Problem 133 - Chemistry Matter and Change

Question

How many moles are in 100.0 g of each compound? a. dinitrogen oxide\(\left(\mathrm{N}_{2} \mathrm{O}\right)\) b. methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\)

Step-by-Step Solution

Answer

In 100.0 g of each compound, there are 2.27 moles of dinitrogen oxide (N2O) and 3.12 moles of methanol (CH3OH).

Step 1: Find the molar mass of dinitrogen oxide (N2O)

To find the molar mass of N2O, we add the molar masses of 2 nitrogen atoms and 1 oxygen atom: Molar mass of N2O = 2 * (Molar mass of N) + (Molar mass of O) The molar masses of nitrogen (N) and oxygen (O) are 14.01 g/mol and 16.00 g/mol, respectively. Therefore, Molar mass of N2O = 2 * 14.01 g/mol + 16.00 g/mol = 28.02 g/mol + 16.00 g/mol = 44.02 g/mol

Step 2: Calculate the moles of dinitrogen oxide (N2O)

Now that we have the molar mass of N2O, we can find the number of moles in 100.0 g using the formula: Moles = mass / molar mass Moles of N2O = 100.0 g / 44.02 g/mol = 2.27 mol (rounded to two decimal points)

Step 3: Find the molar mass of methanol (CH3OH)

To find the molar mass of CH3OH, we add the molar masses of 1 carbon atom, 4 hydrogen atoms, and 1 oxygen atom: Molar mass of CH3OH = (Molar mass of C) + 4 * (Molar mass of H) + (Molar mass of O) The molar masses of carbon (C) and hydrogen (H) are 12.01 g/mol and 1.01 g/mol, respectively. So, Molar mass of CH3OH = 12.01 g/mol + 4 * 1.01 g/mol + 16.00 g/mol = 12.01 g/mol + 4.04 g/mol + 16.00 g/mol = 32.05 g/mol

Step 4: Calculate the moles of methanol (CH3OH)

With the molar mass of CH3OH, we can find the number of moles in 100.0 g using the formula: Moles = mass / molar mass Moles of CH3OH = 100.0 g / 32.05 g/mol = 3.12 mol (rounded to two decimal points) In conclusion, there are 2.27 moles of dinitrogen oxide (N2O) and 3.12 moles of methanol (CH3OH) in 100.0 g of each compound.

Key Concepts

Molar Mass

The molar mass of a compound is the weight of one mole of its particles, expressed in grams per mole (g/mol). This is fundamental in chemistry for converting between mass and the number of moles. Understanding the molar mass is key when performing stoichiometry calculations. To determine the molar mass of a compound:

• Identify the elements in the compound.
• Look up the atomic masses of these elements on the periodic table.
• Multiply the atomic mass of each element by the number of atoms of that element in the molecular formula.
• Add up these values to find the total molar mass of the compound.

For instance, in dinitrogen oxide, the formula is N extsubscript{2}O. You combine the molar mass of two nitrogen atoms with a single oxygen atom to find the overall molar mass of the compound.

Dinitrogen Oxide

Dinitrogen oxide, or laughing gas, is a chemical compound with the formula N extsubscript{2}O. It consists of two nitrogen atoms and one oxygen atom. To calculate its molar mass:

• The molar mass of nitrogen (N) is 14.01 g/mol.
• The molar mass of oxygen (O) is 16.00 g/mol.
• Add twice the molar mass of nitrogen to the molar mass of oxygen.

Thus, the molar mass of N extsubscript{2}O = (2 × 14.01) + 16.00 = 44.02 g/mol. Knowing this, you can determine how many moles are in a given mass of dinitrogen oxide using the formula: Moles = mass / molar mass. For 100.0 grams, you find 2.27 moles.

Methanol

Methanol, ext{CH} extsubscript{3} ext{OH}, is a simple alcohol used as a solvent and antifreeze. It contains one carbon, four hydrogen, and one oxygen atom.

• The molar mass of carbon (C) is 12.01 g/mol.
• The molar mass of hydrogen (H) is 1.01 g/mol, and there are four H atoms in methanol.
• The molar mass of oxygen (O) is 16.00 g/mol.

Add these together to find methanol's molar mass: 12.01 + 4 × 1.01 + 16.00 = 32.05 g/mol. Once you know the molar mass, you can calculate the moles in 100.0 grams using the formula: Moles = mass / molar mass. This gives approximately 3.12 moles.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. It is rooted in the conservation of mass and the mole concept. By using balanced chemical equations:

• You can calculate how much of a product will form from given reactants.
• Or determine how much of a substance is needed to completely react with another.

The key is the conversion between mass, moles, and molecules, facilitated by molar mass. For example, when calculating moles from a given mass, you apply stoichiometry principles to ensure the correct proportions and amounts of substances. It is essential for predicting quantities in both industrial and laboratory chemical processes.