Okay, so I need to figure out the total number of hydrogen atoms in two liquids of mixture X based on the given information. Let me start by breaking down the problem step by step.

First, let's recap the scenario. We have two mixtures, X and Y. Mixture X is an equimolar mixture of two liquids that decolorizes bromine water. When treated with platinum under heat, mixture X undergoes a disproportionation reaction to form mixture Y, which doesn't decolorize bromine. Then, both mixtures X and Y are hydrogenated in the presence of platinum under severe conditions, resulting in the same hydrocarbon Z with a hydrogen mass fraction of 14.28%. Z is a component of Y and is widely used as a solvent. Importantly, Z doesn't react further with hydrogen, and mixture X has no conjugated double bonds in their molecules.

The question is asking for the total number of hydrogen atoms in the two liquids of mixture X. The options are A. 22, B. 12, C. 16, D. 18.

Let me start by understanding each part of the problem.

1. **Decolorization by Bromine Water**: The fact that mixture X decolorizes bromine water suggests that the components of X are likely to be unsaturated compounds, such as alkenes or alkynes. Because when an alkene reacts with bromine water, it causes decolorization (addition of Br2). Similarly, an alkyne might also decolorize bromine in some cases, but I need to confirm that.

2. **Disproportionation with Platinum**: Disproportionation typically involves the splitting of a molecule into two parts with different oxidation states. For example, if a molecule with a central atom in a certain oxidation state splits into two molecules where one has a higher oxidation state and the other a lower. Platinum is often a catalyst in such reactions, especially when heating is involved. Since the result is an equimolar mixture Y of two other liquids, each of these liquids must be formed from one of the original components in X. So, each component in X might split into two different products.

3. **Hydrogenation of X and Y**: Both X and Y are hydrogenated under severe conditions with platinum catalyst. This suggests that the products (hydrocarbon Z) are fully hydrogenated alkenes or alkynes. The fact that both X and Y hydrogenate to the same product Z indicates that the original molecules in X and Y must be such that their hydrogenation leads to the same structure. However, since Z is a component of Y, it's possible that Y has a mixture of a hydrogenated product and another structure that doesn't require hydrogenation. But Z is a constituent of Y, so maybe one of the products of the disproportionation is a compound that hydrogenates to Z, and the other product doesn't (but Z is a component of both X and Y after hydrogenation? Wait, no. Wait, the question says that both X and Y, when hydrogenated, give Z. So X and Y, when hydrogenated, result in Z. Also, Z is part of Y. Hmm. Let me think again.

Wait, the problem states: "Hydrogenation of both mixture X and mixture Y in the presence of platinum under rather severe conditions gives only one substance, a certain hydrocarbon Z (mass fraction of hydrogen is 14.28%), which is a constituent of mixture Y and widely used as a solvent." So X and Y both hydrogenate to Z. But Z is a component of Y. Wait, that's a bit confusing. Let me parse this again.

- X is treated with Pt under heat to form Y (disproportionation). So X is split into two parts, each of which becomes a component in Y. Then, both X and Y are hydrogenated to Z. But Z is a constituent of Y. Wait, that might mean that when Y is hydrogenated, one of its components becomes Z. But Z is a constituent of Y, so maybe Y has a part that is Z already, and another part that also hydrogenates to Z. But the wording is a bit unclear. Let me re-read the problem.

"Hydrogenation of both mixture X and mixture Y in the presence of platinum under rather severe conditions gives only one substance, a certain hydrocarbon Z (mass fraction of hydrogen is 14.28%), which is a constituent of mixture Y and widely used as a solvent. Substance Z does not react further with hydrogen."

So, when X is hydrogenated, it becomes Z. When Y is hydrogenated, it also becomes Z. But Z is a constituent of Y. So Y must have a part that is Z already, and the other part must also hydrogenate to Z. Alternatively, perhaps both X and Y hydrogenate to Z, but Z is part of Y. That might not make sense. Wait, maybe the wording is that Z is a constituent of Y, meaning that when Y is hydrogenated, one of the products is Z. But since Z is a constituent of Y, maybe Y has a part that is Z, and another part that is a more unsaturated compound that can be hydrogenated to Z. Hmm. Alternatively, perhaps Y is a mixture of Z and another compound that also hydrogenates to Z. So when Y is hydrogenated, both parts become Z. But the problem says that the result is only Z, with a mass fraction of hydrogen 14.28%. Wait, maybe the entire mixture X and Y hydrogenate to Z, which has a certain hydrogen mass fraction. But Z is part of Y. Hmm. I might need to approach this differently.

Let me think about the hydrogenation of X and Y. If both X and Y hydrogenate to Z, then X must consist of alkenes and alkynes (since they decolorize bromine), and their hydrogenation would lead to alkanes. Since Z is a product of hydrogenation, it's an alkane. The mass fraction of hydrogen in Z is 14.28%. Let's calculate the molecular formula of Z.

The mass fraction of H in Z is 14.28%. Let's assume Z is an alkane with formula CnH2n+2. The molecular weight of H is 1, so the total mass of H in Z is (2n+2) * 1 = 2n+2. The molecular weight of the entire molecule is (12n) + (2n+2) = 14n + 2. The mass fraction of H is (2n+2)/(14n + 2) = 0.1428. Let's solve for n.

(2n + 2) = 0.1428*(14n + 2)
Multiply both sides by 1000 to eliminate decimals:
(2n + 2) * 1000 = 1428*(14n + 2)
But maybe a better approach is to set up the equation:

(2n + 2)/(14n + 2) = 14.28/100 = 0.1428

Multiply both sides by (14n + 2):

2n + 2 = 0.1428*(14n + 2)

Calculate 0.1428 *14n = 1.9992n ≈ 2n (since 0.1428*14=2)

But let's do it more accurately.

0.1428 *14n = 0.1428*14*n = 2n (exactly, since 14*0.1428=2)

0.1428*2 = 0.2856

So:

2n + 2 = 2n + 0.2856

Subtract 2n from both sides:

2 = 0.2856

Wait, that can't be right. That would imply 2 = 0.2856, which is impossible. So my assumption that Z is a simple alkane must be wrong. Maybe Z has a different structure, like a cyclic alkane or something else. Wait, but the problem says Z is a constituent of mixture Y, which is formed from the disproportionation of mixture X. Let me think again.

Alternatively, perhaps Z is a mixture of alkanes. Wait, but the problem states that Z is a certain hydrocarbon. Hmm. Maybe Z is a mixture of alkanes and another compound. But the problem says "only one substance", so Z is a single hydrocarbon. Therefore, Z must be an alkane. But then the calculation leads to a contradiction. Let's check the math again.

Let me set up the equation again:

(2n + 2)/(14n + 2) = 0.1428

Multiply both sides by (14n + 2):

2n + 2 = 0.1428*(14n + 2)

Calculate 0.1428*14n = 2n (since 14*0.1428=2 exactly)

0.1428*2 = 0.2856

So:

2n + 2 = 2n + 0.2856

Subtract 2n:

2 = 0.2856

This is impossible. Therefore, my initial assumption that Z is an alkane must be incorrect. Maybe Z is a different type of hydrocarbon, like a cycloalkane? The molecular formula of cycloalkane would be similar to an alkane, so CnH2n. Let's try that.

If Z is a cycloalkane, formula CnH2n. Then:

Mass fraction of H = (2n)/(12n + 2n) = 2n/(14n) = 1/7 ≈ 0.142857, which is approximately 14.2857%. That's very close to the given 14.28%. So Z is likely a cycloalkane. Therefore, Z has the formula CnH2n.

So the mass fraction of H in Z is (2n)/(14n) = 1/7 ≈ 14.2857%. The problem states 14.28%, which is very close. Therefore, Z is a cycloalkane, specifically a cycloalkane with n carbons. Since the mass fraction is almost exactly 14.2857%, which is 1/7, Z must be a cycloalkane. Therefore, the molecular formula of Z is CnH2n.

Therefore, the molecular formula of Z is CnH2n. Since Z is a constituent of mixture Y, Y must contain Z as one of its components. But Y is the result of the disproportionation of X. So X, which is an equimolar mixture of two liquids that decolorize bromine (so likely alkenes or alkynes), when treated with Pt, undergoes disproportionation to form two other liquids in Y. One of these liquids is Z (cycloalkane), and the other is another compound. However, when both X and Y are hydrogenated, they both yield Z, which is a cycloalkane. 

Wait, but if Y is a mixture of Z (cycloalkane) and another compound, and when Y is hydrogenated, the cycloalkane (Z) doesn't change (since it's already an alkane), and the other component also hydrogenates to Z. Therefore, the other component in Y must be a cycloalkane with one more carbon, or maybe a different structure. Wait, but Z is a constituent of Y, so Y has Z as one of its components. When Y is hydrogenated, Z remains as is, and the other component in Y (which is another molecule) is hydrogenated to Z. Therefore, the other component in Y must be a cycloalkane with one more carbon than Z. Wait, but that might not necessarily be the case. Alternatively, the other component in Y could be a cycloalkyne or something else. Hmm, this is getting complicated.

Alternatively, perhaps Y is a mixture of Z and another compound, say A. When Y is hydrogenated, Z (which is already an alkane) remains, and A is hydrogenated to Z. Therefore, A must be a compound that upon hydrogenation gives Z. Since Z is a cycloalkane, A could be a cycloalkyne. For example, cycloalkyne (CnH2n-2) when hydrogenated becomes cycloalkane (CnH2n). Let's check:

Take cycloalkyne CnH2n-2. Upon hydrogenation (adding H2), each triple bond becomes single bonds. The formula would change as follows: Each triple bond (C≡C) adds two hydrogens. For a cycloalkyne with m triple bonds, each triple bond contributes two H2 molecules. Wait, no. Let's think. For a cycloalkyne with one triple bond (like cycloheptatriyne?), but actually, a cycloalkyne would have one triple bond. Let me take an example: cyclopropane has 3 carbons and no triple bonds. Cyclobutene has a double bond. Cyclopentadiene has two double bonds. Wait, maybe I need to think of a cycloalkyne. For example, cycloheptatriyne would have three triple bonds, but that's not possible. Wait, actually, cycloalkynes are generally not common except for small rings. Wait, maybe the other component in Y is a diene or something else. Hmm.

Alternatively, perhaps the other component in Y is a cycloalkane with a triple bond? No, that's not possible. Wait, maybe the other component in Y is a cycloalkyne. Let's consider a cycloalkyne with formula CnH2n-2. When hydrogenated, it would gain two hydrogens per triple bond. For example, if a cycloalkyne has one triple bond, adding two H2 molecules would convert it to a cycloalkane. Let me check:

Take a cycloalkyne, say cyclopentyne (C5H8). Wait, cyclopentyne would have a triple bond. Its formula is C5H8. Upon hydrogenation, each triple bond (sp-hybridized) would add two hydrogens. Wait, but cyclopentyne (C5H8) would have a triple bond, so if we add two H2 molecules, it would become C5H10. But C5H10 is a cyclopentane. However, cyclopentane is C5H10, and Z is a cycloalkane. So if Y has a cycloalkyne (C5H8) and a cycloalkane (C5H10), then when Y is hydrogenated, the cycloalkyne becomes cyclopentane (C5H10), and the cycloalkane remains unchanged. But Z is C5H10. But the mass fraction of H in Z is 14.28%, which corresponds to 1/7. For C5H10, the molecular weight is (5*12) + (10*1) = 60 +10=70. Mass of H is 10, so 10/70=1/7≈14.28%. So that fits. Therefore, Z is C5H10 (cyclopentane). Therefore, the other component in Y must be a cycloalkyne with formula C5H8 (cyclopentyne). So Y is a mixture of C5H10 (Z) and C5H8 (cyclopentyne). When Y is hydrogenated, the cyclopentyne becomes cyclopentane (Z), and the Z component remains Z. Therefore, when Y is hydrogenated, both components become Z. Therefore, Y is a mixture of Z and a cycloalkyne.

But wait, in the problem statement, Y is an equimolar mixture of two other liquids. So if Y is a mixture of cyclopentane (Z) and cyclopentyne (C5H8), then when Y is hydrogenated, the cyclopentyne becomes cyclopentane, so the result is only cyclopentane, which is Z. Therefore, the hydrogenation of Y gives Z. Similarly, hydrogenation of X gives Z. So X must be a mixture of two alkenes or alkynes that, upon hydrogenation, give Z (cyclopentane). But wait, X is an equimolar mixture of two liquids that decolorize bromine. Decolorization by bromine indicates unsaturation. So X is a mixture of two alkenes or alkynes. When X is hydrogenated, it becomes Z. Since Z is C5H10 (cyclopentane), then each component in X must have the formula C5H10 with two fewer hydrogens (since hydrogenation adds two hydrogens per double bond or triple bond). Therefore, each component in X must have the formula C5H8 (if it's an alkene) or C5H6 (if it's an alkyne). Wait, no. Wait, hydrogenation adds H2 across double or triple bonds. For example, an alkene (C5H10) would become C5H12 upon hydrogenation. But Z is C5H10. Wait, that's confusing. Let me think again.

If X is an equimolar mixture of two liquids that decolorize bromine, so they are unsaturated. When X is hydrogenated, it becomes Z (C5H10). Therefore, each component in X must have one double bond (so when hydrogenated, it becomes C5H12), but Z is C5H10. Wait, that doesn't add up. Alternatively, perhaps X contains cyclic alkenes or alkynes. Wait, maybe X is a mixture of cyclopentene and another compound. Let me check.

Wait, let's think differently. Suppose X is a mixture of two alkenes. Each alkene has the formula CnH2n. Upon hydrogenation, each alkene (CnH2n) becomes CnH2n+2. If the product is Z (C5H10), then each alkene in X must be C5H10 with two fewer hydrogens, so C5H8. Wait, but C5H8 is a cycloalkene. For example, cyclopentene (C5H8) upon hydrogenation becomes cyclopentane (C5H10). So if X is a mixture of two cyclopentenes, but that's not possible since X is an equimolar mixture of two liquids. Wait, but if X is a mixture of two different alkenes, each of which upon hydrogenation gives Z (C5H10), then each alkene must be C5H8. But if X is a mixture of two alkenes, then each alkene must have the formula C5H10 with one double bond. Wait, no. Wait, the formula of an alkene is CnH2n. If the alkene is C5H10, then upon hydrogenation, it becomes C5H12. But Z is C5H10. Therefore, that can't be. Therefore, perhaps X is a mixture of two alkyne compounds. For example, an alkyne is CnH2n-2. When hydrogenated, it becomes CnH2n. So if X is a mixture of two alkynes, each of which upon hydrogenation gives Z (C5H10), then each alkyne in X must have the formula C5H8. Because C5H8 (an alkyne) upon hydrogenation becomes C5H10 (Z). Therefore, X is a mixture of two alkynes, each of formula C5H8. Since X is an equimolar mixture of two liquids, each of these alkynes is present in equimolar amounts. Therefore, each component in X is C5H8 (an alkyne). But wait, if X is a mixture of two different alkynes, each of which upon hydrogenation gives Z (C5H10), then each alkyne must have the formula C5H8. But an alkyne has the general formula CnH2n-2. So for C5H8: 2n-2 =8 → 2n=10 → n=5. So yes, each alkyne is C5H8. Therefore, X is a mixture of two different alkynes, each with formula C5H8. But the question says "an equimolar mixture X of two liquids". So X is a mixture of two different alkynes, each with the formula C5H8. Therefore, each component in X is C5H8. Wait, but that would mean that X is a mixture of two different isomers of C5H8? But C5H8 can have different isomers, such as cis and trans pent-2-ynes. However, the problem states that X is an equimolar mixture of two liquids. So if X consists of two isomers of the same compound, then the total number of hydrogens in each molecule would be 8 (since each molecule is C5H8). Therefore, each liquid in X has 8 hydrogens per molecule. Since there are two liquids in X, the total number of hydrogen atoms in two liquids would be 8 + 8 = 16. Therefore, the answer would be 16, which is option C.

Wait, but let's confirm this. If X is a mixture of two different alkynes, each with formula C5H8, then each molecule contributes 8 hydrogens. Since there are two liquids in X, each in equimolar amounts, the total number of hydrogens in the two liquids would be 8 + 8 = 16. Therefore, the answer is 16, which is option C.

But let's make sure that this fits with the rest of the problem. X is a mixture of two liquids (two different alkynes, each C5H8). When X is hydrogenated, each alkyne becomes cyclopentane (C5H10). Then, Y is the result of the disproportionation of X. So X is two alkynes, which upon heating with Pt, undergo disproportionation. But how does that work? Disproportionation typically involves a single molecule splitting into two parts. But X is a mixture of two different molecules. Wait, maybe the two different alkynes in X undergo disproportionation to form two different products. For example, one alkyne splits into two molecules of one product, and the other alkyne splits into two of another product. But the problem states that Y is an equimolar mixture of two other liquids. So each alkyne in X splits into two parts, each part becoming a component in Y. Therefore, if X has two different alkynes, each splitting into two parts, Y would have four components. But the problem states that Y is an equimolar mixture of two liquids. Therefore, perhaps each alkyne splits into the same two products. For example, each alkyne in X (C5H8) splits into two molecules of the same compound. But that would mean Y has two components, each coming from the same alkyne in X. Wait, but since X has two different alkynes, each splitting into two products, then Y would have four components. But the problem states that Y is an equimolar mixture of two liquids. Therefore, perhaps each alkyne in X splits into two molecules of the same product. For example, each alkyne in X (C5H8) splits into two molecules of cyclopentane (C5H10). Therefore, each alkyne in X (C5H8) would split into two cyclopentane molecules. Since X is a mixture of two different alkynes, each in equimolar amounts, then each alkyne would split into two cyclopentane molecules. Therefore, Y would consist of four cyclopentane molecules, but the problem says Y is an equimolar mixture of two liquids. Therefore, perhaps each alkyne in X splits into two parts, each part being the same molecule. For example, if an alkyne splits into two alkenes, which then become two different products. Wait, but the problem states that Y has two liquids. Therefore, perhaps the two different alkynes in X split into two different products. For example, each alkyne in X splits into two different products, but since there are two alkynes, each splitting into two products, then Y would have four products. But the problem states that Y is an equimolar mixture of two liquids. Therefore, perhaps each alkyne in X splits into two molecules of the same product, and since X has two different alkynes, Y would have two products (each from one alkyne). Therefore, each alkyne in X splits into two molecules of the same product, leading to Y having two products, each from one alkyne. For example, if one alkyne in X splits into two molecules of product A, and the other alkyne splits into two molecules of product B. Then Y would be a mixture of product A and product B. But according to the problem statement, Y is an equimolar mixture of two liquids. Therefore, each alkyne in X must split into two molecules of the same product, and since there are two alkynes, Y would have two products, each present in equimolar amounts. Therefore, each alkyne in X splits into two molecules of the same product, so Y has two products, each from one alkyne. Therefore, if each alkyne in X (C5H8) splits into two molecules of cyclopentane (C5H10), then Y would consist of two cyclopentane molecules (from each alkyne in X), but since X is equimolar, Y would have two cyclopentane molecules. Wait, but that doesn't make sense. Let me think again.

Alternatively, perhaps the two alkynes in X undergo disproportionation to form two different products. For example, one alkyne splits into two alkenes, and the other alkyne splits into one alkene and one alkyne. But this would complicate the analysis. However, the problem states that Y is an equimolar mixture of two liquids, so perhaps each alkyne in X splits into two molecules of the same product. For example, each alkyne (C5H8) splits into two cyclopentane molecules (C5H10). Therefore, if X has two different alkynes, each in equimolar amounts, then Y would have four cyclopentane molecules (two from each alkyne). But the problem states that Y is an equimolar mixture of two liquids. Therefore, perhaps each alkyne in X splits into two molecules of the same product, and since there are two different alkynes, Y would have two products, each present in equimolar amounts. Therefore, each alkyne in X splits into two molecules of a specific product, so Y is a mixture of two products (each from one alkyne), each in equimolar amounts. Therefore, each alkyne in X splits into two molecules of the same product. For example, if one alkyne splits into two molecules of product A, and the other splits into two molecules of product B, then Y is a mixture of A and B. But since the problem states that Y is an equimolar mixture of two liquids, then each product must come from each alkyne in X. Therefore, each alkyne in X (C5H8) splits into two molecules of the same product. For example, each alkyne splits into two cyclopentane molecules. Therefore, if X has two different alkynes, each in equimolar amounts, then Y would have four cyclopentane molecules (two from each alkyne). But the problem states that Y is a mixture of two liquids, which would mean two cyclopentane molecules and another product. This is getting confusing. Maybe I need to approach this differently.

Let me summarize what we have so far:

- Z is cyclopentane (C5H10), mass fraction of H is ~14.28%.
- Y is a mixture of Z (C5H10) and another compound. When Y is hydrogenated, it becomes Z. The other compound in Y must hydrogenate to Z. Therefore, that other compound must be a cycloalkyne (C5H8), which upon hydrogenation becomes C5H10 (Z).
- X is a mixture of two liquids that decolorize bromine. These liquids are alkenes or alkynes. Upon hydrogenation, they become Z (C5H10). Therefore, each liquid in X must be an alkyne with formula C5H8 (since hydrogenation of C5H8 (alkyne) gives C5H10 (alkane)).
- Therefore, X is a mixture of two alkynes, each C5H8. Since they are in equimolar amounts, each molecule contributes 8 hydrogens. Therefore, two liquids in X contribute 8 + 8 = 16 hydrogens. Therefore, the answer is 16, which is option C.

But let me check if this fits with the disproportionation reaction. If X is a mixture of two different alkynes (C5H8), then upon heating with Pt, each alkyne undergoes disproportionation. Disproportionation of an alkyne would typically produce two alkenes. For example, 2 HC≡C-CH2-CH2-CH3 → 2 HC≡C-CH2-CH2-CH3 → but that doesn't make sense. Wait, more accurately, the general disproportionation reaction for an alkyne is:

2 R-C≡C-R → R-C≡C-R + 2 R-CH2-R (alkene?)

Wait, no. Let's take a specific example. Take 2-pentyne (CH3CH2C≡CCH2CH3). Upon heating with Pt, it undergoes disproportionation. The typical product of the disproportionation of an alkyne is two alkenes. For example, the alkyne breaks into two alkenes. The exact products depend on the structure. For example:

2 HC≡C-CH2-CH2-CH3 → 2 CH2=CH-CH2-CH2-CH3 (if it breaks into two molecules of 1-pentene). But this would require the alkyne to be symmetric. If the alkyne is asymmetric, the products would be a mixture. However, since X is an equimolar mixture of two different alkynes, each alkyne would split into two alkenes. Therefore, Y would consist of four alkenes (two from each alkyne). But the problem states that Y is an equimolar mixture of two liquids. Therefore, perhaps each alkyne in X splits into two identical alkenes, and since there are two different alkynes, Y would have four alkenes. But the problem states that Y is a mixture of two liquids, so this contradicts. Therefore, perhaps the two different alkynes in X split into two different alkenes each. For example, each alkyne in X splits into two alkenes, but since there are two different alkynes, Y would have four alkenes. But the problem states that Y is a mixture of two liquids, so perhaps each alkyne splits into two alkenes, but the two alkynes split into the same two alkenes. For example, both alkynes in X split into the same two alkenes. Therefore, Y would be a mixture of two alkenes, each present in equimolar amounts. Therefore, each alkyne in X splits into two alkenes, but the two different alkynes split into the same two alkenes. For example, each alkyne in X splits into Alkene A and Alkene B. Therefore, Y would have Alkene A and Alkene B, each present in equimolar amounts. Therefore, X, which is a mixture of two alkynes, each splitting into two alkenes, leads to Y being a mixture of two alkenes. Therefore, when X is hydrogenated, each alkyne in X becomes cyclopentane (Z). When Y is hydrogenated, each alkene in Y becomes cyclopentane (Z). Therefore, the problem holds.

Therefore, the total number of hydrogen atoms in two liquids of X is 8 + 8 = 16, which is option C.
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