A method for selectively recovering rhodium from iron-removed liquid containing rhodium by two-stage micro-flow counter-jet enhanced reduction precipitation

Abstract

This invention discloses a two-stage microfluidic jet-enhanced reduction precipitation selective recovery method for Rh-containing iron removal liquid, comprising: taking waste catalyst stock solution, filtering with a filter membrane to remove suspended particles and colloidal impurities, and collecting the clarified waste liquid for later use; passing the clarified waste liquid and sodium sulfite solution into a microfluidic jet reactor, where the two solutions converge to undergo an enhanced reduction reaction, reducing ferric iron to ferrous iron; adjusting the pH of the mixture after the first-stage reaction with alkali solution, and passing the first-stage filtrate obtained by vacuum filtration and sodium borohydride alkali solution into the microfluidic jet reactor to undergo a selective enhanced reduction reaction, reducing Rh ions to elemental particles, while ferrous iron remains in the solution; filtering the mixture to collect the precious metal rhino filter residue, and detecting the residual Rh and iron in the filtrate. This invention utilizes microfluidic jet-enhanced mass transfer, reducing the reaction time to milliseconds, directly obtaining elemental rhino, and producing hydrogen as a byproduct. The process is compact, the reagents are controllable, highly efficient and environmentally friendly, and has broad prospects for industrial application.

Description

Technical Field

[0001] This invention relates to the fields of waste catalyst resource utilization, precious metal Rh recovery, and microfluidic enhanced reaction technology, and particularly to a method for selectively recovering Rh from rhodium-containing iron removal liquid by two-stage microfluidic spray-enhanced reduction precipitation. Background Technology

[0002] In the fields of petrochemicals, fine chemicals, and automotive exhaust purification, precious metal catalysts are widely used due to their excellent catalytic activity and chemoselectivity.

[0003] After long-term continuous use, catalysts will experience problems such as activity decay and structural damage, resulting in a large amount of waste catalysts.

[0004] The rhodium-containing iron removal solution obtained after enriching and leaching waste catalysts not only contains high-value platinum group metal ions such as Rh, but also a large number of impurity ions such as ferric ions.

[0005] Directly discharging this waste liquid would not only cause a serious loss of precious metal resources, but also lead to environmental problems such as heavy metal water pollution and soil pollution. Therefore, the efficient recovery of precious metals from rhodium-containing iron removal liquid has become a key research direction in the field of precious metal resource utilization.

[0006] Currently, the mainstream wet process for recovering precious metals from waste liquid is the traditional precipitation method, which usually uses a precipitant in combination with a large mechanical stirring device. This process still has some shortcomings.

[0007] Firstly, traditional stirring methods have low mass transfer efficiency, resulting in uneven mixing of the precipitant and the solution to be treated, and a slow reaction rate.

[0008] Secondly, conventional precipitants lack selectivity. While precipitating precious metal ions such as Rh, they also precipitate other impurity metal ions such as iron ions in the solution. The final precious metal product has an excessive impurity content, and the precipitated products are mostly hydroxides or complex compounds. They need to be calcined and reduced at high temperature to obtain elemental rhodium, which is a lengthy and energy-intensive process.

[0009] Third, some processes simply use filter membranes to remove suspended impurities from waste liquid without controlling the valence state of iron ions, which cannot solve the problem of co-precipitation of iron impurities, making it difficult to guarantee the purity of precious metal products.

[0010] Furthermore, when using strong reducing agents such as sodium borohydride, hydrogen is generated during the reaction process. Existing processes often directly release this hydrogen, which not only wastes energy but also poses certain safety hazards, failing to achieve resource utilization.

[0011] Sodium sulfite can reduce ferric ions to ferrous ions. In the alkaline sodium borohydride reduction system, the oxidizing power of the noble metal rhodium ion is much stronger than that of the ferrous ion. Therefore, the rhodium ion can preferentially gain electrons and be reduced to the metallic element.

[0012] By controlling the amount of sodium borohydride added and the pH of the system, millisecond-level mixing is achieved using microfluidic spraying technology. This allows the reducing agent to preferentially react completely with rhodium ions, while ferrous ions do not have enough time to undergo significant reduction and flow out with the fluid, thus achieving highly selective separation of rhodium and iron. This process can directly reduce rhodium ions to elemental rhodium particles, avoiding subsequent calcination reduction steps, and also produces high-purity hydrogen gas, which can be collected and used as a new energy feedstock.

[0013] Based on this, existing precious metal recovery processes for rhodium-containing iron removal solutions suffer from drawbacks such as iron impurity co-precipitation, low reaction efficiency, poor product purity, the need for additional calcination and reduction, cumbersome procedures, and waste of hydrogen resources. This paper proposes a two-stage microfluidic spray reduction and precipitation process that integrates impurity pretreatment, iron ion valence state control, selective reduction and precipitation of precious metals, direct acquisition of elemental rhodium, and hydrogen resource recovery. This process achieves selective recovery of the precious metal Rh and retention of iron impurities in the liquid phase, possessing significant practical value and potential for widespread application. Summary of the Invention

[0014] In view of this, the present invention provides a method for selectively recovering Rh from rhodium-containing iron removal solution by enhanced reduction precipitation through two-stage microfluidic spraying. The present invention achieves stepwise reduction through two-stage microfluidic spraying: the first stage spraying uses sodium sulfite to regulate the valence state of iron ions; the second stage spraying uses sodium borohydride alkaline solution to selectively reduce precious metal ions, directly generating elemental rhodium precipitate. At the same time, the by-product hydrogen can be recovered and used as a new energy raw material, while iron ions remain in the solution. Combined with membrane pretreatment, vacuum filtration to remove impurities, and hydrogen collection processes, the invention achieves efficient, high-purity selective recovery of precious metals and full utilization of resources.

[0015] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0016] A method for selectively recovering Rh from rhodium-containing iron removal solution by two-stage microfluidic jet-enhanced reduction precipitation includes the following steps:

[0017] (1) Waste liquid pretreatment:

[0018] Take the waste catalyst stock solution, filter it with a filter membrane to remove suspended particles and colloidal impurities from the solution, and collect the clarified waste liquid for later use;

[0019] (2) First-order microfluidic jet reaction:

[0020] The clarified waste liquid and sodium sulfite solution are passed into a micro-flow jet reactor. The two solutions converge and undergo an enhanced reduction reaction, reducing the ferric ions in the solution to ferrous ions.

[0021] (3) Adjust pH:

[0022] Transfer the mixed solution after the first-stage spray reaction to a beaker, add alkali solution to adjust the pH;

[0023] (4) Secondary microfluidic jet reaction:

[0024] The first-stage filtrate obtained after filtration of the solution obtained in step (3) and the sodium borohydride alkaline solution are fed into a micro-flow jet reactor. The two solutions converge and undergo a selective enhanced reduction reaction, reducing Rh ions to elemental particles, while ferrous ions remain in the solution.

[0025] (5) Final filtration and detection recycling:

[0026] The mixed solution after the secondary spray reaction was filtered, the precious metal filter residue was collected, and the residual content of Rh and iron ions in the secondary filtrate was detected by an ICP detector.

[0027] Preferably, in step (1), the pore size of the filter membrane is 0.45 μm.

[0028] Preferably, in step (2), the concentration of the sodium sulfite solution is 50~150g / L;

[0029] The volume ratio of clarified waste liquid to sodium sulfite solution is 1:0.5-1:2, and the injection pump push rate is controlled at 10-100 mm / min.

[0030] Preferably, in steps (2) and (4), the microfluidic jet reactor used is self-designed and manufactured by 3D printing;

[0031] The diameter of the injection channels on both sides of the reactor is 200-1000μm, the included angle between the two channels is 15-45° and they converge toward the center;

[0032] The two injection channels in the middle of the reactor have a diameter of 200-800μm and are arranged vertically downwards;

[0033] Both stages of enhanced spraying reactions occurred 15 times consecutively.

[0034] Preferably, in step (3), the pH is adjusted to 1.1-1.2.

[0035] Preferably, in step (4), vacuum filtration is used and qualitative filter paper is selected as the filter material to completely intercept the flocculent colloidal impurities generated in the primary reaction.

[0036] Preferably, in step (4), the sodium borohydride alkaline solution is a compound solution of sodium borohydride and sodium hydroxide, wherein the concentration of sodium borohydride is 5-20 g / L and the concentration of sodium hydroxide is 5-20 g / L;

[0037] The volume ratio of primary filtrate to sodium borohydride alkaline solution is 1:0.5-1:2, and the injection pump push rate is controlled at 10-100 mm / min.

[0038] Preferably, in step (5), the gas-liquid separator is directly connected to the outlet of the microfluidic jet reactor, and the purity of the separated and collected hydrogen meets the requirements for use as a new energy raw material.

[0039] The residual concentration of the precious metal Rh in the secondary filtrate obtained after final filtration was less than 0.0005 g / L, and the iron ions in the solution were basically retained in the divalent form.

[0040] Preferably, the two-stage microfluidic spraying process uses the same microfluidic spraying reactor, and the entire process runs continuously without the need for intermediate material transfer.

[0041] The present invention achieves the following technical effects compared to the prior art:

[0042] (1) Eliminating iron co-precipitation, simplifying the purification process and improving product purity: This invention uses a two-stage step-by-step reduction combined with iron valence state control. First, sodium sulfite is used to reduce Fe³⁺ to Fe²⁺, and then the potential difference is used to allow sodium borohydride to preferentially reduce rhodium ions, so that iron always remains in the liquid phase. In principle, this avoids the problem of iron co-precipitation during the rhodium reduction process. There is no need to set up a special iron removal process, which simplifies the recycling process and effectively improves the purity of rhodium products.

[0043] (2) Enhance selective reduction, improve separation efficiency and reduce production costs: The two-stage reduction reaction of this invention is completed in the self-developed 3D printed microfluidic jet reactor, which can achieve instantaneous uniform mixing of reducing agent and feed liquid in milliseconds. The excellent rapid mass transfer effect provides a precise kinetic control window for selective reduction, which ensures that sodium borohydride reacts preferentially with rhodium ions and avoids local over-reduction of reducing agent leading to reduction of ferrous iron. This effectively improves the utilization rate of reagents, enhances the rhodium-iron separation effect, and reduces the overall production cost of the recovery process.

[0044] (3) Achieve continuous integrated operation, with compact process connection and strong equipment versatility: This invention has developed a multi-stage integrated impurity removal process, which achieves the system purification step by step by a combination of 0.45μm filter membrane pre-filter removal of suspended impurities and first-stage vacuum filtration removal of reaction flocs; at the same time, the two-stage spray reactors have the same structure and unified operating parameters, with good equipment versatility and compact connection of each process, which can realize the continuous integrated operation of the recovery process;

[0045] (4) Shorten the recycling process, save energy and reduce consumption, and achieve synergistic efficiency of resources: The process of the present invention can directly reduce rhodium ions to elemental rhodium particles through sodium borohydride alkaline solution in the secondary microfluidic spray reaction, without the need for additional elemental conversion process, shortening the overall recycling process and reducing production energy consumption; the high-purity hydrogen produced by the reduction process can be collected in real time through the gas-liquid separation system and used as a new energy raw material, thus achieving synergistic efficiency of rhodium recycling and clean energy production. Attached Figure Description

[0046] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] This invention discloses a method for selectively recovering Rh from rhodium-containing iron removal liquid through a two-stage microfluidic jet-enhanced reduction precipitation process, comprising the following steps:

[0049] (1) Waste liquid pretreatment:

[0050] Take the waste catalyst stock solution, filter it with a filter membrane to remove suspended particles and colloidal impurities from the solution, and collect the clarified waste liquid for later use;

[0051] (2) First-order microfluidic jet reaction:

[0052] The clarified waste liquid and sodium sulfite solution are passed into a micro-flow jet reactor. The two solutions converge and undergo an enhanced reduction reaction, reducing the ferric ions in the solution to ferrous ions.

[0053] (3) Adjust pH:

[0054] Transfer the mixed solution after the first-stage spray reaction to a beaker, add alkali solution to adjust the pH;

[0055] (4) Secondary microfluidic jet reaction:

[0056] The first-stage filtrate obtained after filtration of the solution obtained in step (3) and the sodium borohydride alkaline solution are fed into a micro-flow jet reactor. The two solutions converge and undergo a selective enhanced reduction reaction, reducing Rh ions to elemental particles, while ferrous ions remain in the solution.

[0057] (5) Final filtration and detection recycling:

[0058] The mixed solution after the secondary spray reaction was filtered, the precious metal filter residue was collected, and the residual content of Rh and iron ions in the secondary filtrate was detected by an ICP detector.

[0059] In step (1), the pore size of the filter membrane is 0.45 μm.

[0060] In step (2), the concentration of the sodium sulfite solution is 50~150g / L;

[0061] The volume ratio of clarified waste liquid to sodium sulfite solution is 1:0.5-1:2, and the injection pump push rate is controlled at 10-100 mm / min.

[0062] In steps (2) and (4), the microfluidic jet reactor used was designed independently and fabricated using 3D printing.

[0063] The diameter of the injection channels on both sides of the reactor is 200-1000μm, the included angle between the two channels is 15-45° and they converge toward the center;

[0064] The two injection channels in the middle of the reactor have a diameter of 200-800μm and are arranged vertically downwards;

[0065] Both stages of enhanced spraying reactions occurred 15 times consecutively.

[0066] In step (3), the pH is adjusted to 1.1-1.2.

[0067] In step (4), vacuum filtration is used, and qualitative filter paper is selected as the filter material to completely intercept the flocculent colloidal impurities generated in the first-stage reaction.

[0068] In step (4), the sodium borohydride alkaline solution is a compound solution of sodium borohydride and sodium hydroxide, wherein the concentration of sodium borohydride is 5-20 g / L and the concentration of sodium hydroxide is 5-20 g / L;

[0069] The volume ratio of primary filtrate to sodium borohydride alkaline solution is 1:0.5-1:2, and the injection pump push rate is controlled at 10-100 mm / min.

[0070] In step (5), the gas-liquid separator is directly connected to the outlet of the microfluidic jet reactor, and the purity of the separated and collected hydrogen meets the requirements for use as a new energy raw material.

[0071] The two-stage microfluidic spraying process uses the same microfluidic spraying reactor, and the entire process runs continuously without the need for intermediate material transfer.

[0072] Example 1: Experiment on selective reduction of conventional rhodium-containing iron removal solution by two-stage microfluidic spraying

[0073] 1. Experimental materials and equipment

[0074] Raw materials: initial iron removal solution (initial pH=-0.5, precious metal content: Rh-0.272g / L; iron ion content 41.02g / L), anhydrous sodium sulfite, sodium borohydride, sodium hydroxide;

[0075] Auxiliary consumables: 0.45μm filter membrane, qualitative filter paper;

[0076] Experimental equipment: vacuum filtration device, 60ml syringe, high-precision injection pump, self-developed 3D printed microfluidic jet reactor, vacuum filtration device, ICP element content analyzer.

[0077] 2. Waste liquid pretreatment

[0078] Take a sufficient amount of the waste catalyst stock solution and filter it using a vacuum filtration device with a 0.45μm filter membrane to completely remove suspended particles and colloidal impurities from the solution. Collect all the clarified waste liquid, seal it, and store it at room temperature for later use.

[0079] 3. First-order microfluidic jet reaction

[0080] Prepare a sodium sulfite solution with a concentration of 100 g / L; mix the pretreated clarified waste liquid and the sodium sulfite solution at a volume ratio of 1:1 and load them into two pumps, which are then connected to a microfluidic spray reactor via corrosion-resistant pipes.

[0081] Start the syringe pump, and the two solutions are sprayed and mixed at high speed to complete the first-stage enhanced reduction reaction, reducing ferric ions to ferrous ions.

[0082] 4. Adjust pH

[0083] Transfer the mixed solution after the first-stage spray reaction to a beaker, add 200 g / L NaOH solution, and adjust the pH to 1.13.

[0084] 5. Secondary microfluidic jet reaction

[0085] Multiple groups of sodium borohydride alkaline solutions were prepared (sodium borohydride concentrations of 10 g / L, 12 g / L, and 14 g / L, combined with sodium hydroxide concentrations of 10 g / L, 12 g / L, and 14 g / L).

[0086] The pH-adjusted mixed solution and sodium borohydride alkaline solutions of different concentrations were mixed in a 1:1 volume ratio and injected into an injection pump, which was then connected to the same type of microfluidic jet reactor.

[0087] The equipment is started to carry out a secondary selective enhanced reduction reaction, in which Rh ions are reduced to elemental particles, while ferrous ions are basically retained in the solution.

[0088] The tail end is connected to a gas collection device to collect hydrogen gas, a byproduct of the reaction.

[0089] 7. Final filtration and content detection

[0090] Collect the secondary reaction mixtures of each group and filter them, and collect the filter residue of precious metal elements; take the secondary filtrate of each group and use an ICP detector to detect the residual concentrations of Rh and iron ions respectively.

[0091] 8. Analysis of Experimental Results

[0092] This experiment included 5 control groups. The specific experimental conditions and test results are shown in Table 1 below:

[0093] Table 1:

[0094]

[0095] Table 1 shows that when the NaOH concentration is fixed at 10 g / L, as the NaBH4 concentration increases from 10 g / L to 12 g / L, the residual Rh concentration in the secondary filtrate rapidly decreases to below 0.0005 g / L, while the residual iron ion content remains stable above 39 g / L. This indicates that under these conditions, both sufficient reduction and precipitation of Rh are achieved, and co-precipitation of iron ions is effectively avoided. When the NaOH concentration increases while the NaBH4 concentration remains fixed at 10 g / L, the residual Rh concentration in the filtrate gradually decreases, but the residual iron ion content also decreases simultaneously. This indicates that excessive alkalinity can induce iron ion precipitation, reducing the selectivity of rhodium-iron separation. Considering both recovery efficiency and separation selectivity, when the NaOH concentration is 10 g / L and the NaBH4 concentration is 12-14 g / L, this process can achieve optimal Rh selective recovery, with an Rh recovery rate of over 99.8%, and more than 96% of the iron ions remain stably in the liquid phase, demonstrating excellent separation performance.

[0096] This invention discloses a two-stage microfluidic jet-enhanced reduction precipitation selective recovery method for the precious metal Rh from rhodium-containing iron removal solutions. First, the waste liquid is pretreated with a 0.45 μm filter membrane to remove impurities. Then, through a first-stage microfluidic jet, the waste liquid is mixed with a sodium sulfite solution in a microreactor within milliseconds, directionally removing Fe... 3+ Reduced to Fe 2+ To avoid co-precipitation of iron impurities from a mechanistic perspective; after adjusting the pH to 1.1-1.2 and filtration, a two-stage microfluidic jet is used to pass the filtrate and sodium borohydride alkaline solution into a microreactor, utilizing Rh... 3+ / Rh and Fe 2+ The reduction potential difference of Fe causes sodium borohydride to preferentially react with rhodium ions, selectively reducing Rh directly to elemental particles. 2+ It remains stable in the liquid phase. The hydrogen produced during the reduction process is collected as high-purity hydrogen through gas-liquid separation. Finally, it is filtered to obtain elemental rhodium product. ICP analysis shows that the Rh precipitation rate is 99.8%, and the iron precipitation rate is about 2%.

[0097] As can be seen, this invention, through a continuous process of "membrane pretreatment—first-stage microfluidic spray reduction to regulate iron valence state—second-stage microfluidic spray selective reduction," effectively solves the industry problem of co-precipitation of iron impurities in rhodium-containing iron removal solutions. This method utilizes microfluidic spraying to enhance mass transfer, achieving directional valence state conversion of iron ions and preferential reduction of rhodium ions within milliseconds. The rhodium precipitation rate can reach 99.8%, while the iron precipitation rate is only about 2%. Particularly noteworthy is that the second-stage reduction directly generates elemental rhodium particles, and high-purity hydrogen is simultaneously recovered as a new energy feedstock. This avoids the safety hazards of hydrogen emissions and significantly improves the greenness and economic benefits of the process. The overall process features controllable reagent dosage, universal equipment, and a compact workflow, providing an efficient and feasible new path for the high-purity, low-energy, and full-component recovery of rhodium from waste catalysts.

[0098] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the technical scope of the present invention. Therefore, any minor modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method for selectively recovering Rh from rhodium-containing iron removal solution by two-stage microfluidic jet-enhanced reduction precipitation, characterized in that, Includes the following steps: (1) Waste liquid pretreatment: Take the waste catalyst stock solution, filter it with a filter membrane to remove suspended particles and colloidal impurities from the solution, and collect the clarified waste liquid for later use; (2) First-order microfluidic jet reaction: The clarified waste liquid and sodium sulfite solution are passed into a micro-flow jet reactor. The two solutions converge and undergo an enhanced reduction reaction, reducing the ferric ions in the solution to ferrous ions. (3) Adjust pH: Transfer the mixed solution after the first-stage spray reaction to a beaker, add alkali solution to adjust the pH; (4) Secondary microfluidic jet reaction: The first-stage filtrate obtained after filtration of the solution obtained in step (3) and the sodium borohydride alkaline solution are fed into a micro-flow jet reactor. The two solutions converge and undergo a selective enhanced reduction reaction, reducing Rh ions to elemental particles, while ferrous ions remain in the solution. (5) Final filtration and detection recycling: The mixed solution after the secondary spray reaction was filtered, the precious metal filter residue was collected, and the residual content of Rh and iron ions in the secondary filtrate was detected by an ICP detector.

2. The method for selectively recovering Rh from rhodium-containing iron removal liquid by two-stage microfluidic spray-enhanced reduction precipitation according to claim 1, characterized in that, In step (1), the pore size of the filter membrane is 0.45 μm.

3. The method for selectively recovering Rh from rhodium-containing iron removal solution by two-stage microfluidic jet-enhanced reduction precipitation according to claim 1, characterized in that, In step (2), the concentration of the sodium sulfite solution is 50~150g / L; The volume ratio of clarified waste liquid to sodium sulfite solution is 1:0.5-1:2, and the injection pump push rate is controlled at 10-100 mm / min.

4. The method for selectively recovering Rh from rhodium-containing iron removal solution by two-stage microfluidic jet-enhanced reduction precipitation according to claim 1, characterized in that, In steps (2) and (4), the microfluidic jet reactor used is self-designed and manufactured by 3D printing; The diameter of the injection channels on both sides of the reactor is 200-1000μm, the included angle between the two channels is 15-45° and they converge toward the center; The two injection channels in the middle of the reactor have a diameter of 200-800μm and are arranged vertically downwards; Both stages of enhanced spraying reactions occurred 15 times consecutively.

5. The method for selectively recovering Rh from rhodium-containing iron removal solution by two-stage microfluidic spray-enhanced reduction precipitation according to claim 1, characterized in that, In step (3), the pH is adjusted to 1.1-1.

2.

6. The method for selectively recovering Rh from rhodium-containing iron removal liquid by two-stage microfluidic spray-enhanced reduction precipitation according to claim 1, characterized in that, In step (4), vacuum filtration is used, and qualitative filter paper is selected as the filter material to completely intercept the flocculent colloidal impurities generated in the first-stage reaction.

7. The method for selectively recovering Rh from rhodium-containing iron removal liquid by two-stage microfluidic jet-enhanced reduction precipitation according to claim 1, characterized in that, In step (4), the sodium borohydride alkaline solution is a compound solution of sodium borohydride and sodium hydroxide, wherein the concentration of sodium borohydride is 5-20 g / L and the concentration of sodium hydroxide is 5-20 g / L. The volume ratio of primary filtrate to sodium borohydride alkaline solution is 1:0.5-1:2, and the injection pump push rate is controlled at 10-100 mm / min.

8. The method for selectively recovering Rh from rhodium-containing iron removal liquid by two-stage microfluidic jet-enhanced reduction precipitation according to claim 1, characterized in that, In step (5), the gas-liquid separator is directly connected to the outlet of the microfluidic jet reactor, and the purity of the separated and collected hydrogen meets the requirements for use as a new energy raw material.

9. The method for selectively recovering Rh from rhodium-containing iron removal liquid by two-stage microfluidic spray-enhanced reduction precipitation according to claim 1, characterized in that, The two-stage microfluidic spraying process uses the same microfluidic spraying reactor, and the entire process runs continuously without the need for intermediate material transfer.

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