A chemical compound is found to have the following composition :
`C=19.57%,Fe=15.2%,N=22.83%,K=42.39%`
Calculate the empirical formula of the compound. What will be its molecular formula if the molecular mass of the compound is 368 ? Name the compound.

Explanation

To solve the problem of determining the empirical formula and molecular formula of the given compound, we will follow these steps:

### Step 1: Convert the percentages to grams
Assuming we have 100 grams of the compound, the composition in grams will be:
- Carbon (C) = 19.57 g
- Iron (Fe) = 15.2 g
- Nitrogen (N) = 22.83 g
- Potassium (K) = 42.39 g

### Step 2: Calculate the number of moles of each element
To find the number of moles, we will use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Using the molar masses:
- Molar mass of C = 12 g/mol
- Molar mass of Fe = 56 g/mol
- Molar mass of N = 14 g/mol
- Molar mass of K = 39 g/mol

Calculating the moles:
- Moles of C = \(\frac{19.57}{12} = 1.63\) moles
- Moles of Fe = \(\frac{15.2}{56} = 0.271\) moles
- Moles of N = \(\frac{22.83}{14} = 1.63\) moles
- Moles of K = \(\frac{42.39}{39} = 1.09\) moles

### Step 3: Find the simplest mole ratio
To find the simplest ratio, we will divide each mole value by the smallest number of moles calculated:
- Moles of C = \(\frac{1.63}{0.271} \approx 6\)
- Moles of Fe = \(\frac{0.271}{0.271} = 1\)
- Moles of N = \(\frac{1.63}{0.271} \approx 6\)
- Moles of K = \(\frac{1.09}{0.271} \approx 4\)

### Step 4: Write the empirical formula
From the simplest mole ratio, we can write the empirical formula as:
\[ \text{Empirical formula} = K_4FeC_6N_6 \]

### Step 5: Calculate the empirical formula mass
Now, we calculate the empirical formula mass:
- Mass of K = \(4 \times 39 = 156\) g/mol
- Mass of Fe = \(1 \times 56 = 56\) g/mol
- Mass of C = \(6 \times 12 = 72\) g/mol
- Mass of N = \(6 \times 14 = 84\) g/mol

Total empirical formula mass = \(156 + 56 + 72 + 84 = 368\) g/mol

### Step 6: Determine the molecular formula
Given that the molecular mass of the compound is also 368 g/mol, we can find the value of \(n\) using:
\[ n = \frac{\text{Molecular mass}}{\text{Empirical formula mass}} = \frac{368}{368} = 1 \]
Thus, the molecular formula is the same as the empirical formula:
\[ \text{Molecular formula} = K_4FeC_6N_6 \]

### Step 7: Name the compound
The compound is named potassium ferrocyanide.

### Final Answers:
- Empirical formula: \(K_4FeC_6N_6\)
- Molecular formula: \(K_4FeC_6N_6\)
- Name of the compound: Potassium ferrocyanide

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