Okay, let's tackle this organic chemistry problem step by step. So, the question is about selecting the correct reagents (A and B) for two reactions. The options are given as A, B, C, D, each pairing different reagents. Let's break down each reaction separately and figure out the reagents needed.

First reaction: butan-2-one + NaCN + A → 2-hydroxy-2-methylbutanenitrile. 

Butan-2-one is (CH3)2CO, a ketone. NaCN is sodium cyanide. So, this looks like a nucleophilic substitution reaction. But wait, ketones can undergo various reactions. Since NaCN is a source of CN- (cyanide ion), which is a nucleophile, maybe it's an addition-elimination reaction here. But with a ketone, typically the cyanide might add to the carbonyl. Wait, but butan-2-one is a ketone, so addition of CN- would give something like (CH3)2C(O)CN. But that's not the product here. The product given is 2-hydroxy-2-methylbutanenitrile. Let's write the structure: the main chain is CH2(CN)-CH(CH3)-OH? Wait, maybe the structure is (CH3)2CHCH2CN with a hydroxyl group? Hmm, perhaps I'm getting confused. Let me draw it out.

Butan-2-one is (CH3)2CO. Adding CN- would typically form a cyanohydrin. The cyanide would attack the carbonyl carbon, and then the hydroxide (from the workup) would form the hydroxyl group. Wait, but in the product, the cyanide is at the 2-position, and there's a hydroxyl group at the same position. So, the cyanide addition would be to the ketone, then protonation or workup would form the hydroxyl. So the product would be (CH3)2C(OH)CN. Wait, but the product is 2-hydroxy-2-methylbutanenitrile. Let's count the carbons. Butan-2-one is four carbons, with the ketone at position 2. So, adding cyanide would give a five-carbon compound? Wait, maybe I'm miscalculating. Let's see: butan-2-one is (CH3)2CO. Adding CN- would form (CH3)2C(OH)CN. That would be (CH3)2CH(OH)CN, but that's four carbons. Wait, but the product is 2-hydroxy-2-methylbutanenitrile. Let's parse that name. The nitrile is at position 1 (since butanenitrile is CH2CH2CH2CN). Wait, but the numbering would be different. Alternatively, maybe the structure is (CH2)2CH(CN)-OH, but I'm getting a bit confused. Alternatively, perhaps the correct structure is CH2(CN)(CH3)COH. Wait, maybe the product is (CH3)2CHCH2CN with a hydroxyl group on the same carbon as the nitrile. Wait, perhaps the structure is CH2(CN)(CH2CH3)COH? No, that doesn't seem right. Alternatively, maybe the product is (CH3)2CH(OH)CH2CN. Hmm, perhaps I should approach this differently. 

Wait, butan-2-one is (CH3)2CO. When you add NaCN to a ketone, you typically get a cyanohydrin. So the cyanide would add to the carbonyl carbon, and the hydroxide would form on the adjacent carbon. Wait, but in a ketone, the carbonyl is between two methyl groups. So the addition would be (CH3)2C(OH)CN. Wait, but that's a tertiary alcohol with a cyanide group. The product given is 2-hydroxy-2-methylbutanenitrile. Let's write that structure. The nitrile is at position 1, the hydroxyl at position 2, and a methyl group at position 2. So, the structure would be CH2(CN)(CH3)COH. Wait, but butanenitrile is four carbons. So, the nitrile is at the end. So, 2-hydroxy-2-methylbutanenitrile would be: CH2(CN)(CH3)CH2OH. Wait, but that's five carbons. Wait, but butan-2-one is four carbons. Hmm. Let me check the IUPAC name again. The product is 2-hydroxy-2-methylbutanenitrile. Let's break it down. The parent chain is butane, so four carbons. The nitrile group is on carbon 1 (since butanenitrile is CH2CH2CH2CN), but wait, nitriles are at the end, so butanenitrile is CH2CH2CH2CN. Wait, but butanenitrile is actually CH2CH2CH2CH2CN? No, wait, butane is four carbons. So butanenitrile would be CH2CH2CH2CH2CN? Wait, no. Wait, butane is CH3CH2CH2CH3. Butanenitrile would be CH2CH2CH2CH2CN? Wait, no. Wait, the correct structure is CH2CH2CH2CN. Wait, no, butanenitrile is CH2CH2CH2CN. Wait, maybe it's better to write it as CH2CH2CH2CN, but that's three carbons. Wait, perhaps butanenitrile is CH2CH2CH2CH2CN? Wait, no. Let me think. The nitrile group is at the end of the carbon chain. So butanenitrile would be CH2CH2CH2CH2CN, but that's five carbons. Wait, no, butane has four carbons. So butanenitrile is CH2CH2CH2CN, with the nitrile on the fourth carbon. Wait, but that would be four carbons in a row: CH2CH2CH2CN. Wait, maybe the correct structure is CH2CH2CH2CH2CN? No, that's five carbons. Wait, perhaps butanenitrile is CH2CH2CH2CN, with the nitrile on the fourth carbon. Wait, but that's three carbons. I'm getting confused here. Let me check: butan-2-one is (CH3)2CO. When you add NaCN, you get a cyanohydrin. The structure would be (CH3)2C(OH)CN. Wait, but that's four carbons in total. The nitrile is on the same carbon as the hydroxyl. So the product is (CH3)2CH(OH)CN. Wait, but that's four carbons: the ketone is (CH3)2CO, adding CN to the carbonyl gives (CH3)2C(OH)CN. So the product would be (CH3)2CH(OH)CN? Wait, but that would be five carbons. Wait, maybe the product is (CH3)2CH(OH)CN, which is 2-hydroxy-2-methyl-2-cyanobutane? Wait, the name given is 2-hydroxy-2-methylbutanenitrile. Let's parse that: butane is four carbons. The nitrile is on carbon 1 (since butanenitrile is CH2CH2CH2CN). The hydroxyl is on carbon 2, and a methyl group on carbon 2. So the structure would be CH2(CN)(CH3)CH2OH. Wait, but butane has four carbons. So the structure is CH2(CN)(CH3)CH2OH. That would be four carbons: carbon 1 is CH2, carbon 2 is CH2OH, carbon 3 is CH3, and carbon 4 is CN? Wait, no, that doesn't make sense. Alternatively, maybe the structure is CH2(CN)(CH3)COH. But that's five carbons. Wait, I'm getting stuck here. Let me think differently. Maybe the product is (CH3)2CH(CN)OH. But that's four carbons. So the product would be 2-hydroxy-2-methylpropanenitrile? Hmm, but the name given is butanenitrile, which is four carbons. So perhaps the product is (CH3)2CHCH2CN with a hydroxyl group on the second carbon. Wait, that's five carbons. I'm getting confused. Maybe I should move on to the second reaction and see if that gives me any clues about the reagents.

Second reaction: 2-(4-benzylphenyl)-2-hydroxybutanenitrile + B (H2O) → 2-(4-benzylphenyl)-2-hydroxybutanoic acid. 

So here, the starting material is a butanenitrile with a hydroxyl group on the second carbon and a substituent at the 2-position. The product is the corresponding carboxylic acid. So the nitrile group is converted to a carboxylic acid. The reagent B is in the presence of water (H2O). So what reaction converts nitriles to carboxylic acids? The typical way is via hydrolysis. Nitriles can be hydrolyzed under acidic or basic conditions to carboxylic acids. The reagent B is likely a catalyst for this hydrolysis. 

In acidic conditions, nitrile hydrolysis usually requires H2O (as solvent) and an acid catalyst like H2SO4. But wait, the product here is a carboxylic acid, so the reaction is likely under acidic conditions. Alternatively, under basic conditions, but the presence of H2O suggests that the reaction is aqueous. 

Wait, but the second reaction is written as 2-(4-benzylphenyl)-2-hydroxybutanenitrile + B (H2O) → 2-(4-benzylphenyl)-2-hydroxybutanoic acid. So the nitrile group is being converted to a carboxylic acid. The standard way to do this is via hydrolysis. The reagents for nitrile to carboxylic acid hydrolysis are typically H2SO4 and H2O, or sometimes with H3O+ (acidic conditions). 

Now, looking at the options for reagent B. The choices for B are HCl, HCl (option A), HCl (option B), CH3COOH (option C), CH3COOH (option D). Also, H3O+ is another possibility. 

Wait, but in the second reaction, the reagent is B (H2O). So the reagent B is added along with H2O. So the reagent B is probably the acid catalyst. If the reaction is hydrolysis under acidic conditions, then H3O+ (HCl in water) or H2SO4. But the options don't include H2SO4. The options for B are HCl or CH3COOH. So if the reaction is under acidic conditions, HCl would be the reagent. If it's under basic conditions, maybe NaOH, but that's not in the options. 

Therefore, for the second reaction, the reagent B should be HCl (acidic hydrolysis) or H2SO4. Since the options have HCl (option A and B) or CH3COOH (options C and D), and the correct reagent here is HCl (for acidic hydrolysis), then B should be HCl. 

Now, going back to the first reaction. If B is HCl for the second reaction, then for the first reaction, the reagent A should be something else. Let's revisit the first reaction. 

Butan-2-one + NaCN + A → 2-hydroxy-2-methylbutanenitrile. 

Assuming that the cyanide is adding to the ketone to form a cyanohydrin. The cyanohydrin formation typically uses an acid workup. Wait, but in the product, there's a hydroxyl group and a nitrile group on the same carbon. So the reaction is a nucleophilic addition of CN- to the ketone, followed by protonation to form the hydroxyl group. 

Wait, but in the first reaction, the reagent is NaCN and A. So the reaction is between a ketone and NaCN. The typical reaction for a ketone with NaCN is a nucleophilic addition, forming a cyanohydrin. The workup after the addition would usually involve acid or base. If the addition is done under basic conditions (like using NaCN and NaOH), then the workup with acid would protonate the hydroxyl group. But in this case, the reagent A is the workup reagent. 

Wait, but the question states that the reagent A is added along with NaCN. So the first step is the nucleophilic addition of CN- to the ketone. The workup is done with reagent A, which is either HCl, H3O+, or CH3COOH. 

So, if the reaction is a cyanohydrin formation, the workup is typically acidic. Because after the addition, the hydroxide would form, and then acid would protonate it. So the workup reagent A would be an acid like HCl or H2SO4. But looking at the options, the possible reagents for A are H3O+ (in options A and B), HCl (A and B), or CH3COOH (C and D). 

Wait, but the product here is a secondary alcohol with a nitrile group. So the reaction is a cyanohydrin. The structure would be (CH3)2C(OH)CN. To form this, the ketone (CH3)2CO reacts with CN- to form (CH3)2C(O)CN, then protonated to (CH3)2C(OH)CN. The workup reagent A would be an acid, like HCl or H3O+. 

Looking at the options, if A is H3O+, that would be option B (A = H3O+, B = HCl) or option B (A = H3O+, B = HCl). Wait, no. Let's check the options again. 

Options:
A. A = NaHSO3, B = HCl
B. A = H3O+, B = HCl
C. A = H3O+, B = CH3COOH
D. A = NaHSO3, B = CH3COOH

Wait, in the first reaction, if the workup is acidic (H3O+), then A would be H3O+. Then for the second reaction, B is HCl. So option B (A = H3O+, B = HCl) would be correct. But let's check the second reaction again. The second reaction uses H2O as the solvent, so the reagent B is the acid used. If the reaction is hydrolysis under acidic conditions, then B would be HCl. So option B would have A = H3O+ and B = HCl. 

But wait, let's confirm the first reaction. If A is H3O+, then the workup is acidic. The product would have the hydroxyl group protonated. So the product is (CH3)2C(OH)CN. But the correct product is 2-hydroxy-2-methylbutanenitrile. Wait, perhaps the structure is (CH3)2CH(OH)CN? Wait, but that's five carbons. Wait, but butanenitrile has four carbons. This is getting me confused again. Let me think. The starting material is butan-2-one, which is (CH3)2CO. Adding CN- gives (CH3)2C(OH)CN. Then protonating gives (CH3)2C(OH)CN. Wait, but that's four carbons in the ketone, plus the nitrile. Wait, no, the nitrile is a separate group. Wait, maybe the structure is (CH3)2CHCN with a hydroxyl group. No, that's not right. Alternatively, maybe the product is (CH3)2CH(OH)CN, which would be butanenitrile with a hydroxyl on the second carbon. So the name would be 2-hydroxy-2-methylbutanenitrile. Yes, that makes sense. So the structure is CH2(CN)(CH3)CH2OH. Wait, but that's five carbons. Wait, no. Let me count. The nitrile is on the first carbon, the hydroxyl on the second, and a methyl on the second. So the structure would be CH2(CN)(CH3)CH2OH. Wait, that's five carbons. But the product is butanenitrile, which is four carbons. So perhaps I'm miscounting. Alternatively, maybe the structure is (CH3)2CH(OH)CN. Let's write that. The nitrile is at the end, so CN-CH2-CH(CH3)-OH. Wait, but that's four carbons. So the structure would be CH2(CN)(CH3)CH2OH. Wait, but that's five carbons. Hmm. Maybe I need to accept that the product is (CH3)2CH(OH)CN, which is 2-hydroxy-2-methylbutanenitrile. So the reaction is a cyanohydrin formation. To form the cyanohydrin, the workup is acidic. So reagent A is H3O+ (option B). Then for the second reaction, the nitrile to carboxylic acid is done with HCl (acidic conditions), so reagent B is HCl (option B). 

But wait, let's check the options. Option B is A = H3O+, B = HCl. Option A is A = NaHSO3, B = HCl. Option C is A = H3O+, B = CH3COOH. Option D is A = NaHSO3, B = CH3COOH. 

In the first reaction, using H3O+ as the workup reagent would protonate the hydroxyl group, giving the correct product. In the second reaction, using HCl as the reagent would provide the necessary acidic conditions for hydrolysis. So option B seems correct. But let's check the other options. 

Option A: A = NaHSO3. NaHSO3 is sodium bisulfate, which is a mild acid. If the workup is with NaHSO3, that would protonate the hydroxyl group. But sodium bisulfate is used in some cases as a catalyst for certain reactions, but typically, for cyanohydrin formation, the workup is with acid like HCl or H3O+. 

Option C: B = CH3COOH. If the second reaction uses CH3COOH as the reagent, then the nitrile would be hydrolyzed under basic conditions (since CH3COOH is acidic, but maybe with another base). Wait, no. Hydrolysis of nitriles to carboxylic acids can be done under acidic or basic conditions. Acidic hydrolysis uses H2O with acid catalyst (like HCl), while basic hydrolysis uses H2O with a base like NaOH. The product here is a carboxylic acid, so the conditions matter. If the second reaction uses CH3COOH as the reagent, that's acidic. So B would be CH3COOH, but the question states "reagent B (H2O)", meaning that B is added along with H2O. So if B is CH3COOH, then the reaction is H3O+ (from CH3COOH and H2O) and the acid would be CH3COOH, which is less strong than HCl. But I think nitrile hydrolysis under acidic conditions typically uses HCl. 

Wait, but the product is a carboxylic acid, which is a stronger acid than a nitrile. So under acidic conditions, HCl is a better catalyst. Therefore, reagent B should be HCl. 

So if the first reaction uses H3O+ as the workup (A = H3O+), and the second reaction uses HCl (B = HCl), then option B is correct. 

But let's check the other options. Option D has A = NaHSO3 and B = CH3COOH. NaHSO3 is sodium bisulfate monohydrate, which acts as a weak acid. If the first reaction uses NaHSO3, the workup would be mildly acidic. But for the cyanohydrin, we need a stronger acid, perhaps. Alternatively, maybe it's a different reaction. 

Alternatively, perhaps the first reaction is an SN2 substitution. But butan-2-one is a ketone. CN- is a strong nucleophile. The carbonyl is a good electrophile. So the addition would be a nucleophilic addition. But if NaCN is used, the reaction is likely the cyanohydrin formation. 

Wait, another possibility: if the ketone is treated with NaCN, it forms a nitrile. Wait, but that's not right. NaCN would add to the carbonyl to form a cyanohydrin. The product would be a secondary alcohol with a nitrile group. So the workup after the addition would be acidic. 

Therefore, reagent A is H3O+ (option B or C). Then reagent B is HCl (option B). So option B (A = H3O+, B = HCl) is the correct answer. 

But let's check the other options. Option C has B = CH3COOH. If the second reaction uses CH3COOH, then the conditions are basic, which would give a carboxylate instead of a carboxylic acid. But the product is a carboxylic acid, so B must be an acid catalyst. Therefore, option B is correct. 

Wait, but in the second reaction, the product is a carboxylic acid. If B is CH3COOH, then the solution would be basic (since CH3COOH is a weak acid). Wait, no, the reagent B is added along with H2O. So if B is CH3COOH, then the reaction is in a mixture of H2O and CH3COOH, which is acidic. So the nitrile would be hydrolyzed to the carboxylic acid under acidic conditions. So B = CH3COOH would also work. But the question is, which reagent is correct? 

Wait, but the hydrolysis of nitriles to carboxylic acids can be done with either HCl or CH3COOH as the acid. However, the reaction conditions depend on the desired byproduct. For example, using H2SO4 would give a better catalyst for the hydrolysis, but the options don't include H2SO4. 

In the context of the options given, if B is CH3COOH, then the reaction would proceed under acidic conditions, but using a weaker acid. However, the question is about the correct reagents. Both HCl and CH3COOH are strong enough acids, but HCl is a stronger acid. However, the product is the same in both cases. 

But the key is that the first reaction uses H3O+ (option B or C) and the second reaction uses HCl (option B) or CH3COOH (option C). 

Now, looking at the possible answers, option B is A = H3O+, B = HCl. Option C is A = H3O+, B = CH3COOH. 

Which one is correct? Let's think about the first reaction again. The product is 2-hydroxy-2-methylbutanenitrile. If the workup is with H3O+, then the hydroxyl group is protonated, giving (CH3)2C(OH)CN. But the name 2-hydroxy-2-methylbutanenitrile implies four carbons. Let's count: the nitrile is on carbon 1, the hydroxyl on carbon 2, and a methyl on carbon 2. So the structure is CH2(CN)(CH3)CH2OH. Wait, but that's five carbons. Wait, no, the butanenitrile has four carbons. So the structure is CH2(CN)(CH3)CH2OH. Wait, that's five carbons. Hmm, perhaps I'm overcomplicating. But regardless, the reaction uses H3O+ as the workup, so option B would have A = H3O+ and B = HCl.

Alternatively, if NaHSO3 is used as the workup (option A), then the hydroxyl would be protonated, but I'm not sure if NaHSO3 is a common workup for cyanohydrin. Usually, HCl or H2SO4 are used. 

Therefore, the correct answer is option B: A = H3O+, B = HCl.
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