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Calculate the molar mass for each of the following: a. \(\mathrm{Cl}_{2}\) b. \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3}\) c. \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Short Answer

Expert verified
a. 70.90 g/mol, b. 90.09 g/mol, c. 262.87 g/mol.

Step by step solution

01

Understanding Molar Mass

The molar mass of a molecule is calculated by summing the atomic masses of all atoms in the molecule. Atomic masses can be found on the periodic table.
02

Calculate Molar Mass for \(\mathrm{Cl}_{2}\)

Chlorine (Cl) has an atomic mass of approximately 35.45 g/mol. Since \(\mathrm{Cl}_{2}\) has two chlorine atoms, the calculation is: \[\text{Molar mass of }\mathrm{Cl}_{2} = 2 \times 35.45 = 70.90 \text{ g/mol}\]
03

Calculate Molar Mass for \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3}\)

Carbon (C) has an atomic mass of approximately 12.01 g/mol, Hydrogen (H) has an atomic mass of approximately 1.01 g/mol, and Oxygen (O) has an atomic mass of approximately 16.00 g/mol. Sum these for all atoms in \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3}\): \[\text{Molar mass of } \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3} = (3 \times 12.01) + (6 \times 1.01) + (3 \times 16.00) = 36.03 + 6.06 + 48.00 = 90.09 \text{ g/mol}\]
04

Calculate Molar Mass for \(\mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2}\)

Magnesium (Mg) has an atomic mass of approximately 24.31 g/mol, Phosphorus (P) has an atomic mass of approximately 30.97 g/mol, and Oxygen (O) has an atomic mass of approximately 16.00 g/mol. Sum these for all atoms in \(\mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2}\): \[\text{Molar mass of } \mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2} = (3 \times 24.31) + (2 \times 30.97) + (8 \times 16.00) = 72.93 + 61.94 + 128.00 = 262.87 \text{ g/mol}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

molecular weight
The molecular weight is also known as the molar mass. It represents the mass of one mole of a given molecule and is expressed in grams per mole (g/mol). To calculate it, you sum up the atomic masses of all atoms within the molecule. Understanding molecular weight is essential because it allows chemists to measure quantities of a substance on a molecular scale. For instance, knowing that the molecular weight of \(\text{Cl}_2\) is 70.90 g/mol means that one mole of chlorine molecules weighs 70.90 grams.

This is crucial in chemical reactions where precise measurements are key. Imagine you are baking: just as you need the right amount of flour and sugar to make a cake, chemists need the correct molecular weights to ensure reactions proceed correctly.
atomic mass
Atomic mass is the mass of an individual atom and is typically measured in atomic mass units (amu). It's based on the number of protons and neutrons in the atom's nucleus. Each element on the periodic table has a specific atomic mass.

For example:
  • Chlorine (Cl) has an atomic mass of approximately 35.45 amu.
  • Carbon (C) has an atomic mass of about 12.01 amu.
  • Hydrogen (H) around 1.01 amu.
  • Oxygen (O) approximately 16.00 amu.

  • These values are used to calculate molecular weights. In the case of \(\text{C}_3\text{H}_6\text{O}_3\), the individual atomic masses (multiplied by the number of each atom) are summed to yield the final molar mass.
    stoichiometry
    Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's essentially the 'recipe' of chemistry, ensuring that you have the right amounts of each substance to achieve a desired reaction.

    • Using molar mass calculations helps in balancing and executing chemical equations.
    • It involves using proportions based on the molecular and atomic masses of involved substances.

    For instance, if you need to prepare a solution containing a certain number of moles of a compound, knowing the molar mass allows you to measure the exact amount needed.
    This becomes critically useful in various fields, from pharmaceutical formulations to industrial processes.
    periodic table
    The periodic table is a chart where all known elements are organized based on their atomic number, electron configurations, and recurring chemical properties. It's a crucial tool in chemistry for understanding and predicting the behavior of elements.

    Each element's atomic mass, which is essential for molar mass calculations, is listed on the periodic table. When solving molar mass problems, you'll frequently refer to the atomic masses mentioned on this table.

    Key points of the periodic table:
  • Organized by atomic number (number of protons).
  • Helps visualize trends (e.g., element reactivity, atomic size).
  • Essential for identifying elements in compounds and calculating molar mass.

  • Without the periodic table, determining the atomic masses needed for molar mass computations would be complex and tedious.

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    Most popular questions from this chapter

    The carbohydrate fructose found in honey and fruits has an empirical formula of \(\mathrm{CH}_{2} \mathrm{O}\). If the experimental molar mass of fructose is \(180 \mathrm{~g}\), what is its molecular formula?

    Calculate the number of atoms of \(\mathrm{N}\) in each of the following: a. \(0.755 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) b. \(0.82 \mathrm{~g}\) of \(\mathrm{NaNO}_{3}\) c. \(40.0 \mathrm{~g}\) of \(\mathrm{N}_{2} \mathrm{O}\) d. \(6.24 \times 10^{23}\) molecules of \(\mathrm{NH}_{3}\) e. \(1.4 \times 10^{22}\) molecules of \(\mathrm{N}_{2} \mathrm{O}_{4}\)

    Writc the cmpirical formula for cach of the following substances: a. \(\mathrm{H}_{2} \mathrm{O}_{2}\), peroxide b. \(\mathrm{C}_{18} \mathrm{H}_{12}\), chrysene, used in the manufacture of dyes c. \(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}_{2}\), chrysanthemic acid, in pyrethrum flowers d. \(\mathrm{C}_{9} \mathrm{H}_{18} \mathrm{~N}_{6}\), altretamine, an anticancer medication e. \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{~N}_{2} \mathrm{O}_{2}\), oxamide, a fertilizer

    Aluminum sulfate, \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\), is used in some antiperspirants. a. How many moles of sulfur are present in \(3.0 \mathrm{~mol}\) of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} ?\) b. How many moles of aluminum ions are present in \(0.40 \mathrm{~mol}\) of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} ?\) c. How many moles of sulfate ions \(\left(\mathrm{SO}_{4}^{2-}\right)\) are present in \(1.5 \mathrm{~mol}\) of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} ?\)

    Chloral hydrate, a sedative, contains \(14.52 \% \mathrm{C}, 1.83 \% \mathrm{H}\), \(64.30 \% \mathrm{Cl}\), and \(19.35 \%\) O. If it has an experimental molar mass of \(165 \mathrm{~g}\), what is the molecular formula of chloral hydrate?

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