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When 0.5000 grams of an unknown hydrocarbon, [tex]C_xH_y[/tex], is completely combusted with excess oxygen, 1.037 L of [tex]CO_2[/tex] gas is produced at 98.3 °C and 1.000 atm.

What is the empirical formula of the hydrocarbon?

(Note: [tex]R = 0.08206 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}[/tex])

Answer :

Answer: C₃H₈

Explanation:

From PV = nRT

Moles of CO2 = PV / RT =(1 x 1.037)/(0.08206 x ( 273+98.3)) = 0.0340 moles of CO2

CxHy + (x + (y/2))O₂ ----> xCO₂ + yH₂O

there is 1 mole of C in each mole of CO2 so moles of C in CO₂ = 0.0340 moles

mass of C in CO₂ = 0.0340 x 12 = 0.41 g

This means mass of C in the hydrocarbon = 0.41g

so mass of H in the hydrocarbon = 0.50 - 0.41= 0.09 g

moles of H in the hydrocarbon = mass/molar mass = 0.09/1 = 0.09 moles

molar ratio of C:H = 0.034 : 0.09 = 1 :2.67

or 3 :8

empirical formula is C3H8

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Rewritten by : Barada

Final answer:

To find the empirical formula of the hydrocarbon, calculate the moles of carbon dioxide produced using the ideal gas law and the moles of carbon and hydrogen in the hydrocarbon. The empirical formula is C12H1.

Explanation:

In order to determine the empirical formula of the hydrocarbon, we need to find the mole ratio of carbon to hydrogen in the compound. To do this, we first calculate the moles of carbon dioxide (CO2) produced using the ideal gas law:



n = (PV)/(RT) = (1.000 atm)(1.037 L)/(0.08206 L.atm/mol.K)(98.3 + 273.15 K) = 0.0443 mol



Since the combustion of 1 mole of hydrocarbon produces 1 mole of CO2, we can conclude that the moles of hydrocarbon consumed is also 0.0443 mol. Next, we calculate the moles of carbon and hydrogen in the hydrocarbon:



moles of carbon = (mass of carbon in hydrocarbon) / (molar mass of carbon) = (12.01 g/mol)(0.5000 g) / (1 g) = 6.003 mol



moles of hydrogen = (mass of hydrogen in hydrocarbon) / (molar mass of hydrogen) = (1.008 g/mol)(0.5000 g) / (1 g) = 0.5008 mol



The empirical formula of the hydrocarbon is then C6H0.5008. We can simplify this ratio by multiplying all the subscripts by 2 (the smallest whole number ratio) to get the empirical formula: C12H1.

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