Question

Calculate the number of moles of the indicated substance present in each of the following samples. a. \(1.95 \times 10^{-3} \mathrm{~g}\) of lithium carbonate b. \(4.23 \mathrm{~kg}\) of calcium chloride c. \(1.23 \mathrm{mg}\) of strontium chloride d. 4.75 g of calcium sulfate e. \(96.2 \mathrm{mg}\) of nitrogen(IV) oxide f. \(12.7 \mathrm{~g}\) of mercury(I) chloride

Short answer

The moles of the given substances are as follows: a. \(2.64 \times 10^{-5} \mathrm{~mol}\) b. \(38.11 \mathrm{~mol}\) c. \(7.75 \times 10^{-6} \mathrm{~mol}\) d. \(0.0349 \mathrm{~mol}\) e. \(0.00105 \mathrm{~mol}\) f. \(0.0269 \mathrm{~mol}\)

Step-by-step solution

Convert mass to grams (if necessary)

For some substances, you'll need to convert the given mass to grams. In this exercise, you need to change the mass of calcium chloride, strontium chloride, and nitrogen(IV) oxide from kg and mg to g. a. No conversion needed b. \[4.23 \mathrm{~kg} * 1000 = 4230\mathrm{~g}\] c. \[1.23 \mathrm{~mg} * \dfrac{1}{1000} = 0.00123\mathrm{~g}\] d. No conversion needed e. \[96.2 \mathrm{~mg} * \dfrac{1}{1000} = 0.0962\mathrm{~g}\] f. No conversion needed

Calculate the molar mass of each substance

Determine the molar mass of each substance by looking up the atomic mass of each element and multiplying it by the number of atoms of that element in the molecule. a. \(Li_2CO_3\), lithium carbonate: \(2(6.94) + 12.01 + 3(16) = 73.89 \mathrm{~g/mol}\) b. \(CaCl_2\), calcium chloride: \(40.08 + 2(35.45) = 110.98 \mathrm{~g/mol}\) c. \(SrCl_2\), strontium chloride: \(87.62 + 2(35.45) = 158.52\mathrm{~g/mol}\) d. \(CaSO_4\), calcium sulfate: \(40.08 + 32.06 + 4(16) = 136.14\mathrm{~g/mol}\) e. \(N_2O_4\), nitrogen(IV) oxide: \(2(14.01) + 4(16) = 92.02\mathrm{~g/mol}\) f. \(Hg_2Cl_2\), mercury(I) chloride: \(2(200.59) + 2(35.45) = 472.08\mathrm{~g/mol}\)

Calculate the number of moles using the formula

Using the formula \(N = \dfrac{m}{M}\), calculate the number of moles for each substance: a. \(N_{Li_2CO_3} = \dfrac{1.95 \times 10^{-3}}{73.89} = 2.64 \times 10^{-5} \mathrm{~mol}\) b. \(N_{CaCl_2} = \dfrac{4230}{110.98} = 38.11 \mathrm{~mol}\) c. \(N_{SrCl_2} = \dfrac{0.00123}{158.52} = 7.75 \times 10^{-6} \mathrm{~mol}\) d. \(N_{CaSO_4} = \dfrac{4.75}{136.14} = 0.0349 \mathrm{~mol}\) e. \(N_{N_2O_4} = \dfrac{0.0962}{92.02} = 0.00105 \mathrm{~mol}\) f. \(N_{Hg_2Cl_2} = \dfrac{12.7}{472.08} = 0.0269 \mathrm{~mol}\)

Key concepts

Understanding Molar Mass

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance. A mole is a unit in chemistry that signifies a specific number of particles, usually atoms or molecules. This number is known as Avogadro's number, which is approximately 6.022 x 10²³.

The molar mass is usually expressed in grams per mole (g/mol) and can be found by summing the atomic masses of all the atoms in a molecule. For instance, water (H₂O) has a molar mass of approximately 18 g/mol because it has two hydrogen atoms (each with an atomic mass of 1 g/mol) and one oxygen atom (with an atomic mass of 16 g/mol).

To calculate the molar mass, simply look up the atomic masses on the periodic table and add them up according to the formula of the substance. For instance, calcium chloride (CaCl₂) has a molar mass of 40.08 g/mol for calcium and 35.45 g/mol for each chlorine atom, leading to a molar mass of 40.08 + (2 x 35.45) = 110.98 g/mol.

Chemical Quantities and the Mole

Chemical quantities in chemistry often refer to the amount of substance present in terms of moles. The mole is the bridge between the microscopic world of atoms and the macroscopic world we observe. Since counting individual atoms is impractical, the concept of the mole allows chemists to work with quantities that can be measured in the lab.

To move from the mass of a sample to the number of moles it contains, we use the molar mass as a conversion factor. The process involves dividing the mass of the sample by its molar mass. This calculation is crucial in chemistry, as it enables scientists to measure and react precise quantities of various substances for reactions, based on the balanced equation – this refers to stoichiometry, which we'll explore next.

Remember, accurate chemical measurements are essential for experiments' success, so understanding the mole concept and its relation to molar mass is key.

Stoichiometry: The Arithmetic of Chemistry

Stoichiometry is the area of chemistry that pertains to the calculation of reactants and products in chemical reactions. It is based on the conservation of mass and the concept of the mole. Understanding stoichiometry can help predict the amount of product formed from given reactants or the amount of reactant needed to create a certain amount of product.

Stoichiometry relies on balanced chemical equations because they show the ratio in which substances react. For example, if the equation states that two moles of hydrogen react with one mole of oxygen to form two moles of water, then you can predict that starting with 4 moles of hydrogen will produce 4 moles of water, assuming you have sufficient oxygen.

Executing stoichiometric calculations involves a clear grasp of molar mass and chemical quantities, as seen in our textbook exercise. Always ensure the chemical equation is balanced before calculating the moles of each substance. The balance in the equation reflects the conservation of mass and allows for the precise calculation of the involved substances.