2 H2O (l) → 2 H2 (g) + O2 (g)

What volume of water in gallons would need to be split to store the same amount of energy as found in 10.0 gallons of gasoline? (Gasoline contains 44.4 MJ/kg, or 32.0 MJ/L, and has a density of 0.72 g/mL where 1 L = 0.2641775 gal). Include your work.

John--How much have you done?

find the heat in 10 gal gasoline:

heat= 44.4MJ/kg*.72kg/liter*1liter/.264gal*10 gal

now, having that.

You need the Heat of formation for H2O, or the heat of reaction for the reaction above.
heatabove=Hfwater(in J/mole)*1mole/18grams*1kg/liter*1liter/.264gal*XXXGal
solve for xxxgal

I am so disappointed in you.

To find the volume of water that would store the same amount of energy as 10.0 gallons of gasoline, we first need to calculate the energy content of the gasoline in MJ.

Given:
Gasoline energy content: 32.0 MJ/L
Gasoline density: 0.72 g/mL
Conversion: 1 L = 0.2641775 gal

1. Convert the volume of gasoline to liters:
10.0 gallons = 10.0 x 0.2641775 L/gal
= 2.641775 L

2. Calculate the energy content of the gasoline:
Energy content = 32.0 MJ/L x 2.641775 L
= 84.5368 MJ

Now, we need to find the equivalent volume of water that would store the same amount of energy.

From the balanced chemical equation, we know that 2 moles of water (H2O) produce 2 moles of hydrogen gas (H2) and 1 mole of oxygen gas (O2).

The molar mass of water (H2O) = 2(1.00784 g/mol, for H) + 15.999 g/mol (for O) = 18.015 g/mol.

To find the moles of water, we can divide the grams of water (which equals the density of water times the volume of water) by the molar mass of water.

3. Convert the volume of water from gallons to liters:
Let's assume the density of water is 1 g/mL.
Volume of water = 10.0 gallons x 0.2641775 L/gal
= 2.641775 L

4. Calculate the mass of water:
Mass of water = density of water x volume of water
= 1 g/mL x 2.641775 L
= 2.641775 g

5. Calculate the moles of water:
Moles of water = mass of water / molar mass of water
= 2.641775 g / 18.015 g/mol
≈ 0.14666 mol

Since 2 moles of water produce 2 moles of hydrogen gas and 1 mole of oxygen gas, we can say that 0.14666 mol of water produces 0.14666 mol of hydrogen gas and 0.07333 mol of oxygen gas.

Now, we need to calculate the energy content of the hydrogen gas produced.

From the balanced chemical equation, we know that for every 2 moles of H2 produced, 1 mole of H2O is consumed. Therefore, the energy content of 2 moles of H2 is the same as the energy content of 1 mole of H2O.

6. Calculate the energy content of the hydrogen gas:
Energy content of hydrogen gas = Energy content of 1 mole of H2O
= 84.5368 MJ

Finally, we need to find the volume of water that would store the same energy as 10.0 gallons of gasoline.

Since the energy content of 1 mole of H2 is the same as the energy content of 1 mole of H2O, we can say that the energy content of 0.14666 mol of H2 is the same as the energy content of 0.14666 mol of H2O.

Now, we can calculate the volume of water:

7. Calculate the volume of water:
Volume of water = Moles of water x Molar volume of water
= 0.14666 mol x (22.4 L/mol)
≈ 3.28918 L

Finally, we can convert the volume of water from liters to gallons:

8. Convert the volume of water from liters to gallons:
Volume of water = 3.28918 L x 0.2641775 gal/L
≈ 0.86869 gallons

Therefore, approximately 0.86869 gallons of water would store the same amount of energy as 10.0 gallons of gasoline.