Question

How many molecules are present in \(15.43 \mathrm{~g}\) of butyl alcohol, \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}\) ?

Short answer

The number of molecules in 15.43 g of butyl alcohol is \(1.25 \times 10^{23}\) molecules.

Step-by-step solution

Find out the molar mass of butyl alcohol

Add up the atomic masses of all the atoms in the molecule. The molar mass of carbon (C) is 12.01 g/mol, of hydrogen (H) is 1.01 g/mol, and of oxygen (O) is 16.00 g/mol. The total molecular mass of butyl alcohol (C4H9OH) then is \(4 \times 12.01 + 9 \times 1.01 + 16.00 + 1.01 = 74.14 \mathrm{~g/mol}\).

Calculate the number of moles

Use the molar mass to convert the mass of the sample into moles. The number of moles (n) is equal to the mass of the sample (m) divided by the molar mass (M). So, \(n = \frac{m}{M} = \frac{15.43 \mathrm{~g}}{74.14 \mathrm{~g/mol}} = 0.208 \mathrm{~mol}\).

Calculate the number of molecules

Use Avogadro's number (6.022 x 10^23 molecules/mol) to convert the number of moles into the number of molecules. The number of molecules is equal to the number of moles multiplied by Avogadro's number. So, \( N = n \times (\mathrm{Avogadro's~number}) = 0.208 \mathrm{~mol} \times (6.022 \times 10^{23} \mathrm{~molecules/mol}) = 1.25 \times 10^{23} \mathrm{~molecules}\).

Key concepts

Molar Mass

The molar mass is an essential concept in chemistry, particularly in stoichiometry, which deals with the quantities of substances in chemical reactions. To understand molar mass, think of it as the weight of one mole of a chemical substance. A mole is a standard scientific unit used to measure large quantities of very small entities like atoms, molecules, or other specified particles.

• In calculating the molar mass, you need to sum up the atomic masses of all the different atoms present in a given chemical formula.
• The atomic mass values are found on the periodic table and are typically measured in grams per mole (g/mol).

For example, in the case of butyl alcohol (\( ext{C}_4 ext{H}_9 ext{OH}\)), you simply add:- 4 carbon atoms each weighing 12.01 g/mol- 9 hydrogen atoms each weighing 1.01 g/mol- 1 oxygen atom weighing 16.00 g/molThe final calculated molar mass of butyl alcohol is 74.14 g/mol.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, named after Amedeo Avogadro. It plays a vital role when translating between the macroscopic amounts we can measure and the microscopic quantities that define chemical reactions.

• Avogadro's number is the number of atoms, ions, or molecules in one mole of a substance, which is approximately \(6.022 \times 10^{23}\) particles per mole.
• This means that if you have one mole of butyl alcohol, you have \(6.022 \times 10^{23}\) molecules of butyl alcohol.

Avogadro's number helps in calculating the number of molecules or atoms in a given sample when you know how many moles are present. This connection is vital for ensuring that chemical equations are balanced, following the law of conservation of mass.

Butyl Alcohol

Butyl alcohol, also known as \( ext{C}_4 ext{H}_9 ext{OH}\), is an organic compound with a specific structure and properties that make it useful in various industries. It belongs to a group of chemicals known as alcohols, characterized by the presence of hydroxyl (\(-OH\)) groups.

• Butyl alcohol has four carbon atoms, nine hydrogen atoms, and one oxygen atom in its molecular formula.
• The presence of the hydroxyl group gives it certain chemical properties, such as the ability to form hydrogen bonds.

Butyl alcohol is used in the manufacture of plastics, personal care products, and other chemical applications. Understanding its molecular composition helps when calculating how many molecules are in a given mass of the substance, especially using the concepts of molar mass and Avogadro's number as described earlier.