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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: 42 gof NaHCO \(_{3}, 1.5 \mathrm{mol} \mathrm{CO}_{2}, 6.0 \times 10^{24} \mathrm{Ne}\) atoms.

Short Answer

Expert verified
In short, we rank the samples based on increasing number of atoms by first calculating the number of atoms in each sample: NaHCO3 has \(1.805 \times 10^{24}\) atoms, CO2 has \(2.708 \times 10^{24}\) atoms, and Ne has \(6.0 \times 10^{24}\) atoms. Therefore, the ranking is: NaHCO3 < CO2 < Ne.

Step by step solution

01

Calculate the number of moles of NaHCO3

To find the number of atoms in the given mass of NaHCO3, first, we need to find the number of moles present. We can use the formula: Number of moles = (Given mass) / (Molar mass) The molar mass of NaHCO3 can be calculated as follow (from the periodic table): Na (1 x 22.99) + H (1 x 1.008) + C (1 x 12.01) + O (3 x 16.00) = 84.01 g/mol Now, we can find the number of moles of NaHCO3 in 42 g: Number of moles = 42 g / 84.01 g/mol = 0.5 mol
02

Calculate the number of atoms in NaHCO3

To find the number of atoms in NaHCO3, we'll use Avogadro's number (6.022 x 10^23 atoms/mol) and multiply it by the number of moles. Also, remember that NaHCO3 has 6 atoms in each molecule (Na, H, C, and three O's). Number of atoms in NaHCO3 = 0.5 mol × 6.022 × 10^23 atoms/mol × 6 atoms/molecule = 1.805 × 10^24 atoms
03

Calculate the number of atoms in CO2

We have been given 1.5 moles of CO2, and each molecule of CO2 has 3 atoms (1 C and 2 O). Therefore, we can directly calculate the number of atoms in CO2 by multiplying the given moles, Avogadro's number, and the atoms in each molecule. Number of atoms in CO2 = 1.5 mol × 6.022 × 10^23 atoms/mol × 3 atoms/molecule = 2.708 × 10^24 atoms
04

Compare the number of atoms and rank the samples

Now that we have the number of atoms for all samples, we can compare and rank them: 1. NaHCO3: 1.805 × 10^24 atoms 2. CO2: 2.708 × 10^24 atoms 3. Ne: 6.0 × 10^24 atoms Based on the increasing number of atoms, the order is: NaHCO3 < CO2 < Ne.

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Key Concepts

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

Molar mass
Every substance has a unique molar mass, which is the mass of one mole of that substance. It's measured in grams per mole (g/mol). The molar mass is calculated using the atomic weights of the elements from the periodic table.
For example, in the compound NaHCO₃ (baking soda):
  • Sodium (Na) contributes about 22.99 g/mol.
  • Hydrogen (H) adds 1.008 g/mol.
  • Carbon (C) adds 12.01 g/mol.
  • Oxygen (O), with three atoms, contributes 48.00 g/mol (3 x 16.00).
All these values come together to give the molar mass of NaHCO₃ as approximately 84.01 g/mol.
By knowing the molar mass, you can convert between the mass of a substance and the number of moles, using the equation:\[\text{Number of Moles} = \frac{\text{Given Mass}}{\text{Molar Mass}}\]This conversion is a crucial step in determining the number of atoms in a given sample.
Avogadro's number
Avogadro's number is an essential tool in chemistry, providing a bridge between the microscopic world of atoms and the macroscopic world we observe. It is defined as the number of atoms, ions, or molecules in one mole of a substance, which is approximately 6.022 x 10^23.
This number tells us how many particles are in a mole, allowing us to convert between moles and the actual number of particles. For example, if you have 0.5 moles of NaHCO₃, the number of molecules is calculated as:\[0.5 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} = 3.011 \times 10^{23} \text{ molecules}\]Each molecule contains 6 atoms (Na, H, C, and three O), so multiplying by 6 gives the total number of atoms in the sample. Understanding Avogadro's number helps us scale these microscopic calculations to real-world quantities.
Periodic table
The periodic table is an invaluable tool for chemists, providing information on the atomic structure and properties of elements. Each element's atomic number, symbol, and atomic weight are essential for calculating molar mass and understanding chemical behavior.
Here's how you might use the periodic table when working with a compound like COâ‚‚:
  • Carbon (C) has an atomic weight of 12.01 g/mol.
  • Oxygen (O) has an atomic weight of 16.00 g/mol, and there are two oxygen atoms in COâ‚‚.
The total molar mass of COâ‚‚ is calculated as:\[12.01 \text{ g/mol (C)} + 2 \times 16.00 \text{ g/mol (O)} = 44.01 \text{ g/mol}\]Using the periodic table, you can quickly obtain these values to facilitate calculations in stoichiometry, enhancing your understanding of chemical reactions and compositions.

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Most popular questions from this chapter

The fizz produced when an Alka-Seltzer tablet is dissolved in water is due to the reaction between sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) and citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) :\) $$ \begin{aligned} 3 \mathrm{NaHCO}_{3}(a q)+\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) & \longrightarrow \\ & 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \end{aligned} $$ In a certain experiment 1.00 g of sodium bicarbonate and 1.00 g of citric acid are allowed to react. (a) Which is the limiting reactant? (b) How many grams of carbon dioxide form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed?

Write balanced chemical equations to correspond to each of the following descriptions: (a) When sulfur trioxide gas reacts with water, a solution of sulfuric acid forms. (b) Boron sulfide, \(B_{2} S_{3}(s),\) reacts violently with water to form dissolved boric acid, \(H_{3} B O_{3},\) and hydrogen sulfide gas. (c) Phosphine, PH \(_{3}(g),\) combusts in oxygen gas to form water vapor and solid tetraphosphorus decaoxide. (d) When solid mercury(II) nitrate is heated, it decomposes to form solid mercury(II) oxide, gaseous nitrogen dioxide, and oxygen.(e) Copper metal reacts with hot concentrated sulfuric acid solution to form aqueous copper(II) sulfate, sulfur dioxide gas, and water.

Balance the following equations: $$ \begin{array}{l}{\text { (a) } \mathrm{Al}_{4} \mathrm{C}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{CH}_{4}(g)} \\ {\text { (b) } \mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (c) } \mathrm{Fe}(\mathrm{OH})_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\text { (d) } \mathrm{Mg}_{3} \mathrm{N}_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{MgSO}_{4}(a q)+\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(a q)}\end{array} $$

(a) The characteristic odor of pineapple is due to ethyl butyrate, a compound containing carbon, hydrogen, and oxygen. Combustion of 2.78 mg of ethyl butyrate produces 6.32 \(\mathrm{mg}\) of \(\mathrm{CO}_{2}\) and 2.58 \(\mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of the compound? (b) Nicotine, a component of tobacco, is composed of \(C, H,\) and \(N .\) A 5.250 -mg sample of nicotine was combusted, producing 14.242 \(\mathrm{mg}\) of \(\mathrm{CO}_{2}\) and 4.083 \(\mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula for nicotine? If nicotine has a molar mass of \(160 \pm 5 \mathrm{g} / \mathrm{mol},\) what is its molecular formula?

Aluminum sulfide reacts with water to form aluminum hydroxide and hydrogen sulfide. (a) Write the balanced chemical equation for this reaction. (b) How many grams of aluminum hydroxide are obtained from 14.2 \(\mathrm{g}\) of aluminum sulfide?

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