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Without doing any detailed calculations (but using a periodic table to give atomic weights), rank the following samples in order of increasing numbers of atoms: 0.50 mol \(\mathrm{H}_{2} \mathrm{O}, 23 \mathrm{g} \mathrm{Na}, 6.0 \times 10^{23} \mathrm{N}_{2}\) molecules.

Short Answer

Expert verified
The samples ranked in order of increasing number of atoms are: 23 g Na \(\rightarrow\) 0.50 mol H2O \(\rightarrow\) 6.0 脳 10虏鲁 N2 molecules, with 6.022 脳 10虏鲁 atoms in Na, 9.035 脳 10虏鲁 atoms in H2O, and 1.2 脳 10虏鈦 atoms in N2.

Step by step solution

01

Find molar masses of elements and compounds

Use the periodic table to find the molar mass of H, O, Na, and N. Then, find the molar mass of the compounds H2O (water) and N2. Molar masses of elements from the periodic table: - H: 1 g/mol - O: 16 g/mol - Na: 23 g/mol - N: 14 g/mol Molar masses of compounds: - H2O: (2 脳 1) + 16 = 18 g/mol - N2: 2 脳 14 = 28 g/mol 2. Find the number of atoms in each sample
02

Calculate the number of atoms in each sample

Use the given information for each sample and the molar masses found in step 1 to calculate the number of atoms in the samples. Use Avogadro's number (6.022 脳 10虏鲁 atoms/mol) to convert moles to number of atoms. (a) 0.50 mol H2O - Number of moles of H2O = 0.50 mol - Number of atoms in 1 mole H2O = 3 atoms/molecule 脳 (6.022 脳 10虏鲁 molecules/mol) = 1.807 脳 10虏鲁 atoms/mol - Number of atoms in 0.50 mol H2O = 0.50 mol 脳 1.807 脳 10虏鲁 atoms/mol = 9.035 脳 10虏鲁 atoms (b) 23 g Na - Number of moles of Na = mass / molar mass = 23 g / 23 g/mol = 1 mol - Number of atoms in 1 mol Na = 6.022 脳 10虏鲁 atoms/mol - Number of atoms in 23 g Na = 1 mol 脳 6.022 脳 10虏鲁 atoms/mol = 6.022 脳 10虏鲁 atoms (c) 6.0 脳 10虏鲁 N2 molecules - Number of molecules of N2 = 6.0 脳 10虏鲁 molecules - Number of atoms in 1 molecule N2 = 2 atoms/molecule - Number of atoms in 6.0 脳 10虏鲁 N2 molecules = 6.0 脳 10虏鲁 N2 molecules 脳 2 atoms/molecule = 1.2 脳 10虏鈦 atoms 3. Rank the samples in order of increasing numbers of atoms
03

Rank the samples

List the samples in order of increasing number of atoms based on the calculations in step 2. - 0.50 mol H2O: 9.035 脳 10虏鲁 atoms - 23 g Na: 6.022 脳 10虏鲁 atoms - 6.0 脳 10虏鲁 N2 molecules: 1.2 脳 10虏鈦 atoms So the order of increasing number of atoms is: 23 g Na, 0.50 mol H2O, 6.0 脳 10虏鲁 N2 molecules.

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Key Concepts

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

Atomic Weights
Understanding atomic weights is fundamental in chemistry, as it allows us to quantify the amount of different elements in a chemical reaction. Atomic weights, sometimes referred to as atomic masses, are numbers that represent the average mass of atoms of an element, measured in atomic mass units (amu). These values are relative to the mass of a carbon-12 atom, which is defined as exactly 12 amu.

For example, the atomic weight of hydrogen (H) is approximately 1 amu, meaning a hydrogen atom is roughly one twelfth the mass of a carbon-12 atom. Atomic weights are crucial when we calculate how much of each element is present in a compound or a reaction. In the periodic table, atomic weights are given for each element, thereby providing essential information for chemical calculations such as molar mass, which leads us to the next important concept in chemistry.
Avogadro's Number
Avogadro's number stands as a cornerstone in the realm of chemistry, especially when studying the mole concept. This constant, named after the scientist Amedeo Avogadro, provides the link between the macroscopic scale we can measure and the microscopic scale of atoms and molecules.

Avogadro's number is defined as the number of constituent particles, usually atoms or molecules, that are contained in one mole of a substance. The value of Avogadro's number is approximately 6.022 脳 10虏鲁 per mole. So, when we say we have one mole of carbon atoms, we are referring to approximately 6.022 脳 10虏鲁 individual carbon atoms. This number is incredibly useful when converting between the number of particles and the amount of substance in moles, which is a common task in chemical calculations involving reactions and stoichiometry.
Molar Mass Calculation

Essential Steps for Calculation

The molar mass of a substance is defined as the mass of one mole of that substance. It is typically expressed in grams per mole (g/mol). This provides another vital bridge between the quantitative aspects of a chemical substance and the actual number of atoms or molecules involved in a reaction. To calculate the molar mass of a molecule, you sum up the atomic weights of all the atoms that make up the molecule.

For instance, water (H2O) has a molar mass calculated by adding twice the atomic weight of hydrogen (1 g/mol each) to the atomic weight of oxygen (16 g/mol), resulting in a molar mass of 18 g/mol. The molar mass is a fundamental parameter which allows us to convert between the mass of a substance and the number of moles, thereby making it possible to measure out specific amounts of a substance for a chemical reaction.
Stoichiometry
Stoichiometry is the section of chemistry that involves the calculation of reactants and products in chemical reactions. It is rooted in the conservation of mass and the concept of moles. Using the mole ratio, which is derived from the balanced chemical equation, one can determine the amount of reactants needed to react completely with each other and the amount of products that will be formed.

For example, if a balanced equation states that 2 moles of hydrogen reacts with 1 mole of oxygen to form 2 moles of water, we can use stoichiometry to calculate how many grams of hydrogen are needed to react with a given amount of oxygen or the opposite. Knowledge of the atomic weights and Avogadro's number is essential for such calculations, as stoichiometry relies on these concepts to ensure the correct proportions of substances are used or produced in a chemical reaction. In essence, stoichiometry is the recipe for the chemical world, allowing us to predict and control the outcomes of chemical processes.

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Most popular questions from this chapter

An organic compound was found to contain only \(\mathrm{C}, \mathrm{H},\) and Cl. When a \(1.50-\mathrm{g}\) sample of the compound was completely combusted in air, 3.52 \(\mathrm{g}\) of \(\mathrm{CO}_{2}\) was formed. In a separate experiment, the chlorine in a \(1.00-\mathrm{g}\) sample of the compound was converted to 1.27 g of AgCl. Determine the empirical formula of the compound.

Balance the following equations: $$ \begin{array}{l}{\text { (a) } \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)} \\ {\text { (b) } \mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HNO}_{3}(a q)} \\ {\text { (c) } \mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(l)+\mathrm{HCl}(g)} \\ {\text { (d) } \mathrm{Zn}(\mathrm{OH})_{2}(s)+\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l)}\end{array} $$

Write balanced chemical equations corresponding to each of the following descriptions: (a) Solid calcium carbide, \(\mathrm{CaC}_{2}\) , reacts with water to form an aqueous solution of calcium hydroxide and acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}\) . (b) When solid potassium chlorate is heated, it decomposes to form solid potassium chloride and oxygen gas. (c) Solid zinc metal reacts with sulfuric acid to form hydrogen gas and an aqueous solution of zinc sulfate. (d) When liquid phosphorus trichloride is added to water, it reacts to form aqueous phosphorous acid, \(\mathrm{H}_{3} \mathrm{PO}_{3}(a q)\), and aqueous hydrochloric acid. (e) When hydrogen sulfide gas is passed over solid hot iron(III) hydroxide, the resulting reaction produces solid iron(II) sulfide and gaseous water.

Determine the empirical formula of each of the following compounds if a sample contains \((\mathbf{a})0.104 \mathrm{mol} \mathrm{K}, 0.052 \mathrm{mol}\) \(\mathrm{C},\) and \(0.156 \mathrm{mol} \mathrm{O} ;(\mathbf{b}) 5.28 \mathrm{g} \mathrm{Sn}\) and \(3.37 \mathrm{g} \mathrm{F} ;(\mathbf{c}) 87.5 \% \mathrm{N}\) and 12.5\(\% \mathrm{H}\) by mass.

Define the terms theoretical yield, actual yield, and percent yield. (b) Why is the actual yield in a reaction almost always less than the theoretical yield?(c) Can a reaction ever have 110\(\%\) actual yield?

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