Consider the following reaction: $$ 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-572 \mathrm{~kJ} $$ a. How much heat is evolved for the production of \(1.00 \mathrm{~mol}\) \(\mathrm{H}_{2} \mathrm{O}(l) ?\) b. How much heat is evolved when \(4.03 \mathrm{~g}\) hydrogen is reacted with excess oxygen? c. How much heat is evolved when \(186 \mathrm{~g}\) oxygen is reacted with excess hydrogen? d. The total volume of hydrogen gas needed to fill the Hindenburg was \(2.0 \times 10^{8} \mathrm{~L}\) at \(1.0 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\). How much heat was evolved when the Hindenburg exploded, assuming all of the hydrogen reacted?

Step by step solution

01

Use stoichiometry to find the moles of H2O formed

Since the balanced chemical equation shows that 2 moles of H2 react with 1 mole of O2 to form 2 moles of H2O, it means that for the production of 1 mole of H2O, the reaction consumes 1 mole of H2 and 0.5 moles of O2.

02

Calculate heat evolved

As the enthalpy change given (-572 kJ) is for the reaction of 2 moles of H2 with 1 mole of O2, we need to find the enthalpy change for the formation of 1 mole of H2O. Enthalpy change for 1 mol H2O = \(\frac{-572\,\mathrm{kJ}}{2}\) = \( -286\,\mathrm{kJ}\) Answer: The heat evolved for the production of 1.00 mol H2O is -286 kJ. #b. Heat evolved for 4.03 g of hydrogen reacting#

03

Convert grams to moles

To find the moles of hydrogen gas, we use the molar mass of hydrogen, which is 2.016 g/mol. Moles of H2 = \(\frac{4.03\,\mathrm{g}}{2.016\,\mathrm{g/mol}} \approx 2.00\,\mathrm{mol}\)

04

Calculate heat evolved

Since 2 moles of H2 react with 1 mole of O2 to produce 2 moles of H2O and release -572 kJ, for the reaction of 2 moles of hydrogen gas, the heat evolved will be -572 kJ. Answer: The heat evolved when 4.03 g hydrogen is reacted with excess oxygen is -572 kJ. #c. Heat evolved for 186 g of oxygen reacting#

05

Convert grams to moles

To find the moles of oxygen gas, we use the molar mass of oxygen, which is 32.00 g/mol. Moles of O2 = \(\frac{186\,\mathrm{g}}{32.00\,\mathrm{g/mol}} = 5.8125\,\mathrm{mol}\)

06

Calculate heat evolved

From the balanced chemical equation, 1 mole of O2 reacts with 2 moles of H2 to produce 2 moles of H2O and release -572 kJ of heat. Therefore, for the reaction of 5.8125 moles of oxygen gas: Heat evolved = \((5.8125\,\mathrm{mol\,O_{2}}) \times (-572\,\mathrm{kJ/mol\,O_{2}}) = -3325.25\,\mathrm{kJ}\) Answer: The heat evolved when 186 g oxygen is reacted with excess hydrogen is -3325.25 kJ. #d. Heat evolved for the explosion of the Hindenburg#

07

Determine moles of hydrogen gas

We are given the volume, pressure, and temperature of hydrogen gas in the Hindenburg. We will use the ideal gas law to find the moles of hydrogen gas: PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin. Rearrange the equation to solve for n: n = \(\frac{PV}{RT}\) Given that P = 1.0 atm, V = \(2.0\times10^{8}\,\mathrm{L}\), R = 0.0821 \(L\cdot atm\,K^{-1}\ mol^{-1}\), and T = 298 K (25 degrees Celsius converted to Kelvin): n = \(\frac{(1.0\,\mathrm{atm})(2.0\times10^{8}\,\mathrm{L})}{(0.0821\,\mathrm{L\,atm\,K^{-1}\,mol^{-1}})(298\,\mathrm{K})} = 8.15\times10^{6}\,\mathrm{mol}\) The Hindenburg contains 8.15 x 10^6 moles of hydrogen.

08

Calculate heat evolved

Since the chemical equation shows that 2 moles of H2 react with 1 mole of O2 to produce 2 moles of H2O and release -572 kJ of heat, we can calculate the heat evolved in the explosion by: Heat evolved = \((8.15\times10^{6}\,\mathrm{mol\,H_{2}}) \times \frac{-572\,\mathrm{kJ}}{2\,\mathrm{mol\,H_{2}}} = -2.33\times10^{9}\,\mathrm{kJ}\) Answer: The heat evolved when the Hindenburg exploded, assuming all of the hydrogen reacted, was approximately -2.33 x 10^9 kJ.

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