The so-called hydrogen economy is based on hydrogen produced from water using solar energy. the gas is then burned as a fuel: 2h2(g) + o2(g) → 2h2o(l) a primary advantage of hydrogen as a fuel is that it is nonpolluting. a major disadvantage is that it is a gas and therefore is harder to store than liquids or solids. calculate the volume of hydrogen gas at 28°c and 1.00 atm required to produce an amount of energy equivalent to that produced by the combustion of a gallon of octane (c8h18). the density of octane is 2.66 kg/gal, and its standard enthalpy of formation is −249.9 kj/mol. assume that the products of the combustion of octane are co2(g) and h2o(l).

The volume of hydrogen is 5075.9 L

Explanation:

Step 1: Data given

Temperature = 28.0 °C

Pressure = 1.00 atm

Enthalpy of formation for octane is -249.95 kJ/mol

Enthalpy of formation for CO2 is -393.5 kJ/mol

Enthalpy of formation for liquid water is -285.8 kJ/mol

The standard enthalpy of formation is −249.9 kJ/mol.

Step 2: The balanced equation

C8H18 + 12/2O2 →9H2O + 8 CO2

Step 3: Calculate ΔH° for the reaction

ΔH° = 9*(-241.8/ mol) + 8 *(-393.5 kj/mol) - 1*(-249.9 kj/mol)

ΔH° = -5074  kJ/mol

Step 4: Calculate moles octane

Moles octane = mass octane / molar mass octane

Moles octane = 2660 grams / 114.23 g/mol

Moles octane = 23.2 moles

Step 5: Calculate heat produced by combustion of 23.2 moles of octane

Heat = 23.2 moles * 5074kJ/mol

Heat = 117716.8 kJ

Step 6: Calculate moles H2

The reaction of combustion of hydrogen:

2H2(g) + O2(g) → H2O (l)

ΔH = -286 kJ/mol

To produce the same amount of energy we need:

-286*n = -117716.8

n = 411 moles of H2

Since we calculate this for 2 moles of H2 we have to divide this by 2.

n = 411/2 = 205.5 moles H2

Step 7: Calculate volume of hydrogen

p*V = n *R*T

⇒with p = the pressure of the gas = 1.00 atm

⇒with V = the volume of hydrogen gas = TO BE DETERMINED

⇒with n = the moles of hydrogen = 205.5 moles

⇒with R = the gas constant = 0.08206 L*atm/mol * K

⇒with T = the temperature = 28 °C = 301 K

V = (n*R*T) / p

V = (205.5 * 0.08206 * 301) .1.00

V = 12023 liters = 1.2 * 10^4 L

The volume of hydrogen is 5075.9 L