In a hydrocarbon the mass ratio of hydrogen to carbon is `1:3`. The empirical formula of the hydrocarbon is

Options

A. (a)`CH_(2)`
B. (b)`C_(2)H`
C. (c )`CH_(3)`
D. (d)`CH_(4)`

Explanation

To find the empirical formula of the hydrocarbon given the mass ratio of hydrogen to carbon as 1:3, we can follow these steps:

### Step 1: Understand the Mass Ratio
The mass ratio of hydrogen to carbon is given as 1:3. This means that for every 1 gram of hydrogen, there are 3 grams of carbon.

### Step 2: Convert Mass Ratio to Moles
To find the empirical formula, we need to convert the mass of each element to moles using their molar masses:
- Molar mass of Hydrogen (H) = 1 g/mol
- Molar mass of Carbon (C) = 12 g/mol

Using the mass ratio:
- Mass of H = 1 g
- Mass of C = 3 g

Now, we convert these masses to moles:
- Moles of H = Mass of H / Molar mass of H = 1 g / 1 g/mol = 1 mol
- Moles of C = Mass of C / Molar mass of C = 3 g / 12 g/mol = 0.25 mol

### Step 3: Find the Simplest Whole Number Ratio
Now we have:
- Moles of H = 1 mol
- Moles of C = 0.25 mol

To find the simplest whole number ratio, we divide both by the smallest number of moles:
- Ratio of H = 1 mol / 0.25 mol = 4
- Ratio of C = 0.25 mol / 0.25 mol = 1

### Step 4: Write the Empirical Formula
The ratio of hydrogen to carbon is 4:1, which means the empirical formula of the hydrocarbon is:
- C1H4 or simply CH4.

### Final Answer
The empirical formula of the hydrocarbon is **CH4**.

---