Questions: element mass % carbon 17.9 % hydrogen 2.26 % chlorine 79.7 % Write the empirical chemical formula of X.

Solution Steps

Assume we have 100 grams of the compound. This simplifies the mass percentages directly to grams:

• Carbon: \(17.9 \, \text{g}\)
• Hydrogen: \(2.26 \, \text{g}\)
• Chlorine: \(79.7 \, \text{g}\)

Use the molar masses of each element to convert grams to moles:

• Molar mass of Carbon (C): \(12.01 \, \text{g/mol}\)
• Molar mass of Hydrogen (H): \(1.008 \, \text{g/mol}\)
• Molar mass of Chlorine (Cl): \(35.45 \, \text{g/mol}\)

\[ \text{Moles of Carbon} = \frac{17.9 \, \text{g}}{12.01 \, \text{g/mol}} = 1.4913 \, \text{mol} \]

\[ \text{Moles of Hydrogen} = \frac{2.26 \, \text{g}}{1.008 \, \text{g/mol}} = 2.2421 \, \text{mol} \]

\[ \text{Moles of Chlorine} = \frac{79.7 \, \text{g}}{35.45 \, \text{g/mol}} = 2.2486 \, \text{mol} \]

Divide each mole value by the smallest number of moles calculated:

\[ \text{Ratio for Carbon} = \frac{1.4913}{1.4913} = 1 \]

\[ \text{Ratio for Hydrogen} = \frac{2.2421}{1.4913} = 1.504 \]

\[ \text{Ratio for Chlorine} = \frac{2.2486}{1.4913} = 1.508 \]

Since the ratios for Hydrogen and Chlorine are close to 1.5, we multiply all ratios by 2 to get whole numbers:

\[ \text{Carbon} = 1 \times 2 = 2 \]

\[ \text{Hydrogen} = 1.504 \times 2 \approx 3 \]

\[ \text{Chlorine} = 1.508 \times 2 \approx 3 \]

Final Answer