A certain organic substance used as a solvent in many reactions contains carbon, hydrogen, oxygen and sulphur. Weight % of hydrogen in the compound is 7.7. The weight ratio `C : O : S = 3:2:4`. What is the least possible molar mas of the compound?

Options

A. 86
B. 63
C. 94
D. 78

Answer

To find the least possible molar mass of the organic compound containing carbon (C), hydrogen (H), oxygen (O), and sulfur (S), we will follow these steps:

### Step 1: Determine the mass percentages of C, O, and S
Given that the weight percentage of hydrogen (H) in the compound is 7.7%, we can find the remaining mass percentage for carbon, oxygen, and sulfur.

- Total mass = 100 g
- Mass of H = 7.7 g
- Remaining mass = 100 g - 7.7 g = 92.3 g

The weight ratio of C:O:S is given as 3:2:4. The total parts in this ratio = 3 + 2 + 4 = 9 parts.

### Step 2: Calculate the mass percentages of C, O, and S
Using the ratio, we can find the mass percentages of C, O, and S:

- Mass of C = (3/9) * 92.3 g = 30.73 g
- Mass of O = (2/9) * 92.3 g = 20.52 g
- Mass of S = (4/9) * 92.3 g = 41.04 g

### Step 3: Create a table of mass percentages and atomic masses
Now, we will summarize the information in a table:

| Element | Mass % | Atomic Mass (g/mol) | Moles |
|---------|--------|---------------------|-------|
| C | 30.73 | 12 | 30.73/12 = 2.56 |
| H | 7.7 | 1 | 7.7/1 = 7.7 |
| O | 20.52 | 16 | 20.52/16 = 1.28 |
| S | 41.04 | 32 | 41.04/32 = 1.28 |

### Step 4: Calculate the simplest ratio of moles
Next, we will divide each mole value by the smallest number of moles calculated:

- C: 2.56 / 1.28 = 2
- H: 7.7 / 1.28 = 6
- O: 1.28 / 1.28 = 1
- S: 1.28 / 1.28 = 1

### Step 5: Write the empirical formula
From the simplest ratios, we can write the empirical formula as:
\[ \text{C}_2\text{H}_6\text{O}_1\text{S}_1 \]

### Step 6: Calculate the molar mass of the empirical formula
Now, we will calculate the molar mass of the empirical formula:
- Molar mass = (2 × 12) + (6 × 1) + (1 × 16) + (1 × 32)
- Molar mass = 24 + 6 + 16 + 32 = 78 g/mol

### Conclusion
The least possible molar mass of the compound is **78 g/mol**.

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