Consider the following reaction:

2H2 (g) + O2 (g)  2H2O (l) ΔH = -572 kJ
a. How much heat is evolved for the production of 1.00 mol H2O (l)?
b. How much heat is evolved when 4.03 g hydrogen is reacted with excess oxygen?
c. How much heat is evolved when 186 g oxygen is reacted with excess hydrogen?
d. The total volume of hydrogen gas needed to fill the Hindenburg was 2.0 x 10
8
L at 1.0 atm
and 25
o
C. How much heat was evolved when the Hindenburg exploded, assuming all of the
hydrogen reacted?

a. 572 kJ/2

b. 572 kJ/mol x (4.03/4) = ?

a. Well, if we have 1.00 mol of water, we can simply multiply it by the molar enthalpy change to find the amount of heat evolved. So, 1.00 mol H2O x -572 kJ/mol = -572 kJ. That's some pretty cool heat!

b. To find out how much heat is evolved when 4.03 g of hydrogen is reacted, we first need to determine the number of moles of hydrogen. Using the molar mass of hydrogen (1.01 g/mol), we can find that 4.03 g / 1.01 g/mol = 4.00 mol H2. Since the reaction is in a 2:1 ratio, we can divide the molar enthalpy change by 2 and then multiply it by the number of moles: -572 kJ/mol / 2 x 4.00 mol H2 = -1144 kJ. That's quite a spark!

c. Similar to the previous calculation, we first need to find the number of moles of oxygen. Using the molar mass of oxygen (32.00 g/mol), we can determine that 186 g / 32.00 g/mol = 5.81 mol O2. Again, because the reaction is in a 2:1 ratio, we can divide the molar enthalpy change by 2 and multiply it by the number of moles: -572 kJ/mol / 2 x 5.81 mol O2 = -1668 kJ. That's a lot of hot air!

d. Alright, let's calculate the amount of moles of hydrogen gas present in the Hindenburg using the ideal gas law (PV = nRT). Assuming the temperature is 25 degrees Celsius (or 298 K), the pressure is 1.0 atm, and the volume is 2.0 x 10^8 L, we can calculate the moles of hydrogen: (1.0 atm) x (2.0 x 10^8 L) / (0.0821 L.atm/mol.K x 298 K) = 8.07 x 10^6 mol H2. Now, we can multiply this by the molar enthalpy change to find the heat evolved: 8.07 x 10^6 mol H2 x -572 kJ/mol = -4.62 x 10^9 kJ. That's one explosive amount of heat! Boom!

To solve these problems, we need to use the given reaction:

2H2 (g) + O2 (g) → 2H2O (l) ΔH = -572 kJ

Let's start by calculating the moles of H2O produced in each scenario.

a. How much heat is evolved for the production of 1.00 mol of H2O (l)?

Since the reaction is balanced in stoichiometric coefficients, we can see that 2 moles of H2O are produced for every 2 moles of H2 reacted. Therefore, the amount of heat evolved is the same as the given ΔH.

So, 1.00 mol of H2O evolved -572 kJ of heat energy.

b. How much heat is evolved when 4.03 g of hydrogen is reacted with excess oxygen?

First, we need to convert the mass of hydrogen gas (H2) into moles. To do this, we'll use the molar mass of hydrogen, which is approximately 2 g/mol.

4.03 g H2 * (1 mol H2 / 2 g H2) = 2.015 mol H2

From the balanced reaction, we see that 2 moles of H2 is required to produce 2 moles of H2O and evolve -572 kJ of heat.

Since 2 moles of H2 will produce -572 kJ of heat, 2.015 moles of H2 will produce:

(-572 kJ / 2 mol H2) * 2.015 mol H2 = -576.66 kJ

Therefore, when 4.03 g of hydrogen is reacted, -576.66 kJ of heat is evolved.

c. How much heat is evolved when 186 g of oxygen is reacted with excess hydrogen?

First, convert the mass of O2 into moles. The molar mass of oxygen is approximately 32 g/mol.

186 g O2 * (1 mol O2 / 32 g O2) = 5.8125 mol O2

From the balanced reaction, we can see that 1 mole of O2 is required to produce 2 moles of H2O and evolve -572 kJ of heat.

Since 1 mole of O2 will produce -572 kJ of heat, 5.8125 moles of O2 will produce:

(-572 kJ / 1 mol O2) * 5.8125 mol O2 = -3,326.5 kJ

Therefore, when 186 g of oxygen is reacted, approximately -3,326.5 kJ of heat is evolved.

d. The total volume of hydrogen gas needed to fill the Hindenburg was 2.0 x 10^8 L at 1.0 atm and 25°C. How much heat was evolved when the Hindenburg exploded, assuming all of the hydrogen reacted?

To solve this problem, we need to calculate the number of moles of hydrogen gas (H2) present. We'll use the ideal gas law for this calculation:

PV = nRT

Given:
P = 1.0 atm
V = 2.0 x 10^8 L
T = 25°C = 25 + 273 = 298 K
R = 0.0821 L.atm/mol.K (the ideal gas constant)

Solving for n:

n = PV / RT

n = (1.0 atm) * (2.0 x 10^8 L) / (0.0821 L.atm/mol.K * 298 K)

n ≈ 8.1 x 10^6 mol H2

From the balanced reaction, we know that 2 moles of H2 is required to produce 2 moles of H2O and evolve -572 kJ of heat.

Since 2 moles of H2 will produce -572 kJ of heat, 8.1 x 10^6 moles of H2 will produce:

(-572 kJ / 2 mol H2) * (8.1 x 10^6 mol H2) = -2.31 x 10^9 kJ

Therefore, when the Hindenburg exploded, approximately -2.31 x 10^9 kJ of heat was evolved assuming all of the hydrogen reacted.

To solve these questions, we can use the concept of stoichiometry and the given equation with its associated enthalpy change.

a. To determine the amount of heat evolved for the production of 1.00 mol of H2O, we can use the stoichiometry of the reaction. From the balanced equation, we see that the coefficient of water (H2O) is 2. This means that for every 2 moles of H2O produced, -572 kJ of heat is evolved according to the given enthalpy change. Therefore, for 1.00 mol of H2O, the amount of heat evolved can be calculated using the following proportion:

(1.00 mol H2O / 2 mol H2O) = (x kJ / -572 kJ)

Solving for x, we find that x = -286 kJ. Therefore, 286 kJ of heat is evolved for the production of 1.00 mol of H2O.

b. To determine the amount of heat evolved when 4.03 g of hydrogen is reacted with excess oxygen, we need to convert the mass of hydrogen to moles. The molar mass of hydrogen (H2) is 2.02 g/mol. So, we can calculate the number of moles of hydrogen as follows:

Number of moles = (mass of hydrogen / molar mass of hydrogen)
Number of moles = (4.03 g / 2.02 g/mol) = 2.00 mol

Now, we can use the stoichiometry of the reaction to calculate the amount of heat evolved. From the balanced equation, we see that 2 moles of H2O is produced for every 2 moles of H2 reacted. Therefore, the amount of heat evolved for 2 moles of H2 is -572 kJ, according to the given enthalpy change. Using this proportionality, we can now find the amount of heat for 2.00 mol of H2:

(2.00 mol H2 / 2 mol H2) = (x kJ / -572 kJ)

Solving for x, we find that x = -572 kJ. Therefore, 572 kJ of heat is evolved when 4.03 g of hydrogen is reacted with excess oxygen.

c. To determine the amount of heat evolved when 186 g of oxygen is reacted with excess hydrogen, we need to convert the mass of oxygen to moles. The molar mass of oxygen (O2) is 32.00 g/mol. So, we can calculate the number of moles of oxygen as follows:

Number of moles = (mass of oxygen / molar mass of oxygen)
Number of moles = (186 g / 32.00 g/mol) = 5.81 mol

Using the stoichiometry of the reaction, we know that 2 moles of H2O are produced for every 1 mole of O2 reacted. Therefore, the amount of heat evolved for 5.81 moles of O2 can be calculated using the following proportion:

(5.81 mol O2 / 1 mol O2) = (x kJ / -572 kJ)

Solving for x, we find that x = -2,804 kJ. Therefore, 2,804 kJ of heat is evolved when 186 g of oxygen is reacted with excess hydrogen.

d. To determine how much heat was evolved when the Hindenburg exploded, we need to calculate the number of moles of hydrogen gas required to fill the volume given (2.0 x 10^8 L at 1.0 atm and 25°C).

Firstly, we need to convert the volume of hydrogen gas to moles using the ideal gas law equation:

PV = nRT

Where:
P = pressure (1.0 atm)
V = volume (2.0 x 10^8 L)
n = moles of gas (unknown)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (25°C + 273.15 = 298.15 K)

Rearranging the equation, we find:
n = (PV) / (RT)

n = (1.0 atm * 2.0 x 10^8 L) / (0.0821 L·atm/(mol·K) * 298.15 K) ≈ 990,564 moles

Using the stoichiometry of the reaction, we see that 2 moles of H2 reacts to produce 2 moles of H2O, and the given enthalpy change is -572 kJ for the production of 2 moles of H2O.

Therefore, the amount of heat evolved when the Hindenburg exploded can be calculated using the following proportion:

(990,564 mol H2 / 2 mol H2) = (x kJ / -572 kJ)

Solving for x, we find that x ≈ -2,800,340 kJ. Therefore, approximately 2,800,340 kJ of heat was evolved when the Hindenburg exploded, assuming all of the hydrogen reacted.