Combustion analysis of 0.1500 g of methyl tert-butyl ether, an octane booster used in gasoline, gave 0.3744 g of CO2 and 0.1838 g of H2O. When a flask having a volume of 1.00 L was evacuated and then filled with methyl tertbutyl ether vapor at a pressure of 100.0 kPa and a temperature of 54.8 °C, the mass of the flask increased by 3.233 g. (d) The enthalpy of combustion for methyl tert-butyl ether is ΔH° combustion = -3368.7 kJ>mol. What is its standard enthalpy of enthalpy of formation, ΔH°f?

Verified step by step guidance

1. Calculate the moles of CO2 and H2O produced in the combustion using their molar masses. For CO2, the molar mass is approximately 44.01 g/mol and for H2O, it is approximately 18.02 g/mol.
2. Use the stoichiometry of the combustion reaction of methyl tert-butyl ether (MTBE) to determine the moles of MTBE that reacted. The balanced chemical equation for the combustion of MTBE is typically C5H12O + 7.5O2 -> 5CO2 + 6H2O.
3. Calculate the molar mass of MTBE by using the increase in mass of the flask when filled with MTBE vapor. Use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
4. Calculate the enthalpy of combustion per mole of MTBE using the given ΔH° combustion and the moles of MTBE combusted.
5. Use Hess's Law to find the standard enthalpy of formation, ΔH°f, for MTBE. This involves using the enthalpies of formation for CO2 and H2O, and the enthalpy of combustion for MTBE. The equation is ΔH°f (MTBE) = ΔH° combustion (MTBE) + Σ[ΔH°f (products)] - Σ[ΔH°f (reactants)].

Key Concepts

Combustion Analysis

Combustion analysis is a technique used to determine the composition of a compound by burning it in excess oxygen and measuring the amounts of products formed, typically carbon dioxide (CO2) and water (H2O). The mass of these products allows for the calculation of the moles of carbon and hydrogen in the original compound, which is essential for determining empirical formulas and understanding the compound's combustion properties.

Enthalpy of Formation (ΔH°f)

The standard enthalpy of formation (ΔH°f) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is a crucial concept in thermodynamics, as it allows chemists to calculate the energy changes associated with chemical reactions, including combustion, and is typically expressed in kJ/mol. Understanding this concept is vital for determining the energy efficiency and environmental impact of fuels.

Enthalpy of Combustion (ΔH° combustion)

The enthalpy of combustion (ΔH° combustion) is the heat released when one mole of a substance is completely burned in oxygen under standard conditions. It is an important measure of the energy content of fuels and is typically negative, indicating that the reaction is exothermic. This value is used to assess the energy yield of fuels and is essential for calculating the standard enthalpy of formation of the compound from its combustion products.