Question

Calculate the number of moles in each sample. a. \(72.5 \mathrm{~g} \mathrm{CCl}_{4}\) b. \(12.4 \mathrm{~g} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. \(25.2 \mathrm{~kg} \mathrm{C}_{2} \mathrm{H}_{2}\) d. \(12.3 \mathrm{~g}\) dinitrogen monoxide

Short answer

a. Approximately 0.471 moles of CCl4, b. Approximately 0.0362 moles of C12H22O11, c. Approximately 968.1 moles of C2H2, d. Approximately 0.2795 moles of N2O.

Step-by-step solution

Calculate the molar mass of CCl4

To find the number of moles of CCl4, start by calculating its molar mass. Carbon (C) has an atomic mass of about 12.01 g/mol, and chlorine (Cl) has an atomic mass of about 35.45 g/mol. With 1 atom of carbon and 4 atoms of chlorine in each molecule of CCl4, the molar mass is calculated as: \( 1 \times 12.01 \, \text{g/mol} + 4 \times 35.45 \, \text{g/mol} = 12.01 \, \text{g/mol} + 141.8 \, \text{g/mol} = 153.81 \, \text{g/mol} \).

Calculate moles of CCl4

Use the formula moles = mass / molar mass to calculate the number of moles of CCl4. Thus, \( \text{moles of CCl4} = \frac{72.5 \, \text{g}}{153.81 \, \text{g/mol}} \approx 0.471 \, \text{moles} \).

Calculate the molar mass of C12H22O11

For sucrose (C12H22O11), carbon (C) has a molar mass of 12.01 g/mol, hydrogen (H) has a molar mass of 1.008 g/mol, and oxygen (O) has a molar mass of 16.00 g/mol. So the molar mass is \( 12 \times 12.01 \, \text{g/mol} + 22 \times 1.008 \, \text{g/mol} + 11 \times 16.00 \, \text{g/mol} = 144.12 \, \text{g/mol} + 22.176 \, \text{g/mol} + 176.00 \, \text{g/mol} = 342.296 \, \text{g/mol} \).

Calculate moles of C12H22O11

Again, use the formula moles = mass / molar mass to calculate the moles of C12H22O11. Therefore, \( \text{moles of C12H22O11} = \frac{12.4 \, \text{g}}{342.296 \, \text{g/mol}} \approx 0.0362 \, \text{moles} \).

Convert kg to g for C2H2

Before calculating the moles of C2H2, convert the mass from kilograms to grams, because molar mass is in grams per mole. \( 25.2 \, \text{kg} = 25,200 \, \text{g} \).

Calculate the molar mass of C2H2

For acetylene (C2H2), the molar mass is \( 2 \times 12.01 \, \text{g/mol} + 2 \times 1.008 \, \text{g/mol} = 24.02 \, \text{g/mol} + 2.016 \, \text{g/mol} = 26.036 \, \text{g/mol} \).

Calculate moles of C2H2

Now, use the formula moles = mass / molar mass to find the moles of C2H2. \( \text{moles of C2H2} = \frac{25,200 \, \text{g}}{26.036 \, \text{g/mol}} \approx 968.1 \, \text{moles} \).

Calculate the molar mass of dinitrogen monoxide (N2O)

Nitrogen (N) has a molar mass of 14.01 g/mol and oxygen (O) has a molar mass of 16.00 g/mol. The molar mass of N2O is \( 2 \times 14.01 \, \text{g/mol} + 1 \times 16.00 \, \text{g/mol} = 28.02 \, \text{g/mol} + 16.00 \, \text{g/mol} = 44.02 \, \text{g/mol} \).

Calculate moles of N2O

Finally, calculate the moles of N2O using the mass and molar mass. \( \text{moles of N2O} = \frac{12.3 \, \text{g}}{44.02 \, \text{g/mol}} \approx 0.2795 \, \text{moles} \).

Key concepts

Molar Mass

Molar mass is fundamental in understanding the microscopic world of atoms and molecules in a way that we can measure and observe. It represents the mass of one mole of a given substance and is expressed in grams per mole (g/mol).

To calculate molar mass, sum the atomic masses of each element in the compound, multiplied by the number of atoms of each element present. For example, in calculating the molar mass of CCl₄, we consider the atomic masses of carbon (12.01 g/mol) and chlorine (35.45 g/mol), and since there are four chlorine atoms, their contributions are multiplied by four. The equation for the molar mass of CCl₄ becomes:
\[ 1 \times 12.01 \, \text{g/mol} + 4 \times 35.45 \, \text{g/mol} = 153.81 \, \text{g/mol} \].

Understanding molar mass is crucial when converting between grams of a substance and moles, a critical step in many chemical calculations.

Avogadro's Number

Avogadro's number, roughly \(6.022 \times 10^{23}\), is the number of atoms, ions, or molecules in one mole of a substance. This constant provides a link between the macroscopic quantities we can measure and the microscopic quantities at the atomic and molecular scale.

Let's assume you need to calculate the number of molecules in a given number of moles. You would simply multiply the number of moles by Avogadro's number. For example, if you had 0.471 moles of CCl₄, the number of molecules would be \(0.471 \times 6.022 \times 10^{23}\). It's an extensive number, but that's the scale we're working with at the molecular level.

This concept is intertwined with molar mass, as Avogadro's number of atoms of any element will have a mass in grams equal to the element's atomic mass.

Stoichiometry

Stoichiometry is like a recipe for chemists. It involves the quantitative relationships of the reactants and products in chemical reactions. Using stoichiometry, chemists can calculate the amounts of reactants needed or products formed in a reaction.

The foundational equation used in stoichiometric calculations is: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]. This equation is pivotal, as it allows the conversion from mass to moles, which is essential in comparing the quantities of different chemicals reacting according to a balanced chemical equation.

For instance, to find the moles of C₁₂H₂₂O₁₁ from the mass given, we apply stoichiometry using the molar mass calculated previously to find that \( 12.4 \, \text{g} \) corresponds to approximately 0.0362 moles of sucrose.

Chemical Formula

A chemical formula is a concise way of expressing information about the atoms that constitute a particular chemical compound. It identifies the elements present and the proportionate number of atoms of each. For example, CCl₄ shows one carbon atom bonded with four chlorine atoms.

These formulas are essential for stoichiometry calculations, as they tell us the ratios of elements and the molar mass to be calculated. When solving problems involving chemical formulas, ensure to get the atomic counts correct, as this directly impacts the mole calculations.

The chemical formula forms the bridge between the symbolic (formula) and the quantitative (moles, mass), allowing us to perform conversions and understand the composition of substances.