What mass of oxygen is required to burn completely 1.oo L of a mixture that is 90 % gasoline(d= 0.782 g/mL) and 10% ethanol (d=0.789 g/mL)by volume?

To determine the mass of oxygen required to burn the gasoline and ethanol mixture completely, we need to follow a few steps:

Step 1: Calculate the total volume of the gasoline and ethanol mixture.
The total volume of the mixture is given as 1.00 L.

Step 2: Calculate the volume of gasoline and ethanol in the mixture.
Since the mixture is 90% gasoline and 10% ethanol, we can calculate the volume of each component:
- Volume of gasoline = 90% of 1.00 L = 0.90 L
- Volume of ethanol = 10% of 1.00 L = 0.10 L

Step 3: Calculate the mass of gasoline and ethanol in the mixture.
To calculate the mass, we need to use the densities of gasoline and ethanol.
- Mass of gasoline = Volume of gasoline × Density of gasoline
= 0.90 L × 0.782 g/mL
= 0.7038 g

- Mass of ethanol = Volume of ethanol × Density of ethanol
= 0.10 L × 0.789 g/mL
= 0.0789 g

Step 4: Calculate the total mass of the gasoline and ethanol mixture.
To get the total mass, we add the masses of gasoline and ethanol together.
- Total mass of the mixture = Mass of gasoline + Mass of ethanol
= 0.7038 g + 0.0789 g
= 0.7827 g

Step 5: Calculate the mass of oxygen required for complete combustion.
The balanced chemical equation for the combustion of gasoline and ethanol involves the consumption of oxygen in a specific ratio. However, since we do not have the exact composition of the gasoline and ethanol, we cannot directly determine the precise amount of oxygen required.

Instead, we can approximate the calculation by assuming the gasoline and ethanol completely combust to form carbon dioxide and water:
- Gasoline: C8H18 + 12.5O2 → 8CO2 + 9H2O
- Ethanol: C2H5OH + 3O2 → 2CO2 + 3H2O

To complete the combustion of gasoline and ethanol, we need to ensure that there is enough oxygen to react with all the carbon and hydrogen atoms. This means we need to provide at least the molar amount of oxygen required for each carbon and hydrogen atom in the gasoline and ethanol.

Given that the molar mass of oxygen is 32 g/mol, we need to determine the molar amount of carbon and hydrogen in the mixture and then calculate the corresponding mass of oxygen required.

Step 5.1: Calculate the molar amount of carbon in the mixture.
- Molar mass of carbon = atomic mass of carbon = 12.01 g/mol
- Molar amount of carbon = Mass of carbon in the mixture / Molar mass of carbon
= (Mass of gasoline × moles of carbon in gasoline) + (Mass of ethanol × moles of carbon in ethanol) / Molar mass of carbon

To calculate the moles of carbon in gasoline and ethanol, we need the molar mass and molecular formula of each substance.

The molar mass of gasoline is approximately 114.22 g/mol, and its molecular formula is C8H18.
- Moles of carbon in gasoline = (Molar mass of gasoline × number of carbon atoms) / Molar mass of carbon
= (114.22 g/mol × 8) / 12.01 g/mol

The molar mass of ethanol is approximately 46.07 g/mol, and its molecular formula is C2H5OH.
- Moles of carbon in ethanol = (Molar mass of ethanol × number of carbon atoms) / Molar mass of carbon
= (46.07 g/mol × 2) / 12.01 g/mol

Step 5.2: Calculate the molar amount of hydrogen in the mixture.
- Molar mass of hydrogen = atomic mass of hydrogen = 1.01 g/mol
- Molar amount of hydrogen = Mass of hydrogen in the mixture / Molar mass of hydrogen
= (Mass of gasoline × moles of hydrogen in gasoline) + (Mass of ethanol × moles of hydrogen in ethanol) / Molar mass of hydrogen

To calculate the moles of hydrogen in gasoline and ethanol, we need the molar mass and molecular formula of each substance.

The molar mass of gasoline is approximately 114.22 g/mol, and its molecular formula is C8H18.
- Moles of hydrogen in gasoline = (Molar mass of gasoline × number of hydrogen atoms) / Molar mass of hydrogen
= (114.22 g/mol × 18) / 1.01 g/mol

The molar mass of ethanol is approximately 46.07 g/mol, and its molecular formula is C2H5OH.
- Moles of hydrogen in ethanol = (Molar mass of ethanol × number of hydrogen atoms) / Molar mass of hydrogen
= (46.07 g/mol × 6) / 1.01 g/mol

Step 5.3: Calculate the mass of oxygen required.
The mass of oxygen required is the sum of the masses of carbon and hydrogen multiplied by the molar mass of oxygen.

- Mass of oxygen required = (Molar amount of carbon × Molar mass of oxygen) + (Molar amount of hydrogen × Molar mass of oxygen)
= (Molar amount of carbon + Molar amount of hydrogen) × Molar mass of oxygen

Considering the values calculated in the previous steps, we can substitute them into the equation to find the mass of oxygen required to burn the gasoline and ethanol mixture completely.