Hydrogen is burned in oxygen to release heat. How many grams of hydrogen gas must be burned to release enough heat to warm a 50.0 g block of iron, giving 5 mol of water?

2 H2(g) + O2(g) → 2 H2O(g) ΔH = −484 kJ
Iron has a specific heat of 0.449 J/(g·°C).

Hydrogen is burned in oxygen to release heat. How many grams of hydrogen gas must be burned to release enough heat to warm a 50.0 g block of iron, giving 5 mol of water?

2 H2(g) + O2(g) → 2 H2O(g) ΔH = −484 kJ
Iron has a specific heat of 0.449 J/(g·°C).

To determine the number of grams of hydrogen gas that must be burned to release enough heat to warm the block of iron, we can follow these steps:

Step 1: Calculate the amount of heat needed to warm the block of iron.
The formula for calculating the heat (Q) is:
Q = m * c * ΔT
where Q is the amount of heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.

In this case:
m = 50.0 g (mass of the iron block)
c = 0.449 J/(g·°C) (specific heat of iron)
ΔT = this information is missing in the question. The value of ΔT is necessary to complete this calculation.

Step 2: Calculate the heat released by burning 5 mol of water.
The balanced equation states that 2 moles of H2 are required to produce 2 moles of H2O.
Hence, 2 mol H2O is produced when 2 mol H2 is burned.

Given that ΔH = -484 kJ for this reaction, we need to understand the heat change for 1 mol of water produced.
The heat change for 2 mol of water can be calculated by multiplying it with the molar enthalpy change:
ΔH (for 2 mol H2O) = 2 * -484 kJ

Step 3: Convert kJ to J.
To ensure all units are consistent, convert the kJ value to J by multiplying by 1000:
ΔH (for 2 mol H2O) = 2 * (-484 kJ) * 1000 = -968000 J

Step 4: Convert heat (Q) to moles of hydrogen gas.
Since the reaction states that 2 mol of H2 is burned to produce the given amount of heat, we can write the molar ratio:
2 mol H2 → -968,000 J

Now, we can solve for the number of moles of H2 required to generate the heat needed to warm the iron block:
5 mol H2O → x mol H2

By using the concept of the molar ratio, we can set up a proportionality equation to solve for x:
5/2 = x/(-968000)

Solving for x:
x = (-968000 * 5) / 2

Step 5: Convert moles of hydrogen gas to grams.
The molar mass of hydrogen (H2) is approximately 2 g/mol. We can use this information to calculate the mass of hydrogen gas needed:
Mass of hydrogen gas (H2) = moles of H2 * molar mass of hydrogen

Now, plug in the value of x from the previous step (moles of H2) into the equation:
Mass of hydrogen gas (H2) = x * 2 g/mol

Calculating the value will give you the mass of hydrogen gas required to release enough heat to warm the 50.0 g block of iron.