# Mathematical model of process of dissolution of nickelous sulphide in the presence of cations Cu (II)

For reception of kinetic model of process of dissolution of nickelous sulphide in the presence of cations Cu ^{ 2 + } the range of influencing factors (0.5 and # 8804 is chosen; C (HNO _{ 3 }) and #8804; 3 mole/dm ^{ 3 }; 298 both #8804; T and #8804; 323 To; 1.6 both #8804; and #969; and #8804; 10.0 with ’ ^{ 1 }).

^{ 3 }. It corresponds to area of zero order on Cu

^{ 2 + }(fig. 4.5).

Table 4.6 - Conditions and results of the experiences executed for construction of model at ion density of copper (II) of 0.002 mo-ekv/dm ^{ 3 }

u | C (HNO, a mole 3 dm | T, TO | and #969;, with ’ ^{ 1 } | W-10 ^{ 7 }, ’ 2 ’ 1 a mole-dm-with | AND #9632; Ig (W) |

1 | 0.5 | 323 | 10 | 0.883 | 7.053 |

2 | 0.5 | 323 | 1.6 | 0.735 | 7.133 |

3 | 0.5 | 293 | 10 | 0.569 | 7.244 |

4 | 0.5 | 293 | 1.6 | 0.539 | 7.268 |

5 | 3 | 323 | 10 | 1.851 | 6.731 |

6 | 3 | 323 | 1.6 | 1.405 | 6.852 |

7 | 3 | 293 | 10 | 1.395 | 6.855 |

8 | 3 | 293 | 1.6 | 1.303 | 6.885 |

Table 4.7 - the Matrix of planning PFE 2 ^{ 3 }, and also results of experiment and settlement values of function of the response on taken over polynomial model (4.5)

u | Õ0 | Õ1 | Õ2 | Hz | Õ1Õ2 | Õ1Õç | Õ2Õ3 | Õ1Õ2Õ3 | ^{ y } u (prakt) | ^{ y } (fashions) |

1 | +1 | -1 | -1 | +1 | +1 | -1 | -1 | +1 | -7.053 | -7.115 |

2 | +1 | -1 | -1 | -1 | +1 | +1 | +1 | -1 | -7.133 | -7.115 |

3 | +1 | -1 | +1 | +1 | -1 | -1 | +1 | -1 | -7.244 | -7.235 |

4 | +1 | -1 | +1 | -1 | -1 | +1 | -1 | +1 | -7.268 | -7.235 |

5 | +1 | +1 | -1 | +1 | -1 | +1 | -1 | -1 | -6.731 | -6.770 |

6 | +1 | +1 | -1 | -1 | -1 | -1 | +1 | +1 | -6.852 | -6.770 |

7 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | -6.855 | -6.891 |

8 | +1 | +1 | +1 | -1 | +1 | -1 | -1 | -1 | -6.885 | -6.891 |

For a finding of value of a dispersion of reproducibility are made

experiences in the plan centre, S ^{ 1 } _{ eocnp } = 0.00082. (f=3, and #945; =0.95).

polynomial model

nachenija regression factors

are resulted in table 4. 8.

Table 4.8 - Settlement values of factors

polynominal model (4.5)

b0 | b1 | b2 | b3 | ^{ b } 12 | ^{ b } 13 | ^{ b } 23 | ^{ b } 123 |

-7.0032 | 0.1721 | -0.0602 | 0.0317 | 0.0211 | 0.0058 | -0.0184 | -0.0043 |

From table 4.8 data follows, that level of a background of errors exceed koeffitsientz b _{ 0 }, bi and b _{ 2 }. The others are recognised by insignificant.

With the account only the polynomial model looks like significant factors:

settlement value of a dispersion of adequacy of model (4.5) S ^{ 2 } _{ a } _{ } = 0.002463 Is found. Hypothesis check about adequacy of model by Fisher's criterion is made. Settlement value And _{ rasch } = 2.99 less than its tabular value F _{ ra } _{ 6 } _{ n } = 9.01. Polynomial model (4.5) is recognised by adequately representing studied process.

Adequate polynomial model transformed to the corresponding equation of speed of process of dissolution:

According to model (4.6) intensity of agitating does not influence speed of transferring of nickel in a solution. Order on acid is close to zero. The dissolution kinetic constant is equal 9.18 and # 8729; 10 ^{-8 } mol^dm ’ ^{ 1 } ’ ^{ 3 } ^ ’ ^{ 1 }. Critical increment of energy is equal 3.6±0.3 a kdzh/MOLE. The kinetic mode of interaction is observed.

Influence of concentration of hydrogen nitrate and temperature in the presence of cations of copper (II) for specific speed of dissolution of nickelous sulphide according to the equation (4.5) is reflected by a surface represented in drawing 4.6. It is visible, that more essential factor influencing for speed of dissolution millerita, the process temperature is. In the investigated area in the presence of cations Cu ^{ 2 + } the greatest size of speed (1.36 and # 8729; 10 ^{-7 } molydm ^{-2 } ·s ^{-1 }) it is reached at C (HNO _{ 3 }) = 3 mole/dm ^{ 3 } and Ò=323 K

Drawing 4.6 - Dependence of speed of dissolution of nickelous sulphide on concentration HNO _{ 3 } and temperatures T at O (Cu ^{ 2 + }) = 0.002 mole-ekv/dm ^{ 3 }

on model (4.5)

dependence of speed of dissolution in wider range T (tab. 4.9, fig. 4.7) is follow-up investigated. From drawing 4.7 it is visible, that in temperature range from 20 to 80 ^{ 0 } With at concentration of hydrogen nitrate an equal 1 mole/dm ^{ 3 } critical increment of energy is equal in the yielded conditions 3.77 + 0.3 kdzh/MOLE, the linear relation that speaks about a kinetic mode of passing of process is observed.

Table 4.9 - Results of experiences on studying of dependence of speed of dissolution from temperature at C (HNO _{ 3 }) = 1 mole/dm ^{ 3 } and C (Cu ^{ 2 + }) = 0,002 molyekv/dm ^{ 3 }

Lg (W)

Drawing 4.7 - Dependence of the logarithm of speed on return temperature of process in hydrogen nitrate with concentration 1 mole/dm ^{ 3 } and C (Cu ^{ 2 + }) = 0,002 molyekv/dm ^{ 3 }

4.2.3

## More on topic Mathematical model of process of dissolution of nickelous sulphide in the presence of cations Cu (II):

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- the Mechanism of dissolution of nickelous sulphide in the presence of cations Cu (II)
- the Mechanism of dissolution of nickelous sulphide in the presence of cations Fe (III)
- Generalization of results on dissolution of nickelous sulphide (II) in hydrogen nitrate in the presence of cations Fe (III) and Cu (II)
**Speed of dissolution of nickelous sulphide (II) in hydrogen nitrate 3 + in the presence of cations Fe****Speed of dissolution of nickelous sulphide (II) in hydrogen nitrate in the presence of cations Cu 2 +**- Influence of concentration of cations Cu 2 + for speed of dissolution of nickelous sulphide
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