Question

How many atoms (or ions) of each element are in \(140.0 \mathrm{~g}\) of the following substances? (a) \(\mathrm{H}_{2}\) (c) \(\mathrm{N}_{2} \mathrm{O}_{2}\) (b) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) (d) \(\mathrm{K}_{2} \mathrm{SO}_{4}\)

Short answer

The number of atoms or ions for each substance is as follows: \n(a) 8.33e+24 hydrogen atoms \n(b) 5.12e+23 Calcium atoms, 1.02e+24 Nitrogen atoms, 3.07e+24 Oxygen atoms \n(c) 1.83e+24 Nitrogen atoms, 1.83e+24 Oxygen atoms \n(d) 9.63e+23 Potassium atoms, 4.82e+23 Sulfur atoms, 1.92e+24 Oxygen atoms.

Step-by-step solution

Calculate Molar Mass

Firstly, calculate the molar mass of each substance, which could be found through the periodic table. This gives us: \((a) \mathrm{H}_{2} = 2.02 \, g/mol\), \((b) \mathrm{Ca}( \mathrm{NO}_{3} )_{2} = 164.087 \, g/mol\), \((c) \mathrm{N}_{2}\mathrm{O}_{2} = 92.02 \, g/mol\), and \((d) \mathrm{K}_{2}\mathrm{SO}_{4} = 174.26 \, g/mol\).

Convert grams to moles

To convert grams to moles, we divide the given mass by the molar mass. Using the weights provided we get: \((a) 140.0 \, g \, / \, 2.02 \, g/mol = 69.31 \, mol\), \((b) 140.0 \, g \, / \, 164.087 \, g/mol = 0.85 \, mol\), \((c) 140.0 \, g \, / \, 92.02 \, g/mol = 1.52 \, mol\), and \((d) 140.0 \, g \, / \, 174.26 \, g/mol = 0.80 \, mol\).

Calculate number of atoms or ions

Using Avogadro's number, we determine the number of atoms or ions for each element in the substance. So in substance a there are \(2*69.31*6.022*10^{23}\) Hydrogen atoms. In substance b, there is \(0.85*6.022*10^{23}\) Ca atoms, \(0.85*2*6.022*10^{23}\) N atoms and \(0.85*6*6.022*10^{23}\) O atoms. In substance c there are \(1.52*2*6.022*10^{23}\) N atoms and \(1.52*2*6.022*10^{23}\) O atoms. Finally in substance d, there is \(0.80*2*6.022*10^{23}\) K atoms, \(0.80*6.022*10^{23}\) S atoms and \(0.80*4*6.022*10^{23}\) O atoms.

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. It is typically expressed in units of grams per mole (g/mol). Molar mass is used as a conversion factor between the amount of a substance in grams and the number of moles. Each element has a unique molar mass, which can be found on the periodic table as the atomic weight.

For compounds, the molar mass is the sum of the molar masses of all the atoms in the molecule. For instance, the molar mass of water (H₂O) is approximately 18.02 g/mol, calculated by adding together the molar masses of two hydrogen atoms (about 1.01 g/mol each) and one oxygen atom (about 16.00 g/mol).

When tackling stoichiometry calculations, it is essential to accurately determine the molar mass of the substances involved to convert between mass and moles effectively.

Avogadro's Number

Avogadro's number, designated as 6.022 x 10²³, is the number of particles in one mole of a substance. It serves as a link between the macroscopic and microscopic worlds, allowing chemists to count atoms, ions, and molecules in a given amount of material.

The concept of Avogadro's number is crucial for understanding the scale of chemical reactions and is used extensively in stoichiometry calculations. It allows us to determine the exact number of entities when we know the number of moles of a substance. For instance, one mole of carbon atoms contains exactly 6.022 x 10²³ carbon atoms, regardless of the element or compound they are a part of.

Grams to Moles Conversion

Converting grams to moles is a common practice in stoichiometry, enabling chemists to use measurable quantities to predict the outcomes of chemical reactions. The conversion relies on the substance's molar mass and is achieved by dividing the mass of the sample by its molar mass.

For example, if you have 18 grams of water, using the molar mass of 18.02 g/mol, the calculation would be \( 18 \, g \div 18.02 \, g/mol = 1 \, mol \). This means you have one mole of water, which corresponds to Avogadro's number of molecules. Such conversions form the basis for all quantitative analysis in chemistry, like determining yields in reactions or balancing chemical equations.

Chemical Formulas

Chemical formulas represent the types and numbers of atoms in a molecule. They provide essential information for stoichiometry calculations, as they determine the molar ratios in which substances react. For instance, the formula for glucose is C₆H₁₂O₆, indicating it has six carbon, twelve hydrogen, and six oxygen atoms per molecule.

In stoichiometric calculations, knowing the correct chemical formula allows us to calculate the molar mass of the substance and subsequently use this to convert between mass and moles. It helps predict the amounts of reactants needed and the products formed in chemical reactions, making it a cornerstone concept in chemistry education.