Okay, so I need to figure out which of the given compounds is the correct one based on the characterization data provided. Let me start by going through each piece of information step by step.

First, the FTIR spectrum shows a very broad absorption around 3000 cm⁻¹. I remember that a broad peak in that region usually indicates the presence of O-H groups, like in carboxylic acids or alcohols. Since the options all have a COOH group, that's a carboxylic acid. The broad peak supports the presence of the -COOH group, which explains the O-H stretch. So that's a good start. The other strong peak at 1700 cm⁻¹ is probably an absorption from an ester or a ketone. Wait, the options all have a COOH group, so maybe the 1700 cm⁻¹ is an ester carbonyl? But none of the options have an ester. Wait, let me check the options again. All four options have a COOH group, so maybe the 1700 cm⁻¹ is a carbonyl from the carboxylic acid. But wait, carboxylic acids usually have a strong absorption around 1700 cm⁻¹ as the carbonyl (C=O) stretch. So that makes sense. So the FTIR data is consistent with a carboxylic acid.

Next, the 1H NMR data. The question states that none of the peaks correspond to vinyl hydrogens. That means there are no protons that are part of a double bond (like CH₂=CH- groups). All the hydrogens in the molecule must be either in a CH3, CH2, or perhaps a CH group attached to something else but not part of a double bond. Let's look at the options:

Option A: CH3C(H)(C2H5)C(H)(C2H5)CH2COOH. Let's parse this. The structure would be something like CH2(C2H5)CH(CH3)CH(CH2CH2?) Wait, maybe I should draw the structure. Let me think. The formula is CH3-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH. So the central part is two C(H)(R) groups. Each R is C2H5. So the structure is CH3-C(C2H5)(H)-C(C2H5)(H)-CH2COOH. So the two CH(CH2CH3) groups. Wait, but each of those would have a CH group attached to a C2H5 and another CH3. Wait, no. Wait, the structure is like (CH3)-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH. So each of the two middle carbons has two substituents: one is a H and one is a C2H5. Wait, but each carbon can't have four bonds. Wait, maybe it's more like each of those carbons is connected to two substituents: one is a H and the other is a C2H5, but that would only give three bonds. Wait, maybe I need to correct this. Let me write the formula properly. The formula for the options is:

Option A: CH3C(H)(C2H5)C(H)(C2H5)CH2COOH. So the structure is:

- The first carbon is CH3.
- The second carbon is C(H)(C2H5), which is attached to the first carbon and has a H and a C2H5 group. So that's CH2(C2H5) connected to the first CH3.
Wait, maybe it's more accurate to write it as:

The structure is CH3-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH.

So the two middle carbons each have two substituents: a H and a C2H5. Wait, but each carbon can only have four bonds. So each of those middle carbons is connected to the adjacent carbons, a H, and a C2H5. So each middle carbon is CH(C2H5)(H)CH2...? Wait, maybe the structure is:

- The first carbon is CH3.
- The second carbon is CH2 connected to C2H5 and the first CH3.
- The third carbon is CH2 connected to another C2H5 and the second carbon.
- The fourth carbon is CH2 connected to the third carbon and the fifth carbon, which is COOH.

Wait, maybe that's not accurate. Let me try again. Let's parse the formula correctly. For option A: CH3C(H)(C2H5)C(H)(C2H5)CH2COOH.

Breaking it down:

- The first part is CH3C(H)(C2H5): that's a CH3 group attached to a carbon that has a H and a C2H5 group. So this carbon is CH2(C2H5)CH3? Wait, no. Wait, the formula is written as CH3-C(H)(C2H5). So the central carbon is connected to CH3, H, and C2H5. So that's a CH2 group? Wait, no. Wait, the formula is written as CH3-C(H)(C2H5), which would be a carbon attached to CH3, H, and C2H5. But that's three substituents, so the carbon would be CH2(C2H5), but wait, that would require four substituents. Wait, maybe I'm misunderstanding the notation. In the IUPAC nomenclature, the formula is written with the substituents in parentheses. So CH3-C(H)(C2H5) would be a carbon attached to CH3, H, and C2H5. But that's three substituents, so the carbon must have another substituent. Wait, maybe the formula is written as CH3-C(H)(C2H5), which implies that the carbon has three substituents: CH3, H, and C2H5. But that's only three bonds. Wait, maybe the formula is written with the substituents as branches. So CH3-C(H)(C2H5) would be a carbon attached to CH3, H, and C2H5. But that's three substituents, so the carbon must have a fourth substituent. Wait, maybe the formula is written as CH3-C(CH2CH3)(H), which would be a CH2 group attached to the carbon. Wait, this is getting confusing. Let me try to draw each option's structure.

Option A: The formula is CH3C(H)(C2H5)C(H)(C2H5)CH2COOH.

So the structure is:

- The central part is a chain with two middle carbons, each connected to a H, a C2H5, and the adjacent carbons. Let's build it step by step.

Start with the first carbon: CH3-C(...). The second carbon is connected to CH3 and has substituents H and C2H5. So that's CH2(C2H5)CH3? Wait, no. Wait, the formula is written as CH3-C(H)(C2H5), which would mean the second carbon is attached to CH3, H, and C2H5. So the second carbon is CH(CH3)(C2H5). But that's three substituents, so the fourth must be a hydrogen. Wait, but the formula is written as C(H)(C2H5), so the substituents are H and C2H5. So the second carbon is CH2(C2H5)CH3? Wait, maybe not. Wait, perhaps the structure is:

CH3-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH.

So the middle two carbons each have a H and a C2H5 attached. So each of those carbons is CH(C2H5)(H). But since each carbon can only have four bonds, each of these middle carbons must also be attached to another group. Wait, perhaps they are CH2 groups. Wait, no. Let me think again. Let's parse the formula correctly. The formula is written as:

CH3-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH.

So each of the two middle carbons is connected to a H and a C2H5. The first middle carbon is connected to the first CH3, the second middle carbon is connected to the first middle carbon, the third middle carbon (CH2) is connected to the second middle carbon, and the last part is CH2COOH.

Wait, maybe the structure is:

- The first carbon is CH3.
- The second carbon is connected to CH3, H, and C2H5. So that's CH2(C2H5)CH3? Wait, but that's not possible because each carbon can have only four bonds. Wait, maybe the second carbon is CH(CH3)(C2H5). But then that's three substituents. So the fourth substituent would be a hydrogen. So the second carbon is CH(CH3)(C2H5)H. That would make sense. So the structure is:

CH3-CH(CH3)(C2H5)-CH(CH2CH3)(C2H5)-CH2-COOH.

Wait, no, the formula is CH3-C(H)(C2H5)-C(H)(C2H5)-CH2COOH. So each of the two middle carbons has a H and a C2H5. So they're each CH(C2H5)(H). But then, each of these middle carbons is connected to two other carbons. Wait, the first middle carbon is connected to the first CH3 and the second middle carbon. The second middle carbon is connected to the first middle carbon and the third part, which is CH2. So the structure would be:

CH3-CH(C2H5)(H)-CH(C2H5)(H)-CH2-COOH.

But that would give each middle carbon two substituents (C2H5 and H) plus the two connecting carbons. Wait, that can't be right because each carbon can only have four bonds. So maybe the middle carbons are CH2 groups. Wait, perhaps the formula is written as CH3-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH, which would imply that each middle carbon is CH2(C2H5)(H)CH2...? I'm getting a bit tangled here. Let me try another approach. Let's consider the molecular structure. The options all have a COOH group, so they are carboxylic acids. The NMR data says that none of the peaks are vinyl hydrogens, so all the hydrogens in the molecule are either CH3, CH2, or CH (but not CH2=CH- groups). So the presence of any CH2=CH group would have been detected as a vinyl peak. Since none are present, the structure must not have any double bonds. So all the structures must be fully saturated.

Looking at the options, all have branches with C2H5 groups, which are ethyl groups, so they are all aliphatic structures without double bonds. So that's consistent with the NMR data. Now, the NMR has two types of signals: one is a doublet of triplets of quartets, and another is a doublet of triplets of triplets. Let's analyze the splitting patterns.

The splitting patterns depend on the neighboring protons. For example, if a proton is adjacent to two sets of protons, the splitting can be more complex. Let's take each option and see what their NMR signals would look like.

Starting with Option A: CH3C(H)(C2H5)C(H)(C2H5)CH2COOH.

The structure is:

CH3-CH(C2H5)(H)-CH(C2H5)(H)-CH2-COOH.

Wait, but each middle carbon is attached to two substituents: H and C2H5. So each middle carbon is CH(C2H5)(H), which would mean they have two hydrogens. But wait, each carbon can have only four bonds. Let's clarify. The formula is written as CH3-C(H)(C2H5)-C(H)(C2H5)-CH2COOH. So each of the two middle carbons is attached to H and C2H5. Therefore, each middle carbon is CH(C2H5)(H), but that only accounts for three substituents. So perhaps there's another substituent, which would be a CH2 group. Wait, maybe the formula is written with branching. Let me consider that the two middle carbons each have two substituents: H and C2H5, and the adjacent carbons. So each middle carbon is CH(C2H5)(CH2...), but I'm not sure. Alternatively, perhaps the structure is:

The first carbon is CH3.

The second carbon is connected to CH3, H, and C2H5, and the third carbon. So the second carbon is CH(CH3)(C2H5), which is a quaternary carbon? Wait, no. Wait, the second carbon would have four bonds: one to CH3, one to C2H5, one to the third carbon, and one hydrogen. So the second carbon is CH(CH3)(C2H5)(H). Similarly, the third carbon is CH(CH3)(C2H5)(H), connected to the fourth carbon (CH2). Then the fourth carbon is CH2 connected to the fifth carbon (COOH). So the structure would be:

CH3-CH(CH2CH3)(CH2CH3)-CH(CH2CH3)(CH2CH3)-CH2-COOH.

Wait, no, because C2H5 is ethyl. So each C2H5 is an ethyl group. So the structure would have two ethyl groups attached to the two middle carbons. Each of the two middle carbons is CH attached to an ethyl group, a hydrogen, and connected to the adjacent carbons. So each middle carbon is CH2-Ethyl. Wait, but that would mean each middle carbon is CH2, but they have substituents. Maybe it's better to think of each middle carbon as CH2 connected to an ethyl group and a hydrogen. Wait, no. Let me try again.

The formula is CH3-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH. So each middle carbon is connected to a H, a C2H5, and the adjacent carbons. So each middle carbon has two substituents: H and C2H5, and the two adjacent carbons. Therefore, the middle carbons are CH2 groups? Wait, no. Wait, each middle carbon is CH2 attached to a substituent. Wait, maybe the structure is:

CH3-CH2-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH. But that would introduce a CH2 group. However, the formula given is CH3-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH. So the two middle carbons are each attached to H, C2H5, and the adjacent carbons. So each middle carbon is CH(C2H5)(H)CH2...? I'm getting confused. Maybe I should move on to the NMR analysis.

In the NMR, there are two types of signals: a doublet of triplets of quartets (dtq) and a doublet of triplets of triplets (dtt). Let's consider each option and see which one fits.

Option B: CH3CH2C(H)(CH3)C(H)(CH3)CH2COOH.

This structure would be:

CH3-CH2-C(CH3)(H)-C(CH3)(H)-CH2-COOH.

Each of the two middle carbons is attached to a methyl group (CH3), a hydrogen, and the adjacent carbons. So the middle carbons are each CH(CH3)(H). Wait, but that would mean each middle carbon is CH2. No, wait, the formula is CH3CH2C(H)(CH3)C(H)(CH3)CH2COOH. So the middle two carbons are C(H)(CH3), which means each is CH(CH3). So the structure is:

CH3-CH2-CH(CH3)-CH(CH3)-CH2-COOH.

So the two middle carbons are each CH(CH3). Each of these carbons is connected to a CH3 group, a hydrogen, and the adjacent carbons. So the protons on these carbons would be split based on their neighboring protons.

For the middle CH(CH3) groups, the protons on the CH would be next to a CH3 and another CH. Let's analyze the splitting. For the first middle carbon (CH(CH3)), the proton would be adjacent to the CH2 group and the CH(CH3) group. Wait, the structure is CH3-CH2-CH(CH3)-CH(CH3)-CH2-COOH.

So the first middle carbon is CH2 connected to the CH(CH3) group. Wait, no. Let's parse it again. The formula is CH3CH2C(H)(CH3)C(H)(CH3)CH2COOH. So the structure is:

CH3-CH2-C(H)(CH3)-C(H)(CH3)-CH2-COOH.

So the two middle carbons are each C(H)(CH3), which means each is CH(CH3). So the structure is:

CH3-CH2-CH(CH3)-CH(CH3)-CH2-COOH.

Now, let's look at the protons on the middle carbons. The first middle carbon (CH(CH3)) is connected to the CH2 group and the next CH(CH3) group. The protons on this carbon would be adjacent to the CH2 group (which has two protons) and the next CH(CH3) group (which has a CH3 group). So the protons on the first middle carbon (CH(CH3)) would be split by the neighboring protons. The CH2 group has two protons, and the adjacent carbon is CH(CH3), which has a CH3 group. Wait, but the adjacent carbon's protons are on the CH3 group. Wait, no. The adjacent carbon is CH(CH3), which has a CH3 group. So the protons on the CH(CH3) carbon are next to the CH2 group and the next CH(CH3) group. The CH2 group has two protons, and the next CH(CH3) group has a CH3 group, which is not adjacent to the protons on the current carbon. Wait, maybe I need to look at the splitting pattern for each proton.

Alternatively, let's consider the possible splitting for each proton in the structure. For the first middle carbon (CH(CH3)), the protons there would be split by the neighboring CH2 group. The CH2 group has two protons. The splitting would depend on the neighboring protons. The first middle carbon's protons would be next to the CH2 group (two protons) and the next CH(CH3) group (which has three protons). Wait, but the next CH(CH3) group is attached to the first middle carbon. So the first middle carbon's protons are next to the CH2 group (two protons) and the adjacent CH(CH3) group (which has three protons). Wait, but the adjacent group is a CH(CH3), so the protons on the first middle carbon are split by the two protons on the CH2 group and the three protons on the adjacent CH(CH3) group. That would make the splitting a doublet of quintets or something more complex. However, the NMR data mentions a doublet of triplets of quartets and a doublet of triplets of triplets. This might not match.

Option C: CH3CH2C(H)(C2H5)C(H)(C2H5)CH2COOH.

This structure would be:

CH3-CH2-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH.

Each of the two middle carbons is C(H)(C2H5), so each is CH(C2H5). So the structure is:

CH3-CH2-CH(C2H5)-CH(C2H5)-CH2-COOH.

Now, the protons on the middle carbons (CH(C2H5)) would be next to the CH2 group and the next CH(C2H5) group. The CH2 group has two protons, and the next CH(C2H5) group has a C2H5 group (ethyl group). So the protons on the middle carbons would be split by the neighboring CH2 group and the adjacent CH(C2H5) group. The CH2 group has two protons, and the CH(C2H5) group has a CH2CH3 group. Wait, the CH(C2H5) group is connected to the middle carbon. The ethyl group (C2H5) is connected to the middle carbon. So the ethyl group is -CH2CH3. So the protons on the middle carbon would be next to the CH2 group (two protons) and the adjacent ethyl group (CH2CH3). Wait, but the ethyl group is -CH2CH3, so the adjacent protons are on the ethyl group. Wait, no. The ethyl group is attached to the middle carbon, so the ethyl group's protons are on the CH2CH3 chain. So the protons on the middle carbon (CH(C2H5)) would be adjacent to the CH2 group (two protons) and the ethyl group (which has a CH2CH3). Wait, but the ethyl group's protons are on the adjacent CH2CH3. So the splitting would depend on the neighboring protons. The middle carbon's protons would be split by the two protons on the CH2 group and the three protons on the ethyl group. That would lead to a quintet splitting or something more complex. However, the NMR data mentions specific splitting patterns, so maybe this option doesn't fit.

Option D: CH3C(H)(C2H5)C(H)(C2H5)CH2COOH.

This structure is:

CH3-C(H)(C2H5)-C(H)(C2H5)-CH2-COOH.

Each middle carbon is C(H)(C2H5), so each is CH(C2H5). The structure is:

CH3-CH(C2H5)-CH(C2H5)-CH2-COOH.

The protons on the middle carbons (CH(C2H5)) would be adjacent to the CH3 group and the adjacent carbons. Wait, the first middle carbon is CH(C2H5), connected to CH3 and the next carbon. The second middle carbon is CH(C2H5), connected to the first middle carbon and the CH2 group. So each middle carbon's protons are next to the adjacent middle carbon and the CH3 or CH2 groups. Let's analyze the splitting for the first middle carbon. The first middle carbon's protons are next to the CH3 group (three protons) and the next middle carbon (which has protons adjacent to it). The next middle carbon has a CH(C2H5) group, so its protons are adjacent to the first middle carbon and the CH2 group. The CH2 group has two protons. So the first middle carbon's protons would be split by the CH3 group (three protons) and the next middle carbon's protons (which are split by the CH2 group and another group). This might lead to a complex splitting pattern. However, the NMR data mentions specific patterns, so maybe this option doesn't fit.

Now, let's go back to the NMR data. The problem states that there are two types of signals: one is a doublet of triplets of quartets (dtq) and the other is a doublet of triplets of triplets (dtt). Let's think about each option's possible splitting patterns.

Option B: CH3CH2C(H)(CH3)C(H)(CH3)CH2COOH.

Structure: CH3-CH2-CH(CH3)-CH(CH3)-CH2-COOH.

Each middle carbon (CH(CH3)) has protons adjacent to the CH2 group and the next CH(CH3) group. The CH2 group has two protons, and the next CH(CH3) group has a CH3 group. Wait, but the next group is CH(CH3), so the protons on the middle carbon are adjacent to the CH2 group (two protons) and the adjacent CH(CH3) group (which has a CH3 group). Wait, the CH3 group is on the adjacent carbon, so the protons on the middle carbon are next to a CH2 group and a CH3 group. The CH2 group has two protons, and the CH3 group has three protons. So the splitting would be a quintet? But the NMR data mentions quartets and triplets. Let me think. The middle protons would be split by the neighboring protons. For the first middle carbon (CH(CH3)), the protons are adjacent to the CH2 group (two protons) and the adjacent CH(CH3) group (which has a CH3 group). The CH2 group's protons would split the signal into a triplet (since each proton on the middle carbon is adjacent to two protons on the CH2 group), and the adjacent CH3 group's protons would split it into a quartet (since the middle carbon's protons are adjacent to three protons from the CH3 group). Wait, but the CH3 group is not adjacent but on the next carbon. Wait, the middle carbon is CH(CH3), so the protons there are adjacent to the CH2 group (two protons) and the adjacent CH(CH3) group (which is another CH3 group). Wait, no, the adjacent group is a CH(CH3), so the protons on the middle carbon are next to the CH2 group and the next CH(CH3) group. Wait, but the next group is another CH(CH3), which is a CH3 group. So the middle carbon's protons are adjacent to the CH2 group (two protons) and the adjacent CH3 group (three protons). So the splitting would be a doublet of triplets of triplets? Let's see. The middle carbon's protons are next to two sets of protons: the CH2 group (two protons) and the CH3 group (three protons). The splitting from the CH2 group would be a triplet (since two neighboring protons), and the splitting from the CH3 group would be a quartet (since three neighboring protons). But since there are two sets of neighboring protons, the overall splitting would be a doublet of triplets of triplets? Wait, no. The splitting pattern would be a doublet of triplets of triplets if there are two coupling constants. Wait, maybe the middle carbon's protons are split by two different sets of protons. The first set is the CH2 group (two protons), leading to a triplet, and the adjacent CH3 group (three protons), leading to a quartet. But since these are two different couplings, the splitting would be a doublet of triplets of quartets (dtq). However, the NMR data mentions a dtq and a dtt. Let's check the other protons.

The other protons in the molecule are the CH2 groups. The CH2 groups are between the CH(CH3) groups. For example, the structure is CH3-CH2-CH(CH3)-CH(CH3)-CH2-COOH. So the CH2 groups are each between two CH(CH3) groups. The protons on these CH2 groups would be adjacent to the CH(CH3) groups on both ends. Each CH2 group has two protons. The splitting for these protons would be due to the adjacent CH(CH3) groups. Each CH(CH3) group has three protons (from the CH3). So the CH2 protons would be split by the adjacent CH(CH3) groups. Since each CH2 proton is adjacent to two protons (from the left CH(CH3)) and two protons (from the right CH(CH3)), the splitting would be a quartet (since four neighboring protons). But wait, the CH2 group is between two CH(CH3) groups, each contributing two protons. So the CH2 protons would be split by two sets of protons, each set contributing two protons. Wait, the splitting would be a doublet of quartets. Because each CH2 proton is adjacent to two CH(CH3) groups, each with two protons. So the splitting would be a doublet of quartets (dq). But the NMR data mentions a dtq and a dtt. So maybe this option doesn't fit.

Option A: CH3C(H)(C2H5)C(H)(C2H5)CH2COOH.

Structure: CH3-CH(C2H5)-CH(C2H5)-CH2-COOH.

Each middle carbon is CH(C2H5), connected to CH3 and CH(C2H5). The protons on these middle carbons are adjacent to the CH3 group and the next middle carbon. The CH3 group has three protons, and the next middle carbon has a CH(C2H5) group. The CH2 group is at the end. Let's analyze the splitting. For the first middle carbon (CH(C2H5)), the protons are adjacent to the CH3 group (three protons) and the next middle carbon (CH(C2H5)). The next middle carbon's protons are adjacent to the first middle carbon and the CH2 group. The CH2 group has two protons. So the protons on the first middle carbon would be split by the CH3 group (three protons) and the next middle carbon's protons (which are split by the CH2 group). The splitting from the CH3 group would be a quartet (since three neighboring protons), and the splitting from the next middle carbon's protons would be a triplet (since two neighboring protons). But since the next middle carbon's protons are also split by the CH2 group, which has two protons, the splitting becomes more complex. Alternatively, the protons on the first middle carbon are split by two sets of protons: the CH3 group (three protons) and the next middle carbon's protons (which are split by the CH2 group). This would lead to a doublet of triplets of triplets (dtt), which matches one of the NMR signals. The protons on the next middle carbon would be adjacent to the first middle carbon's protons (which are split by the CH3 group) and the CH2 group. The CH2 group's protons would be adjacent to the next middle carbon's protons (two protons) and the CH2 group's adjacent to the COOH group (which has no protons). So the CH2 protons would be split by the next middle carbon's protons (two protons), leading to a triplet. But the NMR data mentions a dtq and a dtt. So maybe this option has a dtt and a triplet. But the problem states that there are two signals: one dtq and one dtt. So this might not fit.

Option C: CH3CH2C(H)(C2H5)C(H)(C2H5)CH2COOH.

Structure: CH3-CH2-CH(C2H5)-CH(C2H5)-CH2-COOH.

The protons on the CH2 groups would be adjacent to the CH(C2H5) groups. Each CH2 group has two protons. The splitting for these protons would be due to the adjacent CH(C2H5) groups. Each CH(C2H5) group has a CH2CH3 group attached. Wait, no. The CH(C2H5) group is connected to the middle carbon. The ethyl group (C2H5) is attached to the middle carbon. So the ethyl group's protons are on the adjacent CH2CH3. So the protons on the middle carbon (CH(C2H5)) are next to the CH2 group (two protons) and the ethyl group (CH2CH3). The ethyl group's protons are three (from CH2CH3). So the protons on the middle carbon would be split by the two protons on the CH2 group and the three protons on the ethyl group. This would result in a quintet splitting, which doesn't match the NMR data. Therefore, this option might not fit.

Option D: CH3C(H)(C2H5)C(H)(C2H5)CH2COOH.

Structure: CH3-CH(C2H5)-CH(C2H5)-CH2-COOH.

The protons on the middle carbons (CH(C2H5)) would be adjacent to the CH3 group and the next middle carbon. The CH3 group has three protons, and the next middle carbon has a CH(C2H5) group. The protons on the middle carbons would be split by the CH3 group (three protons) and the next middle carbon's protons (which are split by the CH2 group). The splitting from the CH3 group would be a quartet (since three neighboring protons), and the splitting from the next middle carbon's protons would be a triplet (since two neighboring protons). This would lead to a doublet of triplets of triplets (dtt) for the middle protons. The CH2 group at the end has two protons, adjacent to the next middle carbon's protons (two protons) and the COOH group (no protons). So the CH2 protons would be split by the next middle carbon's protons, leading to a triplet. However, the NMR data mentions a dtq and a dtt. So if this option's protons show a dtt and a triplet, but the problem states there are two signals (dtq and dtt), maybe this doesn't fit either.

Wait, perhaps I need to re-examine the splitting patterns more carefully. Let's focus on option B again. The structure is CH3-CH2-CH(CH3)-CH(CH3)-CH2-COOH.

The CH2 groups are between the CH(CH3) groups. The protons on these CH2 groups would be adjacent to the CH(CH3) groups on both ends. Each CH(CH3) group has three protons (from the CH3). So each CH2 proton is adjacent to two CH(CH3) groups, each contributing three protons. Wait, but each CH2 proton is adjacent to two protons from the left CH(CH3) and two protons from the right CH(CH3)? No, each CH(CH3) group is connected to the CH2 group. Wait, the structure is CH3-CH2-CH(CH3)-CH(CH3)-CH2-COOH. So the CH2 groups are between the CH(CH3) groups. Each CH(CH3) group is connected to a CH2 group. So the CH2 groups are each between two CH(CH3) groups. So the CH2 protons are adjacent to two CH(CH3) groups. The left CH(CH3) group has three protons (from the CH3), and the right CH(CH3) group also has three protons. Wait, but the CH2 group's protons are adjacent to the CH(CH3) groups. The splitting would be based on the neighboring protons. Each CH2 proton is adjacent to two protons from the left CH(CH3) group (since the CH(CH3) is connected to the CH2), and two protons from the right CH(CH3) group. Wait, no. The CH(CH3) group has a single proton (the H) attached to the CH2. Wait, no. The CH(CH3) group is CH(CH3), meaning it has a CH3 group attached to the carbon. The structure of CH(CH3) is C(H)(CH3), so it has one H and one CH3 group. The CH3 group is attached to the carbon. So the CH(CH3) group is connected to the CH2 group. The CH2 group has two protons. So the CH2 protons are adjacent to the CH(CH3) group on both ends. The CH(CH3) group has one H and one CH3. Wait, but the H is attached to the carbon. So the CH(CH3) group has one H and a CH3 group. The H is attached to the C that is connected to the CH2 group. The CH3 group is on the same C. So the H is not adjacent to the CH2 group. Wait, maybe the H is on the same carbon as the CH3 group. So the structure is:

CH3-CH2-C(CH3)(H)-C(CH3)(H)-CH2-COOH.

Wait, that might make more sense. So each CH(CH3) group has a CH3 and a H attached to the same carbon. So the CH2 group is attached to the carbon with the H and CH3. Therefore, the CH2 groups are adjacent to a C that has both a H and a CH3. Therefore, the CH2 groups are next to a CH(CH3) group. So the CH2 protons are adjacent to the CH(CH3) group, which has a H and a CH3. The H is on the same carbon as the CH3 group. So the CH2 protons are adjacent to the H and the CH3 group. The H is a single proton, and the CH3 group has three protons. Therefore, the CH2 protons are split by the neighboring H (one proton) and the neighboring CH3 group (three protons). So the splitting would be a doublet of triplets (dt). But the NMR data mentions dtq and dtt. Hmm, maybe this isn't matching either.

Alternatively, maybe the CH2 groups are adjacent to two different sets of protons. For example, each CH2 group is between two CH(CH3) groups. Each CH(CH3) group has a H and a CH3. The CH2 group's protons would be adjacent to the H from the left CH(CH3) and the H from the right CH(CH3). Wait, but each CH(CH3) group has only one H. So the CH2 group's protons are adjacent to one H from the left and one H from the right. That would lead to a quartet (since four neighboring protons: two from the left and two from the right). But the NMR data mentions a dtq and a dtt. Maybe this isn't the right approach.

Let me think differently. Let's consider the splitting patterns. The problem states that there are two types of signals: one is a doublet of triplets of quartets (dtq) and the other is a doublet of triplets of triplets (dtt). Let's think about each option's possible splitting.

Option B: CH3CH2C(H)(CH3)C(H)(CH3)CH2COOH.

The middle CH2 groups are between the CH(CH3) groups. The protons on these CH2 groups are adjacent to the CH(CH3) groups. Each CH(CH3) group has a H and a CH3. The H is on the same carbon as the CH3. So the CH2 protons are adjacent to the H (one proton) and the CH3 group (three protons). So the splitting would be a doublet of triplets (dt). But the NMR data mentions a dtq and a dtt.

The protons on the middle CH(CH3) groups would be adjacent to the CH2 groups and the next CH(CH3) group. The CH2 groups have two protons each. The next CH(CH3) group has a H and a CH3. So the protons on the middle CH(CH3) groups are split by the CH2 groups (two protons) and the next CH(CH3) group (one H and three CH3 protons). So this would lead to a doublet of triplets of quartets (dtq) and a doublet of triplets of triplets (dtt). Because the splitting from the CH2 group (two protons) would be a triplet, and the splitting from the next CH(CH3) group (three protons) would be a quartet. But since there are two sets of neighboring protons, the overall splitting would be a doublet of triplets of quartets (dtq). The CH2 groups would be split by the adjacent CH(CH3) groups, leading to a doublet of triplets of triplets (dtt). Wait, maybe this matches the NMR data. Because the middle CH(CH3) groups' protons would be split by two sets of protons: the CH2 group (two protons) and the next CH(CH3) group (three protons). This would lead to a dtq (doublet of triplets of quartets). The CH2 groups, being between two CH(CH3) groups, would each have protons split by the adjacent CH(CH3) groups. Each CH(CH3) group has a CH2 group with two protons. So the CH2 protons would be split by two sets of two protons each (from the left and right CH(CH3) groups), leading to a doublet of triplets of triplets (dtt). Therefore, option B fits the NMR data.

The other options might not fit as well. For example, option A has protons on the middle carbons that are split by the CH3 group and the next middle carbon, leading to a dtt. The CH2 groups would be split by the next middle carbon's protons, leading to a triplet. But the NMR data mentions two signals, one dtq and one dtt. Option B's structure seems to have protons that split into dtq and dtt, matching the data.

Additionally, the IR data shows an absorption at 1700 cm⁻¹, which is indicative of a carboxylic acid (COOH group), which all options have. So option B seems to fit all the given data.
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