阅读说明：本技术 一种铅电解用氟硅酸及其制备方法 (Fluosilicic acid for lead electrolysis and preparation method thereof ) 是由 任忠虎 安东 刘泽巨 李龙伍 杨占菊 黎碧玉 马福元 李振昌 刘世浩 杜国栋 于 2020-07-20 设计创作，主要内容包括：本发明提供一种铅电解用氟硅酸及其制备方法,属于化学化工技术领域。其中,制备方法包括：提供低品位氟硅酸溶液,所述低品位氟硅酸溶液掺杂有氟化氢杂质和硫酸杂质。将一定量的石英砂加入低品位氟硅酸溶液进行反应,以对氟化氢杂质进行第一次去除,得到第一清液。将一定量的氧化铅加入第一清液进行反应,以将硫酸杂质去除,并同时对剩余的氟化氢杂质进行第二次去除,得到第二清液,第二清液即为铅电解用氟硅酸。本发明通过采用特殊晶体形貌的石英砂可有效去除氟化氢杂质,并利用氧化铅去除硫酸杂质和剩余的氟化氢杂质,氟化氢杂质的总去除率达99％以上,硫酸杂质的总去除率达98％以上,具有较高的杂质去除率,并且,制备工艺简单,成本较低。(The invention provides fluosilicic acid for lead electrolysis and a preparation method thereof, belonging to the technical field of chemistry and chemical engineering. The preparation method comprises the following steps: providing a low-grade fluorosilicic acid solution, wherein the low-grade fluorosilicic acid solution is doped with hydrogen fluoride impurities and sulfuric acid impurities. Adding a certain amount of quartz sand into a low-grade fluorosilicic acid solution for reaction so as to remove hydrogen fluoride impurities for the first time, thereby obtaining a first clear liquid. Adding a certain amount of lead oxide into the first clear liquid for reaction to remove sulfuric acid impurities, and simultaneously removing the residual hydrogen fluoride impurities for the second time to obtain a second clear liquid, wherein the second clear liquid is the fluosilicic acid for lead electrolysis. According to the invention, the hydrogen fluoride impurities can be effectively removed by adopting the quartz sand with a special crystal morphology, and the lead oxide is utilized to remove the sulfuric acid impurities and the residual hydrogen fluoride impurities, so that the total removal rate of the hydrogen fluoride impurities reaches more than 99%, the total removal rate of the sulfuric acid impurities reaches more than 98%, the impurity removal rate is higher, the preparation process is simple, and the cost is lower.)

1. A preparation method of fluosilicic acid for lead electrolysis is characterized by comprising the following steps:

providing a low-grade fluorosilicic acid solution, wherein the low-grade fluorosilicic acid solution is doped with hydrogen fluoride impurities and sulfuric acid impurities;

adding a certain amount of quartz sand into the low-grade fluorosilicic acid solution for reaction so as to remove the hydrogen fluoride impurities for the first time to obtain a first clear liquid;

adding a certain amount of lead oxide into the first clear liquid for reaction to remove the sulfuric acid impurities, and simultaneously removing the residual hydrogen fluoride impurities for the second time to obtain a second clear liquid, wherein the second clear liquid is the fluosilicic acid for lead electrolysis.

2. The preparation method according to claim 1, wherein adding a certain amount of quartz sand into the low-grade fluorosilicic acid solution for reaction to remove the hydrogen fluoride impurities for the first time to obtain a first clear solution comprises:

analyzing and calculating the content of the hydrogen fluoride impurities in the low-grade fluorosilicic acid solution, and determining the theoretical mass of the required quartz sand according to the content of the hydrogen fluoride impurities;

determining the actual mass of the quartz sand according to the molar ratio range of the theoretical mass of the quartz sand to the actual mass of the quartz sand being 1 (1.5-4);

adding quartz sand with actual mass into the low-grade fluosilicic acid solution, and controlling the reaction under a first preset reaction condition to remove the hydrogen fluoride impurities for the first time to obtain the first clear liquid.

3. The method according to claim 2, wherein the first predetermined reaction condition is:

the reaction temperature range is 15-60 ℃, the stirring intensity range is 80-300 rpm, and the reaction time range is 1.5-5 h.

4. The preparation method according to claim 2, characterized by further comprising, before adding actual quality quartz sand to the low-grade fluosilicic acid:

calcining common quartz sand at 500-1000 ℃ for 2-24 h to obtain the quartz sand, wherein,

the quartz sand is in an alpha crystal form, and the microscopic appearance of the quartz sand is hexagonal cylinder.

5. The method according to claim 4, wherein the quartz sand has a particle size of 3mm or less.

6. The preparation method according to any one of claims 1 to 5, wherein the adding of an amount of lead oxide to the first clear liquid for reaction to remove the sulfuric acid impurities and simultaneously performing a second removal of the remaining hydrogen fluoride impurities to obtain a second clear liquid comprises:

analyzing and calculating the content of the sulfuric acid impurities in the first clear liquid, and determining the required theoretical mass of the lead oxide according to the content of the sulfuric acid impurities;

determining the actual mass of the lead oxide according to the molar ratio range of the theoretical mass of the lead oxide to the actual mass of the lead oxide being 1 (0.5-2);

adding lead oxide with actual mass into the first clear liquid, controlling the reaction under a second preset reaction condition to remove the sulfuric acid impurities, and simultaneously removing the residual hydrogen fluoride impurities for the second time to obtain a second clear liquid.

7. The method according to claim 6, wherein the second predetermined reaction condition is:

the reaction temperature range is 10-60 ℃, the stirring intensity range is 80-300 rpm, and the stirring reaction time range is 0.5-3 h.

8. The preparation method according to claim 6, wherein after adding lead oxide of actual quality into the first clear liquid and controlling the reaction under the second preset reaction condition to remove the sulfuric acid impurity and simultaneously remove the remaining hydrogen fluoride impurity for the second time to obtain the second clear liquid, the method further comprises:

and freezing the second clear liquid at the temperature ranging from-30 ℃ to-5 ℃, and removing the sulfuric acid impurities for the second time to obtain the fluosilicic acid for lead electrolysis.

9. The method according to claim 6, wherein the lead oxide has a particle size of 100 μm or less.

10. A fluorosilicic acid for lead electrolysis prepared by the method of any one of claims 1 to 9.

Technical Field

The invention belongs to the technical field of chemistry and chemical engineering, and particularly relates to a preparation method of fluosilicic acid for lead electrolysis and the fluosilicic acid for lead electrolysis.

Background

Molecular formula of fluosilicic acid H₂SiF₆Molecular weight 144.09, the aqueous solution is a colorless transparent fuming liquid, has relative density of about 1.32, boiling point of 108.50 ℃, has pungent odor, is volatile and soluble in water, has maximum concentration of 60.92 percent, and has no anhydrous product. The acid is highly toxic, can erode mucosa, eyes and skin, has strong corrosion to skin, and is toxic to human respiratory organs; is a basic raw material for preparing sodium fluosilicate, potassium fluosilicate, ammonium fluosilicate, magnesium fluosilicate, copper fluosilicate, barium fluosilicate and silicon tetrafluoride, and is used in the industries of metal electroplating, wood corrosion prevention, brewing industry equipment disinfection, lead electrolytic refining and the like.

Two main industrial production methods are available, one is the by-product fluosilicic acid in the industrial production of phosphoric acid and phosphate fertilizer. Associated fluorine-containing minerals in the phosphate ore mainly exist in the forms of fluorapatite, calcium fluosilicate and the like, and in the acidolysis process of the phosphate ore, fluorine elements in the fluorapatite and the calcium fluosilicate react to generate gaseous hydrogen fluoride and silicon tetrafluoride, and the gaseous hydrogen fluoride and the silicon tetrafluoride are washed and absorbed to obtain a fluosilicic acid byproduct. And the second is the by-product fluosilicic acid in the production of anhydrous hydrogen fluoride by fluorite sulfuric acid method. Calcium fluoride in fluorite reacts with sulfuric acid to generate hydrogen fluoride gas, the generated hydrogen fluoride gas reacts with silicon dioxide in fluorite to produce silicon tetrafluoride gas, and the gaseous hydrogen fluoride and silicon tetrafluoride are washed and absorbed to obtain a fluosilicic acid byproduct. The production process of the fluosilicic acid produced by the two methods determines that the fluosilicic acid contains hydrogen fluoride and sulfuric acid impurity components.

The lead electrolysis industry needs to prepare a certain amount of Pb²⁺The fluosilicic acid solution with concentration is used for meeting the use requirement of grooving or grooving electrolyte, and in addition, as the electrolytic production is carried out, the anode mud layer is gradually thickened and compacted, and Pb is²⁺The diffusion difficulty is increased, the anode current efficiency is lower than the cathode current efficiency, and Pb in the fluosilicic acid electrolyte²⁺The concentration of Pb is continuously depleted, so that Pb needs to be supplemented into the electrolyte²⁺Control of fluosilicic acid electrolyte Pb²⁺The concentration reaches the technological index, thereby ensuring the quality of the cathode lead.

The existing lead electrolyte preparation method is to add a proper amount of lead oxide into industrial fluosilicic acid and lead oxide and fluosilicic acid react to generate lead fluosilicate solution. This method has the following problems: during the production of the fluosilicic acid, the production process determines that the fluosilicic acid contains hydrogen fluoride and sulfuric acid impurity components, and in addition, the fluosilicic acid is decomposed under certain conditions to generate hydrogen fluoride, so that the content of the fluosilicic acid is reduced. In addition, during lead electrolysis, the added lead oxide reacts with hydrogen fluoride and sulfuric acid to generate PbF₂、PbSO₄Precipitation, on one hand, increases the usage amount of lead oxide and greatly increases the production cost of lead electrolyte, and on the other hand, needs PbF₂、PbSO₄The precipitate is separated, and the preparation operation flow of the lead electrolyte is increased.

Therefore, aiming at the low-grade fluosilicic acid which is a byproduct in the production of anhydrous hydrogen fluoride by adopting a fluorite sulfuric acid method at present, a new method for preparing the fluosilicic acid for lead electrolysis needs to be developed, so that the impurity components are reduced, the purity of the fluosilicic acid is improved, and the use requirement of the lead electrolyte is further met.

Disclosure of Invention

The invention aims to at least solve one of the technical problems in the prior art and provides a preparation method of fluosilicic acid for lead electrolysis and the fluosilicic acid for lead electrolysis.

In one aspect of the invention, a preparation method of fluosilicic acid for lead electrolysis is provided, which comprises the following steps:

providing a low-grade fluorosilicic acid solution, wherein the low-grade fluorosilicic acid solution is doped with hydrogen fluoride impurities and sulfuric acid impurities;

adding a certain amount of quartz sand into the low-grade fluorosilicic acid solution for reaction so as to remove the hydrogen fluoride impurities for the first time to obtain a first clear liquid;

adding a certain amount of lead oxide into the first clear liquid for reaction to remove the sulfuric acid impurities, and simultaneously removing the residual hydrogen fluoride impurities for the second time to obtain a second clear liquid, wherein the second clear liquid is the fluosilicic acid for lead electrolysis.

Optionally, adding a certain amount of quartz sand into the low-grade fluorosilicic acid solution for reaction to remove the hydrogen fluoride impurity for the first time, so as to obtain a first clear liquid, including:

analyzing and calculating the content of the hydrogen fluoride impurities in the low-grade fluorosilicic acid solution, and determining the theoretical mass of the required quartz sand according to the content of the hydrogen fluoride impurities;

determining the actual mass of the quartz sand according to the molar ratio range of the theoretical mass of the quartz sand to the actual mass of the quartz sand being 1 (1.5-4);

adding quartz sand with actual mass into the low-grade fluosilicic acid solution, and controlling the reaction under a first preset reaction condition to remove the hydrogen fluoride impurities for the first time to obtain the first clear liquid.

Optionally, the first preset reaction condition is:

the reaction temperature range is 15-60 ℃, the stirring intensity range is 80-300 rpm, and the reaction time range is 1.5-5 h.

Optionally, before adding the quartz sand of practical quality into the low-grade fluosilicic acid, the method further comprises the following steps:

calcining common quartz sand at 500-1000 ℃ for 2-24 h to obtain the quartz sand, wherein,

the quartz sand is in an alpha crystal form, and the microscopic appearance of the quartz sand is hexagonal cylinder.

Optionally, the particle size of the quartz sand is less than or equal to 3 mm.

Optionally, the adding a certain amount of lead oxide into the first clear solution to perform a reaction to remove the sulfuric acid impurity, and simultaneously performing a second removal on the remaining hydrogen fluoride impurity to obtain a second clear solution, including:

analyzing and calculating the content of the sulfuric acid impurities in the first clear liquid, and determining the required theoretical mass of the lead oxide according to the content of the sulfuric acid impurities;

determining the actual mass of the lead oxide according to the molar ratio range of the theoretical mass of the lead oxide to the actual mass of the lead oxide being 1 (0.5-2);

adding lead oxide with actual mass into the first clear liquid, controlling the reaction under a second preset reaction condition to remove the sulfuric acid impurities, and simultaneously removing the residual hydrogen fluoride impurities for the second time to obtain a second clear liquid.

Optionally, the second preset reaction condition is:

the reaction temperature range is 10-60 ℃, the stirring intensity range is 80-300 rpm, and the stirring reaction time range is 0.5-3 h.

Optionally, after adding lead oxide of an actual mass into the first clear liquid and controlling to perform a reaction under a second preset reaction condition to remove the sulfuric acid impurity and simultaneously remove the remaining hydrogen fluoride impurity for a second time to obtain a second clear liquid, the method further includes:

and freezing the second clear liquid at the temperature ranging from-30 ℃ to-5 ℃, and removing the sulfuric acid impurities for the second time to obtain the fluosilicic acid for lead electrolysis.

Optionally, the particle size of the lead oxide is less than or equal to 100 μm.

In another aspect of the present invention, there is provided a fluosilicic acid for lead electrolysis, which is prepared by the above-mentioned method for preparing a fluosilicic acid for lead electrolysis.

The invention provides a preparation method of fluosilicic acid for lead electrolysis, which comprises the following steps: providing a low-grade fluorosilicic acid solution, wherein the low-grade fluorosilicic acid solution is doped with hydrogen fluoride impurities and sulfuric acid impurities, adding a certain amount of quartz sand into the low-grade fluorosilicic acid solution for reaction so as to remove the hydrogen fluoride impurities for the first time to obtain a first clear solution, adding a certain amount of lead oxide into the first clear solution for reaction so as to remove the sulfuric acid impurities, and simultaneously removing the remaining hydrogen fluoride impurities for the second time to obtain a second clear solution, wherein the second clear solution is the fluorosilicic acid for lead electrolysis. The preparation method provided by the invention adopts a two-step method to remove the hydrogen fluoride impurities and the sulfuric acid impurities, the total removal rate of the hydrogen fluoride impurities reaches more than 99 percent, and the total removal rate of the sulfuric acid impurities reaches 98 percent. And the fluosilicic acid for lead electrolysis is directly obtained, so that the preparation operation flow of the lead electrolyte during lead electrolysis production is simplified. The preparation method provided by the invention has the advantages of simple process, convenience in operation and lower cost, and the obtained fluosilicic acid for lead electrolysis does not introduce other impurity components, has higher purity, can meet the use requirement of lead electrolyte, and greatly improves the use efficiency of the lead electrolysis industry.

Drawings

FIG. 1 is a flow chart of a method for preparing fluosilicic acid for lead electrolysis according to an embodiment of the present invention;

FIG. 2 is a scanning electron microscope image of pre-calcination quartz sand used in a method for preparing fluosilicic acid for lead electrolysis according to another embodiment of the present invention;

FIG. 3 is a scanning electron microscope image of calcined quartz sand used in a method for preparing fluosilicic acid for lead electrolysis according to another embodiment of the present invention;

fig. 4 is a scanning electron microscope image of calcined quartz sand used in the method for preparing fluosilicic acid for lead electrolysis according to another embodiment of the present invention.

Detailed Description

In order to make the technical solutions of the present invention better understood, the present invention will be described in further detail with reference to the accompanying drawings and specific embodiments. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention without any inventive step, are within the scope of protection of the invention.

As shown in fig. 1, one aspect of the present invention provides a method S100 for preparing fluosilicic acid for lead electrolysis, specifically including the following steps S110 to S130:

s110, providing a low-grade fluorosilicic acid solution, wherein the low-grade fluorosilicic acid solution is doped with hydrogen fluoride impurities and sulfuric acid impurities.

It should be noted that the low-grade fluorosilicic acid solution provided in this embodiment is a byproduct in the production of anhydrous hydrogen fluoride, and includes the following main components: h₂SiF₆、HF、H₂SO₄For the lead electrolysis industry, doped hydrogen fluoride impurities and sulfuric acid impurities have certain adverse effects, and further removal is needed to obtain high-purity fluosilicic acid so that the low-grade fluosilicic acid can be effectively applied, so that the content of each component in the low-grade fluosilicic acid needs to be analyzed, and then the corresponding impurities are removed according to specific applications.

And S120, adding a certain amount of quartz sand into a low-grade fluorosilicic acid solution for reaction so as to remove hydrogen fluoride impurities for the first time, thereby obtaining a first clear liquid.

Specifically, step S120 includes: analyzing and calculating the content (mass fraction range is 1-30%) of hydrogen fluoride impurities in the low-grade fluorosilicic acid solution, determining the theoretical mass of the quartz sand according to the content of the hydrogen fluoride impurities, and determining the actual mass of the quartz sand according to the molar ratio range of the theoretical mass of the quartz sand to the actual mass of the quartz sand, wherein the molar ratio range is 1 (1.5-4). And then adding quartz sand with actual mass into the low-grade fluosilicic acid solution, controlling the reaction under a first preset reaction condition to remove hydrogen fluoride impurities for the first time, and naturally settling or separating solid from liquid the solid-liquid mixture after the reaction to obtain a first clear liquid and unreacted quartz sand. That is to say, the actual mass of the quartz sand that needs to be added in this embodiment is more than the theoretical mass, and thus, the reaction between the hydrogen fluoride impurity and the silicon dioxide in the quartz sand is facilitated, so as to improve the removal rate of the hydrogen fluoride impurity.

Optionally, the first preset reaction condition in the above step is: the reaction temperature range is 15-60 ℃, the stirring intensity range is 80-300 rpm, and the reaction time range is 1.5-5 h. For those skilled in the art, the specific reaction parameters can be set according to actual needs, and are not particularly limited.

It should be noted that the unreacted quartz sand formed in the above steps can be reused, so that on one hand, the utilization rate of the quartz sand is improved, and on the other hand, the addition amount of lead oxide in the next step of reaction is reduced, so as to obtain better economic benefit.

It is further noted that, because the main component of the quartz sand is silicon dioxide, the silicon dioxide reacts with hydrogen fluoride to generate fluosilicic acid, so that the aim of removing the hydrogen fluoride can be achieved, and the H in the solution can be increased₂SiF₆And (4) concentration. However, the reaction effect of the common quartz sand and hydrogen fluoride is poor, and the micro-topography is shown in fig. 2, so that the embodiment performs pretreatment on the common quartz sand, such as: the quartz sand with a specific crystal morphology is formed by calcining the quartz sand at a certain temperature, so that the removal rate of hydrogen fluoride impurities is improved.

Specifically, before adding quartz sand of practical quality into low-grade fluosilicic acid, the method further comprises the following steps: calcining the common quartz sand at 500-1000 ℃ for 2-24 h to obtain the quartz sand with a specific crystal morphology. As shown in FIG. 3, the calcined quartz sand has a hexagonal prism microstructure, and as shown in FIG. 4, the calcined quartz sand has a loose porous structure and a large specific surface area, which increases the contact area with hydrogen fluoride and is beneficial to improving the removal rate of hydrogen fluoride impurities.

Further, this example further studies the influence of the quartz sand with different particle sizes on the reaction result. Specifically, the particle size of the quartz sand is less than or equal to 3mm, for example, the particle size range of 0.5mm to 3mm is selected for comparative test, so that the effect of the quartz sand with the particle size range of less than 2mm is obviously better than that of the quartz sand with the particle size range of 2mm to 3mm, and especially when the particle size of the quartz sand is less than 0.5mm, the effect of removing hydrogen fluoride impurities is optimal and reaches 99.2%.

The α crystal form, the hexagonal prism micro-morphology and the quartz sand with the particle size less than 2mm adopted by the embodiment have the advantages that the smaller the particle size, the larger the surface area, the more molecules directly participating in the reaction, the more effective reaction collision times and the benefit to SiO in the quartz sand₂React with HF in low-grade fluosilicic acid to generate H₂SiF₆The removal rate of the hydrogen fluoride impurities is over 95 percent, the usage amount of lead oxide in the subsequent process is effectively reduced, and the removal rate of the hydrogen fluoride impurities by the common quartz sand is only about 60 percent. Therefore, the preparation method of the embodiment has high removal rate of hydrogen fluoride impurities, and can increase H₂SiF₆The content of (3) can also reduce the usage amount of lead oxide.

S130, adding a certain amount of lead oxide into the first clear liquid for reaction to remove sulfuric acid impurities, and simultaneously removing the residual hydrogen fluoride impurities for the second time to obtain a second clear liquid, wherein the second clear liquid is the fluosilicic acid for lead electrolysis.

Specifically, step S130 includes: analyzing and calculating the content (mass fraction range is 1-10%) of sulfuric acid impurities in the first clear liquid, determining the required theoretical mass of lead oxide according to the content of the sulfuric acid impurities, and determining the actual mass of the lead oxide according to the molar ratio range of the theoretical mass of the lead oxide to the actual mass of the lead oxide being 1 (0.5-2). And then adding lead oxide with actual mass into the first clear liquid, controlling the reaction under a second preset reaction condition to remove sulfuric acid impurities, and simultaneously removing the residual hydrogen fluoride impurities for the second time to obtain a second clear liquid. That is to say, the mass of the added lead oxide is determined according to actual needs, so that the sulfuric acid impurities and the lead oxide can fully react, the removal rate of the sulfuric acid impurities is improved, and meanwhile, the hydrogen fluoride impurities remaining in step S120 can be further removed, so that the removal rate of the hydrogen fluoride impurities reaches 99%.

It should be noted that, in this embodiment, the lead oxide added in the first clear liquid may react with the sulfuric acid impurity to generate a lead sulfate precipitate, and may also react with the remaining small amount of hydrogen fluoride impurity to generate a lead fluoride precipitate, and then the precipitate by-product is removed by natural sedimentation or filtration separation, so as to obtain a second clear liquid, that is, a fluorosilicic acid solution for lead electrolysis. It is to be noted that since a large amount of hydrogen fluoride impurities have been removed in step S120, the amounts of lead fluoride precipitates and lead sulfate precipitates generated in step S130 are small, that is, by-products are small with the production method of the present embodiment. In addition, in the preparation method of the embodiment, other impurity ions are not introduced except for lead ions, and the generated lead fluosilicate can be directly used as a lead electrolyte while removing sulfuric acid impurities, so that the effect of supplementing lead is achieved, and the need of preparing a certain amount of Pb in the subsequent lead electrolysis process is eliminated²⁺The fluosilicic acid solution with the concentration simplifies the lead electrolysis process flow and greatly improves the application efficiency.

Specifically, the second preset reaction condition in step S130 is: the reaction temperature range is 10-60 ℃, the stirring intensity range is 80-300 rpm, and the stirring reaction time range is 0.5-3 h. In addition, the lead oxide particle size used in the present example is 100 μm or less. For those skilled in the art, the specific reaction parameters can be set according to actual needs, and are not particularly limited.

It should be understood that in order to further remove the remaining sulfuric acid impurities, the present embodiment also employs a freezing method to remove them. Specifically, after adding lead oxide of an actual mass to the first clear liquid and controlling the reaction under a second preset reaction condition to remove the sulfuric acid impurity and simultaneously remove the remaining hydrogen fluoride impurity for a second time to obtain a second clear liquid, the method further includes: and (3) freezing the second clear liquid at the temperature ranging from-30 ℃ to-5 ℃, and removing the residual sulfuric acid impurities for the second time to further remove the sulfuric acid impurities, so that the removal rate of the sulfuric acid impurities reaches 98%, and the high-purity fluosilicic acid for lead electrolysis is obtained.

In the embodiment, hydrogen fluoride impurities and sulfuric acid impurities in the low-grade fluosilicic acid are effectively removed by adopting two-step reaction, wherein the total removal rates of the hydrogen fluoride impurities and the sulfuric acid impurities can respectively reach 99% and 98%, and other impurity ions are not introduced, so that the purity of the formed fluosilicic acid for lead electrolysis is high, the application efficiency of the fluosilicic acid is effectively improved, and the subsequent process flow is simplified.

The preparation of fluosilicic acid for lead electrolysis will be further described with reference to several specific examples: