Calculate the mass (in grams) of water vapor produced when 56.0 grams of pure hydrogen gas burn in the air. Given the information from that, calculate the mass of oxygen gas that would be needed to burn 100 grams of hydrogen gas.
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To calculate the mass of water vapor produced when hydrogen gas burns, we need to understand the chemical equation for the reaction.
The balanced equation for the combustion of hydrogen gas can be written as:
2H₂ + O₂ → 2H₂O
From this equation, we can see that for every 2 moles of hydrogen gas (H₂) that react, we obtain 2 moles of water vapor (H₂O).
To calculate the mass of water vapor produced, we can use the following steps:
Step 1: Calculate the number of moles of hydrogen gas (H₂) used.
To convert grams to moles, we need to use the molar mass of hydrogen gas, which is approximately 2.02 g/mol. So, the number of moles of hydrogen gas is given by:
moles of H₂ = mass of H₂ / molar mass of H₂
Given that the mass of hydrogen gas is 56.0 grams, we can calculate the moles of hydrogen gas:
moles of H₂ = 56.0 g / 2.02 g/mol
Step 2: Calculate the moles of water vapor (H₂O) produced.
From the balanced equation, we know that for every 2 moles of hydrogen gas, we obtain 2 moles of water vapor.
So, the moles of water vapor produced will be the same as the moles of hydrogen gas:
moles of H₂O = moles of H₂
Step 3: Calculate the mass of water vapor (H₂O) produced.
To convert moles to grams, we need to use the molar mass of water, which is approximately 18.02 g/mol.
So, the mass of water vapor produced is given by:
mass of H₂O = moles of H₂O × molar mass of H₂O
Now, let's perform these calculations:
Step 1: Calculate the moles of hydrogen gas:
moles of H₂ = 56.0 g / 2.02 g/mol = 27.72 mol (approximately)
Step 2: Calculate the moles of water vapor:
moles of H₂O = 27.72 mol
Step 3: Calculate the mass of water vapor produced:
mass of H₂O = 27.72 mol × 18.02 g/mol = 499.25 g (approximately)
Therefore, the mass of water vapor produced when 56.0 grams of hydrogen gas burns is approximately 499.25 grams.
Now, let's move on to the second part of the question, calculating the mass of oxygen gas needed to burn 100 grams of hydrogen gas.
From the balanced equation 2H₂ + O₂ → 2H₂O, we can see that the ratio of moles between hydrogen gas (H₂) and oxygen gas (O₂) is 2:1.
Step 1: Calculate the number of moles of hydrogen gas:
moles of H₂ = mass of H₂ / molar mass of H₂
Given that the mass of hydrogen gas is 100 grams:
moles of H₂ = 100 g / 2.02 g/mol
Step 2: Calculate the moles of oxygen gas:
moles of O₂ = moles of H₂ / 2
Step 3: Calculate the mass of oxygen gas needed:
mass of O₂ = moles of O₂ × molar mass of O₂
The molar mass of oxygen gas (O₂) is approximately 32.00 g/mol.
Now, let's perform these calculations:
Step 1: Calculate the moles of hydrogen gas:
moles of H₂ = 100 g / 2.02 g/mol = 49.50 mol (approximately)
Step 2: Calculate the moles of oxygen gas:
moles of O₂ = 49.50 mol / 2 = 24.75 mol (approximately)
Step 3: Calculate the mass of oxygen gas needed:
mass of O₂ = 24.75 mol × 32.00 g/mol = 792.00 g (approximately)
Therefore, to burn 100 grams of hydrogen gas, approximately 792.00 grams of oxygen gas is needed.