/2 Example 2 6 Example 2 6 Example 2
1
2335-2338
Example 2 6 Example 2 6 Example 2 6 Example 2
1
2336-2339
6 Example 2 6 Example 2 6 Example 2 6 Example 2
1
2337-2340
6 Example 2 6 Example 2 6 Example 2 6 Solution Solution Solution Solution Solution Fig
1
2338-2341
6 Example 2 6 Example 2 6 Solution Solution Solution Solution Solution Fig 2
1
2339-2342
6 Example 2 6 Solution Solution Solution Solution Solution Fig 2 7: Variation of Lm against c½
1
2340-2343
6 Solution Solution Solution Solution Solution Fig 2 7: Variation of Lm against c½ Rationalised 2023-24 49 Electrochemistry Kohlrausch examined L°m values for a number of strong electrolytes and observed certain regularities
1
2341-2344
2 7: Variation of Lm against c½ Rationalised 2023-24 49 Electrochemistry Kohlrausch examined L°m values for a number of strong electrolytes and observed certain regularities He noted that the difference in L°m of the electrolytes NaX and KX for any X is nearly constant
1
2342-2345
7: Variation of Lm against c½ Rationalised 2023-24 49 Electrochemistry Kohlrausch examined L°m values for a number of strong electrolytes and observed certain regularities He noted that the difference in L°m of the electrolytes NaX and KX for any X is nearly constant For example at 298 K: L° m (KCl) – L° m (NaCl) = L° m (KBr) – L° m (NaBr) = L° m (KI) – L° m (NaI) ≃ 23
1
2343-2346
Rationalised 2023-24 49 Electrochemistry Kohlrausch examined L°m values for a number of strong electrolytes and observed certain regularities He noted that the difference in L°m of the electrolytes NaX and KX for any X is nearly constant For example at 298 K: L° m (KCl) – L° m (NaCl) = L° m (KBr) – L° m (NaBr) = L° m (KI) – L° m (NaI) ≃ 23 4 S cm2 mol–1 and similarly it was found that L° m (NaBr)– L° m (NaCl) = L° m (KBr) – L° m (KCl) ≃ 1
1
2344-2347
He noted that the difference in L°m of the electrolytes NaX and KX for any X is nearly constant For example at 298 K: L° m (KCl) – L° m (NaCl) = L° m (KBr) – L° m (NaBr) = L° m (KI) – L° m (NaI) ≃ 23 4 S cm2 mol–1 and similarly it was found that L° m (NaBr)– L° m (NaCl) = L° m (KBr) – L° m (KCl) ≃ 1 8 S cm2 mol–1 On the basis of the above observations he enunciated Kohlrausch law of independent migration of ions
1
2345-2348
For example at 298 K: L° m (KCl) – L° m (NaCl) = L° m (KBr) – L° m (NaBr) = L° m (KI) – L° m (NaI) ≃ 23 4 S cm2 mol–1 and similarly it was found that L° m (NaBr)– L° m (NaCl) = L° m (KBr) – L° m (KCl) ≃ 1 8 S cm2 mol–1 On the basis of the above observations he enunciated Kohlrausch law of independent migration of ions The law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte
1
2346-2349
4 S cm2 mol–1 and similarly it was found that L° m (NaBr)– L° m (NaCl) = L° m (KBr) – L° m (KCl) ≃ 1 8 S cm2 mol–1 On the basis of the above observations he enunciated Kohlrausch law of independent migration of ions The law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte Thus, if l° Na+ and l° Cl – are limiting molar conductivity of the sodium and chloride ions respectively, then the limiting molar conductivity for sodium chloride is given by the equation: L°m (NaCl) = l° Na+ + l° Cl – (2
1
2347-2350
8 S cm2 mol–1 On the basis of the above observations he enunciated Kohlrausch law of independent migration of ions The law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte Thus, if l° Na+ and l° Cl – are limiting molar conductivity of the sodium and chloride ions respectively, then the limiting molar conductivity for sodium chloride is given by the equation: L°m (NaCl) = l° Na+ + l° Cl – (2 24) In general, if an electrolyte on dissociation gives n+ cations and n– anions then its limiting molar conductivity is given by: L°m = n+ l° + + n– l° – (2
1
2348-2351
The law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte Thus, if l° Na+ and l° Cl – are limiting molar conductivity of the sodium and chloride ions respectively, then the limiting molar conductivity for sodium chloride is given by the equation: L°m (NaCl) = l° Na+ + l° Cl – (2 24) In general, if an electrolyte on dissociation gives n+ cations and n– anions then its limiting molar conductivity is given by: L°m = n+ l° + + n– l° – (2 25) Here, l° + and l° – are the limiting molar conductivities of the cation and anion respectively
1
2349-2352
Thus, if l° Na+ and l° Cl – are limiting molar conductivity of the sodium and chloride ions respectively, then the limiting molar conductivity for sodium chloride is given by the equation: L°m (NaCl) = l° Na+ + l° Cl – (2 24) In general, if an electrolyte on dissociation gives n+ cations and n– anions then its limiting molar conductivity is given by: L°m = n+ l° + + n– l° – (2 25) Here, l° + and l° – are the limiting molar conductivities of the cation and anion respectively The values of l° for some cations and anions at 298 K are given in Table 2
1
2350-2353
24) In general, if an electrolyte on dissociation gives n+ cations and n– anions then its limiting molar conductivity is given by: L°m = n+ l° + + n– l° – (2 25) Here, l° + and l° – are the limiting molar conductivities of the cation and anion respectively The values of l° for some cations and anions at 298 K are given in Table 2 4
1
2351-2354
25) Here, l° + and l° – are the limiting molar conductivities of the cation and anion respectively The values of l° for some cations and anions at 298 K are given in Table 2 4 Table 2
1
2352-2355
The values of l° for some cations and anions at 298 K are given in Table 2 4 Table 2 4: Limiting Molar Conductivity for some Ions in Water at 298 K Weak Electrolytes Weak electrolytes like acetic acid have lower degree of dissociation at higher concentrations and hence for such electrolytes, the change in Lm with dilution is due to increase in the degree of dissociation and consequently the number of ions in total volume of solution that contains 1 mol of electrolyte
1
2353-2356
4 Table 2 4: Limiting Molar Conductivity for some Ions in Water at 298 K Weak Electrolytes Weak electrolytes like acetic acid have lower degree of dissociation at higher concentrations and hence for such electrolytes, the change in Lm with dilution is due to increase in the degree of dissociation and consequently the number of ions in total volume of solution that contains 1 mol of electrolyte In such cases Lm increases steeply (Fig
1
2354-2357
Table 2 4: Limiting Molar Conductivity for some Ions in Water at 298 K Weak Electrolytes Weak electrolytes like acetic acid have lower degree of dissociation at higher concentrations and hence for such electrolytes, the change in Lm with dilution is due to increase in the degree of dissociation and consequently the number of ions in total volume of solution that contains 1 mol of electrolyte In such cases Lm increases steeply (Fig 2
1
2355-2358
4: Limiting Molar Conductivity for some Ions in Water at 298 K Weak Electrolytes Weak electrolytes like acetic acid have lower degree of dissociation at higher concentrations and hence for such electrolytes, the change in Lm with dilution is due to increase in the degree of dissociation and consequently the number of ions in total volume of solution that contains 1 mol of electrolyte In such cases Lm increases steeply (Fig 2 6) on dilution, especially near lower concentrations
1
2356-2359
In such cases Lm increases steeply (Fig 2 6) on dilution, especially near lower concentrations Therefore, L°m cannot be obtained by extrapolation of Lm to zero concentration
1
2357-2360
2 6) on dilution, especially near lower concentrations Therefore, L°m cannot be obtained by extrapolation of Lm to zero concentration At infinite dilution (i
1
2358-2361
6) on dilution, especially near lower concentrations Therefore, L°m cannot be obtained by extrapolation of Lm to zero concentration At infinite dilution (i e
1
2359-2362
Therefore, L°m cannot be obtained by extrapolation of Lm to zero concentration At infinite dilution (i e , concentration c ® zero) electrolyte dissociates completely (a =1), but at such low concentration the conductivity of the solution is so low that it cannot be measured accurately
1
2360-2363
At infinite dilution (i e , concentration c ® zero) electrolyte dissociates completely (a =1), but at such low concentration the conductivity of the solution is so low that it cannot be measured accurately Therefore, L°m for weak electrolytes is obtained by using Kohlrausch law of independent migration of ions (Example 2
1
2361-2364
e , concentration c ® zero) electrolyte dissociates completely (a =1), but at such low concentration the conductivity of the solution is so low that it cannot be measured accurately Therefore, L°m for weak electrolytes is obtained by using Kohlrausch law of independent migration of ions (Example 2 8)
1
2362-2365
, concentration c ® zero) electrolyte dissociates completely (a =1), but at such low concentration the conductivity of the solution is so low that it cannot be measured accurately Therefore, L°m for weak electrolytes is obtained by using Kohlrausch law of independent migration of ions (Example 2 8) At any concentration c, if a is the degree of dissociation Ion lllll0/(S cm2mol–1) Ion lllll 0/(S cm2 mol–1) H+ 349
1
2363-2366
Therefore, L°m for weak electrolytes is obtained by using Kohlrausch law of independent migration of ions (Example 2 8) At any concentration c, if a is the degree of dissociation Ion lllll0/(S cm2mol–1) Ion lllll 0/(S cm2 mol–1) H+ 349 6 OH– 199
1
2364-2367
8) At any concentration c, if a is the degree of dissociation Ion lllll0/(S cm2mol–1) Ion lllll 0/(S cm2 mol–1) H+ 349 6 OH– 199 1 Na+ 50
1
2365-2368
At any concentration c, if a is the degree of dissociation Ion lllll0/(S cm2mol–1) Ion lllll 0/(S cm2 mol–1) H+ 349 6 OH– 199 1 Na+ 50 1 Cl– 76
1
2366-2369
6 OH– 199 1 Na+ 50 1 Cl– 76 3 K+ 73
1
2367-2370
1 Na+ 50 1 Cl– 76 3 K+ 73 5 Br– 78
1
2368-2371
1 Cl– 76 3 K+ 73 5 Br– 78 1 Ca2+ 119
1
2369-2372
3 K+ 73 5 Br– 78 1 Ca2+ 119 0 CH3COO– 40
1
2370-2373
5 Br– 78 1 Ca2+ 119 0 CH3COO– 40 9 Mg2+ 106
1
2371-2374
1 Ca2+ 119 0 CH3COO– 40 9 Mg2+ 106 0 SO4 2 160
1
2372-2375
0 CH3COO– 40 9 Mg2+ 106 0 SO4 2 160 0 Rationalised 2023-24 50 Chemistry then it can be approximated to the ratio of molar conductivity Lm at the concentration c to limiting molar conductivity, L 0 m
1
2373-2376
9 Mg2+ 106 0 SO4 2 160 0 Rationalised 2023-24 50 Chemistry then it can be approximated to the ratio of molar conductivity Lm at the concentration c to limiting molar conductivity, L 0 m Thus we have: ° = m m    (2
1
2374-2377
0 SO4 2 160 0 Rationalised 2023-24 50 Chemistry then it can be approximated to the ratio of molar conductivity Lm at the concentration c to limiting molar conductivity, L 0 m Thus we have: ° = m m    (2 26) But we know that for a weak electrolyte like acetic acid (Class XI, Unit 7),     2 2 2 2 = = = a 1 1 m m m m m m m m c c c K                       (2
1
2375-2378
0 Rationalised 2023-24 50 Chemistry then it can be approximated to the ratio of molar conductivity Lm at the concentration c to limiting molar conductivity, L 0 m Thus we have: ° = m m    (2 26) But we know that for a weak electrolyte like acetic acid (Class XI, Unit 7),     2 2 2 2 = = = a 1 1 m m m m m m m m c c c K                       (2 27) Applications of Kohlrausch law Using Kohlrausch law of independent migration of ions, it is possible to calculate L 0 m for any electrolyte from the lo of individual ions
1
2376-2379
Thus we have: ° = m m    (2 26) But we know that for a weak electrolyte like acetic acid (Class XI, Unit 7),     2 2 2 2 = = = a 1 1 m m m m m m m m c c c K                       (2 27) Applications of Kohlrausch law Using Kohlrausch law of independent migration of ions, it is possible to calculate L 0 m for any electrolyte from the lo of individual ions Moreover, for weak electrolytes like acetic acid it is possible to determine the value of its dissociation constant once we know the L 0 m and Lm at a given concentration c
1
2377-2380
26) But we know that for a weak electrolyte like acetic acid (Class XI, Unit 7),     2 2 2 2 = = = a 1 1 m m m m m m m m c c c K                       (2 27) Applications of Kohlrausch law Using Kohlrausch law of independent migration of ions, it is possible to calculate L 0 m for any electrolyte from the lo of individual ions Moreover, for weak electrolytes like acetic acid it is possible to determine the value of its dissociation constant once we know the L 0 m and Lm at a given concentration c Calculate L 0 m for CaCl2 and MgSO4 from the data given in Table 3
1
2378-2381
27) Applications of Kohlrausch law Using Kohlrausch law of independent migration of ions, it is possible to calculate L 0 m for any electrolyte from the lo of individual ions Moreover, for weak electrolytes like acetic acid it is possible to determine the value of its dissociation constant once we know the L 0 m and Lm at a given concentration c Calculate L 0 m for CaCl2 and MgSO4 from the data given in Table 3 4
1
2379-2382
Moreover, for weak electrolytes like acetic acid it is possible to determine the value of its dissociation constant once we know the L 0 m and Lm at a given concentration c Calculate L 0 m for CaCl2 and MgSO4 from the data given in Table 3 4 We know from Kohlrausch law that  mCaCl2   = 2+ – Ca 2Cl      = 119
1
2380-2383
Calculate L 0 m for CaCl2 and MgSO4 from the data given in Table 3 4 We know from Kohlrausch law that  mCaCl2   = 2+ – Ca 2Cl      = 119 0 S cm2 mol–1 + 2(76
1
2381-2384
4 We know from Kohlrausch law that  mCaCl2   = 2+ – Ca 2Cl      = 119 0 S cm2 mol–1 + 2(76 3) S cm2 mol–1 = (119
1
2382-2385
We know from Kohlrausch law that  mCaCl2   = 2+ – Ca 2Cl      = 119 0 S cm2 mol–1 + 2(76 3) S cm2 mol–1 = (119 0 + 152
1
2383-2386
0 S cm2 mol–1 + 2(76 3) S cm2 mol–1 = (119 0 + 152 6) S cm2 mol–1 = 271
1
2384-2387
3) S cm2 mol–1 = (119 0 + 152 6) S cm2 mol–1 = 271 6 S cm2 mol–1  mMgSO4  = 2– 2+ 4 Mg SO      = 106
1
2385-2388
0 + 152 6) S cm2 mol–1 = 271 6 S cm2 mol–1  mMgSO4  = 2– 2+ 4 Mg SO      = 106 0 S cm2 mol–1 + 160
1
2386-2389
6) S cm2 mol–1 = 271 6 S cm2 mol–1  mMgSO4  = 2– 2+ 4 Mg SO      = 106 0 S cm2 mol–1 + 160 0 S cm2 mol–1 = 266 S cm2 mol–1
1
2387-2390
6 S cm2 mol–1  mMgSO4  = 2– 2+ 4 Mg SO      = 106 0 S cm2 mol–1 + 160 0 S cm2 mol–1 = 266 S cm2 mol–1 L 0 m for NaCl, HCl and NaAc are 126
1
2388-2391
0 S cm2 mol–1 + 160 0 S cm2 mol–1 = 266 S cm2 mol–1 L 0 m for NaCl, HCl and NaAc are 126 4, 425
1
2389-2392
0 S cm2 mol–1 = 266 S cm2 mol–1 L 0 m for NaCl, HCl and NaAc are 126 4, 425 9 and 91
1
2390-2393
L 0 m for NaCl, HCl and NaAc are 126 4, 425 9 and 91 0 S cm2 mol–1 respectively
1
2391-2394
4, 425 9 and 91 0 S cm2 mol–1 respectively Calculate L 0 for HAc
1
2392-2395
9 and 91 0 S cm2 mol–1 respectively Calculate L 0 for HAc  mHAc   = + – H Ac      + – – + – + H Cl Ac Na Cl Na                   =       HCl NaAc NaCl m m m         = (425
1
2393-2396
0 S cm2 mol–1 respectively Calculate L 0 for HAc  mHAc   = + – H Ac      + – – + – + H Cl Ac Na Cl Na                   =       HCl NaAc NaCl m m m         = (425 9 + 91
1
2394-2397
Calculate L 0 for HAc  mHAc   = + – H Ac      + – – + – + H Cl Ac Na Cl Na                   =       HCl NaAc NaCl m m m         = (425 9 + 91 0 – 126
1
2395-2398
 mHAc   = + – H Ac      + – – + – + H Cl Ac Na Cl Na                   =       HCl NaAc NaCl m m m         = (425 9 + 91 0 – 126 4 ) S cm2 mol –1 = 390
1
2396-2399
9 + 91 0 – 126 4 ) S cm2 mol –1 = 390 5 S cm2 mol–1
1
2397-2400
0 – 126 4 ) S cm2 mol –1 = 390 5 S cm2 mol–1 The conductivity of 0
1
2398-2401
4 ) S cm2 mol –1 = 390 5 S cm2 mol–1 The conductivity of 0 001028 mol L–1 acetic acid is 4
1
2399-2402
5 S cm2 mol–1 The conductivity of 0 001028 mol L–1 acetic acid is 4 95 × 10–5 S cm–1
1
2400-2403
The conductivity of 0 001028 mol L–1 acetic acid is 4 95 × 10–5 S cm–1 Calculate its dissociation constant if L 0 m for acetic acid is 390
1
2401-2404
001028 mol L–1 acetic acid is 4 95 × 10–5 S cm–1 Calculate its dissociation constant if L 0 m for acetic acid is 390 5 S cm2 mol–1
1
2402-2405
95 × 10–5 S cm–1 Calculate its dissociation constant if L 0 m for acetic acid is 390 5 S cm2 mol–1 m   =
1
2403-2406
Calculate its dissociation constant if L 0 m for acetic acid is 390 5 S cm2 mol–1 m   = 5 1 3 1 4 95 10 Scm 1000cm 0 001028 mol L L c       = 48
1
2404-2407
5 S cm2 mol–1 m   = 5 1 3 1 4 95 10 Scm 1000cm 0 001028 mol L L c       = 48 15 S cm3 mol–1 a =       2 1 2 1 48