Question

Using the average atomic masses given inside the front cover of the text, calculate the mass in grams of each of the following samples. a. 5.0 mol of nitric acid b. 0.000305 mol of mercury c. \(2.31 \times 10^{-5}\) mol of potassium chromate d. 10.5 mol of aluminum chloride e. \(4.9 \times 10^{4}\) mol of sulfur hexafluoride f. 125 mol of ammonia g. 0.01205 mol of sodium peroxide

Short answer

The masses of the given samples are: a. 315 g of nitric acid b. 0.06118 g of mercury c. 4.48 mg of potassium chromate d. 1402 g of aluminum chloride e. 7154 kg of sulfur hexafluoride f. 2125 g of ammonia g. 0.940 g of sodium peroxide

Step-by-step solution

Find the molecular formula and molar mass of each compound

a. Nitric acid (HNO₃): 1 H + 1 N + 3 O = (1) + (14) + 3(16) = 63 g/mol b. Mercury (Hg): 200.59 g/mol c. Potassium chromate (K₂CrO₄): 2 K + 1 Cr + 4 O = 2(39.1) + (52) + 4(16) = 194 g/mol d. Aluminum chloride (AlCl₃): 1 Al + 3 Cl = (27) + 3(35.5) = 133.5 g/mol e. Sulfur hexafluoride (SF₆): 1 S + 6 F = (32) + 6(19) = 146 g/mol f. Ammonia (NH₃): 1 N + 3 H = (14) + 3(1) = 17 g/mol g. Sodium peroxide (Na₂O₂): 2 Na + 2 O = 2(23) + 2(16) = 78 g/mol

Calculate the mass of each sample

To find the mass for each given sample, we will multiply the molar mass by the number of moles. a. \(5.0 \, \text{mol} \, \text{HNO₃} \times \frac{63 \, \text{g}}{1 \, \text{mol}} = 315 \, \text{g} \, \text{HNO₃}\) b. \(0.000305 \, \text{mol} \, \text{Hg} \times \frac{200.59 \, \text{g}}{1 \, \text{mol}} = 0.06118 \, \text{g} \, \text{Hg}\) c. \(2.31 \times 10^{-5} \, \text{mol} \, \text{K₂CrO₄} \times \frac{194 \, \text{g}}{1 \, \text{mol}} = 4.48 \times 10^{-3} \, \text{g} \, \text{K₂CrO₄}\) d. \(10.5 \, \text{mol} \, \text{AlCl₃} \times \frac{133.5 \, \text{g}}{1 \, \text{mol}} = 1402 \, \text{g} \, \text{AlCl₃}\) e. \(4.9 \times 10^{4} \, \text{mol} \, \text{SF₆} \times \frac{146 \, \text{g}}{1 \, \text{mol}} = 7154000 \, \text{g} \, \text{SF₆}\) f. \(125 \, \text{mol} \, \text{NH₃} \times \frac{17 \, \text{g}}{1 \, \text{mol}} = 2125 \, \text{g} \, \text{NH₃}\) g. \(0.01205 \, \text{mol} \, \text{Na₂O₂} \times \frac{78 \, \text{g}}{1 \, \text{mol}} = 0.940 \, \text{g} \, \text{Na₂O₂}\) The calculated mass for each given sample is as follows: a. 315 g of nitric acid b. 0.06118 g of mercury c. 4.48 mg of potassium chromate d. 1402 g of aluminum chloride e. 7154 kg of sulfur hexafluoride f. 2125 g of ammonia g. 0.940 g of sodium peroxide

Key concepts

Molar Mass

Molar mass is a fundamental concept in stoichiometry and chemistry, describing the mass of one mole of a substance. The term 'mole' is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other particles. One mole is equivalent to Avogadro's number \(6.022 \times 10^{23}\) of particles.

The molar mass is expressed in grams per mole \(g/mol\) and can be thought of as the weight of one mole of a given substance. To calculate the molar mass, you need to know the chemical formula of the compound and use the periodic table to find the atomic masses of each element. For instance, the molar mass of water \(H_{2}O\) is calculated by summing the atomic masses of two hydrogen atoms and one oxygen atom, which is approximately \(2 \times 1.008 \text{g/mol} + 16.00 \text{g/mol} = 18.016 \text{g/mol}\).

Importance in Calculations

The molar mass enables the conversion of moles of a substance to grams, a more practical and measurable quantity in labs. This is essential for creating accurate chemical solutions, performing titrations, or conducting reactions that require precise quantities of reactants.

Mole-to-Gram Conversion

Converting moles to grams is a routine practice in chemistry, thanks to a handy tool called the mole-to-gram conversion. This process involves the use of molar mass as a conversion factor and allows chemists to translate the abstract quantity of moles into a tangible mass in grams.

To perform a mole-to-gram conversion, multiply the number of moles by the compound's molar mass. For example, if you have a compound with a molar mass of 50 g/mol and you possess 2 moles of this compound, the mass in grams would be \(2 \text{moles} \times 50 \text{g/mol} = 100 \text{g}\).

Practical Application

In the lab, knowing how to convert from moles to grams is crucial for preparing reaction mixtures or analyzing the outcome of chemical reactions. It is also vital for understanding stoichiometric relationships in chemical equations, which quantify the proportions of reactants and products using mole ratios.

Chemical Formula

A chemical formula is a shorthand representation of the composition of a chemical compound, telling us the types and numbers of atoms combined in a fixed proportion. For elements, the atomic symbol (found on the periodic table) represents the element, while for compounds, the chemical formula includes the symbols for each component element alongside numbers indicating the quantity of each atom present.

For instance, the chemical formula for carbon dioxide \(CO_{2}\) shows that one carbon atom \(C\) bonds with two oxygen atoms \(O\). These numbers are called subscripts and are an essential part of chemical formulas as they provide the exact ratio of atoms in the compound.

Deciphering Chemical Formulas

To better understand stoichiometry and perform various calculations, it's crucial to interpret chemical formulas correctly. They not only allow chemists to grasp the qualitative and quantitative aspects of a substance but are also the basis for determining molar mass and converting between moles and grams. For example, understanding that \(H_{2}O\) contains two hydrogen atoms for every oxygen atom leads to correct molar mass calculations and subsequently accurate conversions.