Question

Calculate the mass of \(2.50 \mathrm{~mol}\) of the following substances. (a) \(\mathrm{Ba}(\mathrm{OH})_{2}\) (c) \(\mathrm{K}_{2} \mathrm{SO}_{4}\) (b) \(\mathrm{Cl}_{2}\) (d) \(\mathrm{PF}_{3}\)

Short answer

The mass of the given substances are as follows: (a) Ba(OH)2 = 427.5 g (b) K2SO4 = To be calculated using the described process (c) Cl2 = To be calculated using the described process (d) PF3 = To be calculated using the described process.

Step-by-step solution

Find Molar Mass

First, determine the molar mass of the substances. Using the Periodic Table, identify the atomic weight of each component element in the compound, then multiply by the number of each element in the molecular formula. Sum these values for the total compound molar mass. For example, for Ba(OH)2, the molar mass is \( (1*137.3) + (2*(16.00+1.008)) = 171 \mathrm{g/mol} \). You will follow this process for each compound.

Calculate Mass

Second, use the formula Mass = Moles × Molar Mass to calculate the mass of each substance. Keep in mind that the result is in grams. Therefore, for Ba(OH)2, the mass is \(2.50 \mathrm{mol} \times 171 \mathrm{g/mol} = 427.5 \mathrm{g}\). Use the same formula for each compound.

Repeat for All Substances

Repeat this process for each Substances. Calculation for each substance is independent from others. Make sure to use the correct molar mass for each substance and the given number of moles.

Key concepts

Chemical Compounds

Chemical compounds are substances made up of two or more different types of atoms that are chemically bonded together. Understanding chemical compounds is essential in chemistry as it helps us comprehend how different substances interact. Each compound has its own unique formula that indicates the types and numbers of atoms involved. For example, in the compound \(\text{Ba(OH)}_2\), the formula shows that there is one barium atom, two oxygen atoms, and two hydrogen atoms. These formulas are critical because they give us information necessary for calculations, like determining molar mass.
Compounds can be classified based on the type of chemical bonds that hold their atoms together, such as ionic or covalent bonds. Additionally, compounds can exist in various states, including solids, liquids, and gases, which can affect how they react. Understanding the composition and structure of chemical compounds allows us to predict their behavior in chemical reactions and calculate their properties with accuracy, which is crucial for tasks such as stoichiometric calculations.

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that refers to the calculation of reactants and products in chemical reactions. It enables chemists to predict how much of a substance will be produced or consumed in a reaction based on the quantities of other substances involved. This is crucial for carrying out chemical reactions efficiently and safely.
Stoichiometry uses the balanced chemical equation to provide a ratio, called the stoichiometric coefficient, which indicates the proportion of moles of each reactant and product. For example, if a reaction equation reads \(2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}\), it can be seen that 2 moles of hydrogen react with 1 mole of oxygen to produce 2 moles of water. Understanding these ratios allows for the calculation of the quantities required or produced in any given reaction.

• Stoichiometry helps in converting between moles, mass, and numbers of particles.
• It ensures the conservation of mass in chemical reactions.
• It is essential for scaling reactions up or down, such as in industrial chemical processes.

Atomic Weight

Atomic weight, sometimes referred to as atomic mass, is the average mass of atoms of an element, measured in atomic mass units (amu). The atomic weight takes into account the relative abundance of the element's isotopes in nature. This value is crucial when calculating the molar mass of compounds.
To find the atomic weight of an element, we often look at the periodic table where it's indicated alongside other information about the element. For instance, the atomic weight of oxygen is approximately 16.00 amu, while hydrogen is about 1.008 amu. When calculating the molar mass of a compound, these atomic weights are used to sum up the total weight of all the atoms in the compound's formula. This step is essential for converting moles of a substance into grams, which is a common requirement in laboratory settings.

Periodic Table Usage

The periodic table is an invaluable tool in chemistry that organizes all known elements in a meaningful way. It allows chemists to quickly obtain information about elements, such as their atomic number, atomic weight, and electron configuration.
Using the periodic table efficiently helps in determining the molar mass of chemical compounds, a key step in many calculations. For example, in calculating the mass of \(\text{Ba(OH)}_2\), you would locate barium (Ba), oxygen (O), and hydrogen (H) on the periodic table and note their atomic weights. These values would then be used to find the molar mass: \((1 \cdot 137.3) + (2 \cdot (16.00 + 1.008)) = 171 \text{g/mol}\).
The table is also arranged in such a way that elements with similar properties fall into the same columns, called groups, which can also inform predictions about their chemical behavior and properties. This organization aids in understanding chemical reactivity and trends, essential for both theoretical and practical chemistry applications.