To determine the number of moles of water that can be produced from 100 grams of hydrogen, we first need to understand the concept of a mole in chemistry. A mole represents a certain number of particles, atoms, or molecules of a substance. Specifically, one mole contains 6.022 x 10^23 particles, which is known as Avogadro’s number.
Quick Answer
100 grams of hydrogen gas contains 6.644 moles of H2 molecules. When burned with oxygen, each mole of H2 produces one mole of H2O. Therefore, 100 grams of hydrogen gas can produce 6.644 moles of water.
Defining a Mole
The mole is a unit that allows us to convert between the mass of a substance and the number of particles or molecules of that substance. For any pure substance, one mole contains the same number of particles, atoms, or molecules. This number – 6.022 x 10^23 – was determined experimentally by chemist Amedeo Avogadro.
For example, one mole of carbon contains 6.022 x 10^23 carbon atoms. One mole of water contains 6.022 x 10^23 water molecules. One mole of sodium contains 6.022 x 10^23 sodium atoms. And one mole of hydrogen gas contains 6.022 x 10^23 H2 molecules.
Molar Mass
Each element has a molar mass, which is the mass in grams of one mole of that element. For example:
- Hydrogen (H): 1.0079 g/mol
- Oxygen (O): 15.9994 g/mol
- Carbon (C): 12.0107 g/mol
For compounds, the molar mass is simply the sum of the molar masses of the elements in the compound. For example:
- Water (H2O): (2 x 1.0079 g/mol) + 15.9994 g/mol = 18.0153 g/mol
- Carbon dioxide (CO2): 12.0107 g/mol + (2 x 15.9994 g/mol) = 44.0095 g/mol
Moles from Grams
Using the molar mass, we can convert between mass and moles of a substance via a simple ratio:
Moles = Mass (g) / Molar mass (g/mol)
For example, to find the number of moles in 18.0153 grams of water:
Moles H2O = 18.0153 g / 18.0153 g/mol = 1 mole
So 18.0153 grams of water is equal to 1 mole of H2O molecules.
Finding Moles of Hydrogen
Now we can apply this information to find the number of moles of hydrogen in 100 grams of H2 gas. The molar mass of H2 is 2 x 1.0079 g/mol = 2.0158 g/mol.
Using the formula:
Moles H2 = Mass (g) / Molar mass (g/mol)
Moles H2 = 100 g / 2.0158 g/mol = 49.48 moles
So 100 grams of hydrogen gas contains 49.48 moles of H2 molecules.
Moles of Water from Hydrogen
When hydrogen gas undergoes combustion with oxygen, each H2 molecule reacts with an O2 molecule to form 2 H2O molecules.
This means each mole of H2 will produce 2 moles of H2O in the reaction.
Since we calculated that 100 g of hydrogen contains 49.48 moles H2, this amount of hydrogen will produce 49.48 x 2 = 98.96 moles of H2O when burned.
Rounding to the nearest hundredth, 100 grams of hydrogen gas will produce 98.96 moles of water.
Conclusion
By defining a mole, determining the molar mass of hydrogen, and using stoichiometry of the combustion reaction, we calculated the following:
- 100 g H2 contains 49.48 moles of H2
- Each mole of H2 produces 2 moles of H2O when burned
- Therefore, 100 g of hydrogen will produce 98.96 moles of water
In summary, given 100 grams of hydrogen gas, the number of moles of water that can be produced is 98.96 moles.
Detailed Explanation and Sample Calculation
Here is a more detailed step-by-step explanation and sample calculation to determine the number of moles of water produced from 100 grams of hydrogen:
- Define a mole: 1 mole = 6.022 x 10^23 particles (Avogadro’s number)
- Find the molar mass of hydrogen gas (H2):
- Mass of 1 H atom: 1.0079 g/mol
- Mass of 1 H2 molecule = 2(1.0079 g/mol) = 2.0158 g/mol
- Use the formula: Moles = Mass (g) / Molar mass (g/mol)
- Sample calculation:
- Mass of hydrogen given: 100 g
- Molar mass of H2: 2.0158 g/mol
- Moles H2 = Mass (g) / Molar mass (g/mol)
- Moles H2 = 100 g / 2.0158 g/mol
- Moles H2 = 49.48 moles
- 1 mole of H2 reacts with 1 mole of O2 to form 2 moles of H2O
- 49.48 moles H2 will produce 49.48 x 2 = 98.96 moles H2O
Therefore, given 100 grams of hydrogen gas (H2), it contains 49.48 moles of H2 molecules. When reacted with oxygen, this amount of hydrogen can produce 98.96 moles of water (H2O).
Visualizing the Data
Here is a table summarizing the data from the sample calculation:
| Starting hydrogen | Moles of H2 | Moles of H2O produced |
|---|---|---|
| 100 g | 49.48 | 98.96 |
This table shows clearly that starting with 100 grams of hydrogen gas (H2), which is equal to 49.48 moles of H2, we can produce 98.96 moles of water (H2O) by burning the hydrogen.
Applications
Understanding mole conversions is important for many applications in chemistry and stoichiometry. Here are some examples:
- Chemical reactions: Moles allow chemists to determine the amount of product that can be produced from a given amount of reactant. This is useful in both laboratory and industrial settings.
- Solution concentration: Molarity measures the number of moles of solute dissolved per liter of solution. Moles are essential for calculating concentration.
- Gas laws: The ideal gas law relates the moles of a gas to its pressure, volume, and temperature. Moles are key for applications involving gases.
- Titration: Titration calculations rely on knowing the moles of analyte and titrant. Endpoints are determined based on stoichiometric mole ratios.
- Nuclear physics: The concept of a mole is applied to atoms undergoing nuclear changes. Isotope mass and decays are quantified in terms of moles.
In summary, being able to interconvert between mass, moles, and number of particles is hugely useful across many quantitative sciences.
Common Mistakes
Some common mistakes when calculating moles include:
- Forgetting to convert mass in grams to moles using molar mass
- Using the molar mass of the wrong substance in the calculation
- Mixing up molar mass and molecular mass
- Incorrectly calculating the molar mass for a compound
- Not accounting for stoichiometric coefficients when relating moles of reactants to products
- Confusing moles, mass, and number of particles
To avoid these errors, it’s important to:
- Always start with the given mass and convert to moles using molar mass
- Check that you are using the molar mass of the correct substance
- Understand the conceptual difference between molar and molecular mass
- Double check the calculation for a compound’s molar mass
- Carefully account for stoichiometry in relating moles of reactants and products
- Keep track of units and understand the difference between mass, moles, and particles
Careful unit analysis and dimensional analysis can help avoid common mole calculation mistakes.
Solving Related Problems
Let’s practice applying these mole concepts to some related example problems:
Problem 1
How many moles of oxygen gas are required to react completely with 12.5 grams of hydrogen gas?
Solution:
- Convert mass of H2 to moles using molar mass:
- 12.5 g H2 * (1 mole H2 / 2.0158 g H2) = 6.207 moles H2
- Use stoichiometric ratio: 1 mole O2 reacts with 1 mole H2
- Therefore, 6.207 moles H2 requires 6.207 moles O2
Answer: 6.207 moles O2 are required
Problem 2
What mass of water is produced from 0.75 moles of hydrogen gas reacting with excess oxygen?
Solution:
- 0.75 moles H2 will produce 0.75 * 2 = 1.5 moles H2O (from stoichiometry)
- Use molar mass: 1 mole H2O has a mass of 18.0153 g
- 1.5 moles H2O * (18.0153 g/mol) = 27.023 g H2O
Answer: 0.75 moles H2 will produce 27.023 g H2O when burned in excess oxygen
Practice Problems
Here are some additional practice problems to test your understanding of mole calculations involving hydrogen and water:
- Convert 75 grams of H2 to moles
- How many molecules are present in 0.5 moles of H2O?
- If 25 grams of hydrogen are burned in oxygen, what volume of water vapor at STP is produced? (Take STP as 0°C and 1 atm)
- How many moles of oxygen are needed to react with 10 moles of H2?
- How many grams of H2 are needed to produce 100 grams of water?
Take time to work through these problems carefully using the concepts we’ve discussed. Having mastery of mole conversions involving hydrogen, oxygen, and water is essential foundational knowledge in chemistry and stoichiometry.
Conclusion
In conclusion, we have demonstrated that:
- A mole represents 6.022 x 10^23 particles and allows interconversion between mass and number of particles.
- The molar mass of H2 is 2.0158 g/mol.
- 100 g H2 contains 49.48 moles H2 based on molar mass calculation.
- When burned, 1 mole H2 produces 2 moles H2O according to chemical stoichiometry.
- Therefore, 100 g of H2 can produce 98.96 moles of H2O by combustion.
Mastering mole calculations involving mass, molar mass, and balanced chemical equations is essential for success in stoichiometry, solution concentration, gas laws, titrations, and many other areas of chemistry. The concepts and examples provided here should provide a strong basis for being able to determine the amount of product that can be obtained from a given reactant.
