when a 8.77g mixture of methane, and ethane is burned in oxygen at constant pressure, 476.6kJ of heat is liberated. What is the percentage by mass of CH4 in the mixture? The standard enthalpies of combustion for CH4 and C2H6 are -890.3kJ/mol and -1569.7kJ/mol, respectively.
To find the percentage by mass of CH4 in the mixture, we need to calculate the moles of CH4 and C2H6 in the given mixture. Then we can find the mass percentage using the formula:
Percentage by mass = (Mass of CH4 / Total mass of mixture) * 100
First, let's find the moles of CH4 and C2H6 in the mixture.
1. Calculate the moles of CH4:
Given: Mass of mixture = 8.77g
Molar mass of CH4 = 12.01g/mol + 4(1.01g/mol) = 16.05g/mol
Number of moles of CH4 = Mass of CH4 / Molar mass of CH4 = 8.77g / 16.05g/mol
2. Calculate the moles of C2H6:
Number of moles of C2H6 = (Total enthalpy change of combustion) / (Enthalpy change of combustion per mole)
Given: Total enthalpy change of combustion = 476.6kJ
Enthalpy change of combustion per mole of CH4 = -890.3kJ/mol
Enthalpy change of combustion per mole of C2H6 = -1569.7kJ/mol
Calculate the ratio of moles of CH4 to moles of C2H6 using the enthalpy change of combustion per mole of each compound:
(476.6kJ / -890.3kJ/mol) CH4 : (476.6kJ / -1569.7kJ/mol) C2H6
Now, we can convert the moles of CH4 and C2H6 to mass using their respective molar masses.
3. Calculate the mass of CH4 and C2H6:
Mass of CH4 = Moles of CH4 * Molar mass of CH4
Mass of C2H6 = Moles of C2H6 * Molar mass of C2H6
4. Calculate the percentage by mass of CH4:
Percentage by mass of CH4 = (Mass of CH4 / Total mass of mixture) * 100
Now you can substitute the values into the equations to find the percentage by mass of CH4 in the mixture.