D-mannose is epimeric wtih D-glucose at `C_2`. Which of the following structure represents `beta` - D - mannopyranose?

Options

A.
B.
C.
D.

Answer

To determine which structure represents β-D-mannopyranose, we need to follow these steps:

### Step 1: Understand the Structure of D-Mannose
D-Mannose is an aldohexose sugar that has the following structure:

- It has six carbon atoms (C1 to C6).
- The hydroxyl groups (OH) are attached to the carbon atoms, with the configuration being specific to D-mannose.

### Step 2: Identify the Epimeric Relationship
D-Mannose is an epimer of D-Glucose at C2. This means that the configuration (the arrangement of atoms) at the second carbon (C2) is different between D-mannose and D-glucose:

- In D-mannose, the hydroxyl group (OH) at C2 is on the left side in the Fischer projection.
- In D-glucose, the hydroxyl group at C2 is on the right side in the Fischer projection.

### Step 3: Draw the Fischer Projection of D-Mannose
The Fischer projection of D-mannose can be drawn as follows:

```
CHO
|
H-C-OH
|
HO-C-H
|
H-C-OH
|
CH2OH
```

### Step 4: Convert to the Pyranose Form
To convert D-mannose into its cyclic form (pyranose), we need to form a six-membered ring:

1. The carbonyl carbon (C1) reacts with the hydroxyl group on C5.
2. This forms a ring structure with one oxygen atom and five carbon atoms.

### Step 5: Determine the Anomeric Configuration
In the cyclic form, the anomeric carbon is C1. For β-D-mannopyranose, the hydroxyl group on C1 must be positioned above the plane of the ring:

- If the OH group on C1 is above the ring, it is β-anomer.
- If it is below the ring, it is α-anomer.

### Step 6: Finalize the Structure of β-D-Mannopyranose
The final structure of β-D-mannopyranose in the Haworth projection looks like this:

```
O
/ \
HO-C C-H
| |
H-C-OH C-H
| |
H-C-OH CH2OH
```

### Step 7: Identify the Correct Structure from Options
Now, we need to compare the drawn structure of β-D-mannopyranose with the given options:

- Look for the structure where:
- The OH group on C1 is above the ring.
- The OH group on C2 is below the ring.

After analyzing the options, the correct structure representing β-D-mannopyranose will be the one that matches these criteria.