Lesson: Chemical Reactions and Equations

Question 1

Why should a magnesium ribbon be cleaned before burning in air?

Solution:

Magnesium is a highly reactive metal. It reacts with oxygen to form a layer of magnesium oxide on its surface. This layer is quite stable and prevents further reaction of magnesium with oxygen. Hence, the magnesium ribbon is cleaned to remove this layer.

Question2

Write the balanced equation for the following chemical reactions.

(i) Hydrogen+ChlorineHydrogen chloride MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamisaiaadMhacaWGKbGaamOCaiaa d+gacaWGNbGaamyzaiaad6gacqGHRaWkcaWGdbGaamiAaiaadYgaca WGVbGaamOCaiaadMgacaWGUbGaamyzaiabgkziUkaadIeacaWG5bGa amizaiaadkhacaWGVbGaam4zaiaadwgacaWGUbGaaeiiaiaadogaca WGObGaamiBaiaad+gacaWGYbGaamyAaiaadsgacaWGLbaaaa@5CAD@

(ii) Barium chloride+Aluminium sulphate MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamOqaiaadggacaWGYbGaamyAaiaa dwhacaWGTbGaaeiiaiaadogacaWGObGaamiBaiaad+gacaWGYbGaam yAaiaadsgacaWGLbGaey4kaSIaamyqaiaadYgacaWG1bGaamyBaiaa dMgacaWGUbGaamyAaiaadwhacaWGTbGaaeiiaiaadohacaWG1bGaam iBaiaadchacaWGObGaamyyaiaadshacaWGLbaaaa@5AA1@

Barium sulphate+Aluminium chloride MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaaGPaVlaaykW7caaMc8UaaGPaVlaa ykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaG PaVlaaykW7cqGHsgIRcaWGcbGaamyyaiaadkhacaWGPbGaamyDaiaa d2gacaqGGaGaam4CaiaadwhacaWGSbGaamiCaiaadIgacaWGHbGaam iDaiaadwgacqGHRaWkcaWGbbGaamiBaiaadwhacaWGTbGaamyAaiaa d6gacaWGPbGaamyDaiaad2gacaqGGaGaam4yaiaadIgacaWGSbGaam 4BaiaadkhacaWGPbGaamizaiaadwgaaaa@7228@

(iii) Sodium+WaterSodium hydroxide+Hydrogen MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaam4uaiaad+gacaWGKbGaamyAaiaa dwhacaWGTbGaey4kaSIaam4vaiaadggacaWG0bGaamyzaiaadkhacq GHsgIRcaWGtbGaam4BaiaadsgacaWGPbGaamyDaiaad2gacaqGGaGa amiAaiaadMhacaWGKbGaamOCaiaad+gacaWG4bGaamyAaiaadsgaca WGLbGaey4kaSIaamisaiaadMhacaWGKbGaamOCaiaad+gacaWGNbGa amyzaiaad6gaaaa@5F90@

Solution:

(i) H 2 ( g )+C l 2 ( g )2HCl( g ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamisa8aadaWgaaWcbaWdbiaaikda a8aabeaakmaabmaabaWdbiaadEgaa8aacaGLOaGaayzkaaWdbiabgU caRiaadoeacaWGSbWdamaaBaaaleaapeGaaGOmaaWdaeqaaOWaaeWa aeaapeGaam4zaaWdaiaawIcacaGLPaaapeGaeyOKH4QaaGOmaiaayk W7caWGibGaam4qaiaadYgapaWaaeWaaeaapeGaam4zaaWdaiaawIca caGLPaaaaaa@4FBC@

(ii) 3BaC l 2 ( s )+A l 2 ( S O 4 ) 3 ( s )3BaS O 4 ( s )+2AlC l 3 ( s ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaaG4maiaadkeacaWGHbGaam4qaiaa dYgapaWaaSbaaSqaa8qacaaIYaaapaqabaGcdaqadaqaa8qacaWGZb aapaGaayjkaiaawMcaa8qacqGHRaWkcaWGbbGaamiBa8aadaWgaaWc baWdbiaaikdaa8aabeaakmaabmaabaWdbiaadofacaWGpbWdamaaBa aaleaapeGaaGinaaWdaeqaaaGccaGLOaGaayzkaaWaaSbaaSqaa8qa caaIZaaapaqabaGcdaqadaqaa8qacaWGZbaapaGaayjkaiaawMcaa8 qacqGHsgIRcaaIZaGaamOqaiaadggacaWGtbGaam4ta8aadaWgaaWc baWdbiaaisdaa8aabeaakmaabmaabaWdbiaadohaa8aacaGLOaGaay zkaaWdbiabgUcaRiaaikdacaWGbbGaamiBaiaadoeacaWGSbWdamaa BaaaleaapeGaaG4maaWdaeqaaOWaaeWaaeaapeGaam4CaaWdaiaawI cacaGLPaaaaaa@61E8@

(iii) 2Na( s )+2 H 2 O( l )2NaOH( aq )+ H 2 ( g ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaaGOmaiaaykW7caWGobGaamyya8aa daqadaqaa8qacaWGZbaapaGaayjkaiaawMcaa8qacqGHRaWkcaaIYa GaaGPaVlaadIeapaWaaSbaaSqaa8qacaaIYaaapaqabaGcpeGaam4t a8aadaqadaqaa8qacaWGSbaapaGaayjkaiaawMcaa8qacqGHsgIRca aIYaGaaGPaVlaad6eacaWGHbGaam4taiaadIeapaWaaeWaaeaapeGa amyyaiaadghaa8aacaGLOaGaayzkaaWdbiabgUcaRiaadIeapaWaaS baaSqaa8qacaaIYaaapaqabaGcdaqadaqaa8qacaWGNbaapaGaayjk aiaawMcaaaaa@5B74@

Question 3

Write a balanced chemical equation with state symbols for the following reactions.

        i.            Solutions of barium chloride and sodium sulphate in water react to give insoluble barium sulphate and the solution of sodium chloride.

      ii.            Sodium hydroxide solution (in water) reacts with hydrochloric acid solution (in water) to produce sodium chloride solution and water.

Solution:

(i) BaC l 2 ( aq )+N a 2 S O 4 ( aq )BaS O 4 ( s )+2NaCl( aq ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamOqaiaadggacaWGdbGaamiBa8aa daWgaaWcbaWdbiaaikdaa8aabeaakmaabmaabaWdbiaadggacaWGXb aapaGaayjkaiaawMcaa8qacqGHRaWkcaWGobGaamyya8aadaWgaaWc baWdbiaaikdaa8aabeaak8qacaWGtbGaam4ta8aadaWgaaWcbaWdbi aaisdaa8aabeaakmaabmaabaWdbiaadggacaWGXbaapaGaayjkaiaa wMcaa8qacqGHsgIRcaWGcbGaamyyaiaadofacaWGpbWdamaaBaaale aapeGaaGinaaWdaeqaaOWaaeWaaeaapeGaam4CaaWdaiaawIcacaGL PaaapeGaey4kaSIaaGOmaiaaykW7caWGobGaamyyaiaadoeacaWGSb WdamaabmaabaWdbiaadggacaWGXbaapaGaayjkaiaawMcaaaaa@60FC@

(ii) NaOH( aq )+HCl( aq )NaCl( aq )+ H 2 O( l ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamOtaiaadggacaWGpbGaamisa8aa daqadaqaa8qacaWGHbGaamyCaaWdaiaawIcacaGLPaaapeGaey4kaS IaamisaiaadoeacaWGSbWdamaabmaabaWdbiaadggacaWGXbaapaGa ayjkaiaawMcaa8qacqGHsgIRcaWGobGaamyyaiaadoeacaWGSbWdam aabmaabaWdbiaadggacaWGXbaapaGaayjkaiaawMcaa8qacqGHRaWk caWGibWdamaaBaaaleaapeGaaGOmaaWdaeqaaOWdbiaad+eapaWaae WaaeaapeGaamiBaaWdaiaawIcacaGLPaaaaaa@58D4@

Question 4

A solution of a substance ‘X’ is used for white washing.

(i) Name the substance ‘X’ and write its formula.

(ii) Write the reaction of the substance ‘X’ named in (i) above with water.

Solution:

(i) The substance ‘X’ is calcium oxide. Its chemical formula is CaO.
(ii)
CaO( s )+ H 2 O( l )Ca ( OH ) 2 ( aq ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaam4qaiaadggacaWGpbWdamaabmaa baWdbiaadohaa8aacaGLOaGaayzkaaWdbiabgUcaRiaadIeapaWaaS baaSqaa8qacaaIYaaapaqabaGcpeGaam4ta8aadaqadaqaa8qacaWG SbaapaGaayjkaiaawMcaa8qacqGHsgIRcaWGdbGaamyya8aadaqada qaa8qacaWGpbGaamisaaWdaiaawIcacaGLPaaadaWgaaWcbaWdbiaa ikdaa8aabeaakmaabmaabaWdbiaadggacaWGXbaapaGaayjkaiaawM caaaaa@52A3@

Question 5

Why is the amount of gas collected in one of the test tubes in Activity1.7 (electrolysis of water) double of the amount collected in the other? Name this gas.

Solution:

The given activity is electrolysis of water. In this activity, hydrogen and oxygen are collected in separate test tubes. A molecule of water ( H 2 O MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamisa8aadaWgaaWcbaWdbiaaikda a8aabeaak8qacaWGpbaaaa@3E40@  ) contains two hydrogen atoms and one oxygen atom. Therefore, the hydrogen and oxygen produced during electrolysis of water is in the ratio 2:1. Thus, the amount of hydrogen gas collected in one of the test tubes is double the amount of oxygen gas collected in the other.

Question 6

Why does the colour of copper sulphate solution change when an iron nail is dipped in it?

Solution:

Iron is more reactive than copper. When an iron nail is dipped in a copper sulphate solution, which is blue in colour, iron displaces copper from the solution and forms ferrous sulphate, which is green in colour.

Fe( s )+CuS O 4 ( aq )FeS O 4 ( aq )+Cu( s ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamOraiaadwgapaWaaeWaaeaapeGa am4CaaWdaiaawIcacaGLPaaapeGaey4kaSIaam4qaiaadwhacaWGtb Gaam4ta8aadaWgaaWcbaWdbiaaisdaa8aabeaakmaabmaabaWdbiaa dggacaWGXbaapaGaayjkaiaawMcaa8qacqGHsgIRcaWGgbGaamyzai aadofacaWGpbWdamaaBaaaleaapeGaaGinaaWdaeqaaOWaaeWaaeaa peGaamyyaiaadghaa8aacaGLOaGaayzkaaWdbiabgUcaRiaadoeaca WG1bWdamaabmaabaWdbiaadohaa8aacaGLOaGaayzkaaaaaa@5840@

Therefore, the colour of the copper sulphate solution changes from blue to green.

Question 7

Give an example of a double displacement reaction.

Solution:

Sodium carbonate reacts with calcium chloride to form calcium carbonate and sodium chloride. This is a double displacement reaction.

N a 2 C O 3 ( aq )+CaC l 2 ( aq )CaC O 3 ( s )+2NaCl( aq ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamOtaiaadggapaWaaSbaaSqaa8qa caaIYaaapaqabaGcpeGaam4qaiaad+eapaWaaSbaaSqaa8qacaaIZa aapaqabaGcdaqadaqaa8qacaWGHbGaamyCaaWdaiaawIcacaGLPaaa peGaey4kaSIaam4qaiaadggacaWGdbGaamiBa8aadaWgaaWcbaWdbi aaikdaa8aabeaakmaabmaabaWdbiaadggacaWGXbaapaGaayjkaiaa wMcaa8qacqGHsgIRcaWGdbGaamyyaiaadoeacaWGpbWdamaaBaaale aapeGaaG4maaWdaeqaaOWaaeWaaeaapeGaam4CaaWdaiaawIcacaGL PaaapeGaey4kaSIaaGOmaiaad6eacaWGHbGaam4qaiaadYgapaWaae WaaeaapeGaamyyaiaadghaa8aacaGLOaGaayzkaaaaaa@5F51@

Question 8

Identify the substances that are oxidised and the substances that are reduced in the following reactions.

(i) 4Na(s)+ O 2 (g)2N a 2 O(s) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaaGinaiaaykW7caWGobGaamyya8aa caGGOaGaam4CaiaacMcapeGaey4kaSIaam4tamaaBaaaleaacaaIYa aabeaak8aacaGGOaGaam4zaiaacMcapeGaeyOKH4QaaGOmaiaaykW7 caWGobGaamyya8aadaWgaaWcbaWdbiaaikdaa8aabeaak8qacaWGpb GaaiikaiaadohacaGGPaaaaa@512F@

(ii) CuO(s)+ H 2 (g)Cu(s)+ H 2 O(l) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaam4qaiaadwhacaWGpbWdaiaacIca caWGZbGaaiyka8qacqGHRaWkcaWGibWdamaaBaaaleaapeGaaGOmaa WdaeqaaOGaaiikaiaadEgacaGGPaWdbiabgkziUkaadoeacaWG1bWd aiaacIcacaWGZbGaaiyka8qacqGHRaWkcaWGibWdamaaBaaaleaape GaaGOmaaWdaeqaaOWdbiaad+eapaGaaiikaiaadYgacaGGPaaaaa@51C4@

Solution:

(i) Sodium (Na) is oxidised as it gains oxygen and oxygen gets reduced.

(ii) Copper oxide (CuO) is reduced to copper (Cu) while hydrogen ( H 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamisa8aadaWgaaWcbaWdbiaaikda a8aabeaaaaa@3D52@  ) gets oxidised to water ( H 2 O MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbmLMB1H hicL2BSLMB11garmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlh9frVeeu0dXdh9vqqj =hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXd ar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaabaGaciaacaqabeaada abauaaaOqaaabaaaaaaaaapeGaamisa8aadaWgaaWcbaWdbiaaikda a8aabeaak8qacaWGpbaaaa@3E40@  ).