Chapter 1: Problem 34
Which of the following pairs contain equal number of atoms? (1) \(11.2 \mathrm{cc}\) of the \(\mathrm{N}_{2}\) and \(0.015 \mathrm{~g}\) of nitric oxide (2) \(22.4\) litres of nitrous oxide and \(22.4\) litres of nitric oxide (3) 1 milli mole of \(\mathrm{HCl}\) and and \(0.5\) milli mole of \(\mathrm{H}_{2} \mathrm{~S}\) (4) 1 mole of \(\mathrm{H}_{2} \mathrm{O}_{2}\) and 1 mole of \(\mathrm{N}_{2} \mathrm{O}_{4}\)
Short Answer
Expert verified
Option 1 contains an equal number of atoms.
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Moles and Molecules
To solve problems about the number of atoms in different substances, it is crucial to understand the relationship between moles and molecules.
A mole is a unit that helps us count very large numbers of tiny entities like molecules and atoms.
One mole contains exactly Avogadro's number of particles, which is approximately \(6.022 \times 10^{23} \text{particles}\).
Thus, if we know the number of moles of a substance, we can easily calculate the number of molecules by multiplying by Avogadro's number.
By converting volumes and masses to moles using gas laws or molar masses, we can make meaningful comparisons between different compounds.
In our exercise, we compare different samples by calculating their moles using ideal gas law or molar masses, and then infer the number of molecules based on these moles.
A mole is a unit that helps us count very large numbers of tiny entities like molecules and atoms.
One mole contains exactly Avogadro's number of particles, which is approximately \(6.022 \times 10^{23} \text{particles}\).
Thus, if we know the number of moles of a substance, we can easily calculate the number of molecules by multiplying by Avogadro's number.
By converting volumes and masses to moles using gas laws or molar masses, we can make meaningful comparisons between different compounds.
In our exercise, we compare different samples by calculating their moles using ideal gas law or molar masses, and then infer the number of molecules based on these moles.
Atomic Structure in Chemistry
Atoms are the fundamental units of matter and consist of smaller particles like protons, neutrons, and electrons.
In the context of our problem, understanding the atomic structure helps us comprehend molecular composition.
For instance, a molecule of Nitric Oxide (NO) consists of one nitrogen atom and one oxygen atom.
Knowing the atomic structure allows us to identify the number of atoms per molecule.
This is very important when we compare different samples to check if they have an equal number of atoms.
In our calculations, by understanding that each \(\text{N}_2\) molecule has two nitrogen atoms and each NO molecule has two atoms (1 N and 1 O), we ensure our comparisons take into account the correct number of atoms.
In the context of our problem, understanding the atomic structure helps us comprehend molecular composition.
For instance, a molecule of Nitric Oxide (NO) consists of one nitrogen atom and one oxygen atom.
Knowing the atomic structure allows us to identify the number of atoms per molecule.
This is very important when we compare different samples to check if they have an equal number of atoms.
In our calculations, by understanding that each \(\text{N}_2\) molecule has two nitrogen atoms and each NO molecule has two atoms (1 N and 1 O), we ensure our comparisons take into account the correct number of atoms.
Gas Laws in Chemistry
Gas laws provide the relationships between volume, temperature, pressure, and number of moles of a gas.
The Ideal Gas Law, given by PV=nRT, is particularly helpful for calculations involving gases.
For conditions at Standard Temperature and Pressure (STP), which is 0 degrees Celsius and 1 atmosphere, 1 mole of gas occupies 22.4 liters.
This direct relationship makes it easy to convert volumes of gases to moles under these conditions.
For example, in our solution, we use the fact that 22.4 liters of \(\text{N}_2\) corresponds to 1 mole.
Thus, for volumes less than 22.4 liters, like 11.2 cc (which is 0.0112 liters), we can calculate the number of moles by simply dividing by 22.4 liters per mole.
This approach simplifies comparison between different gas samples.
The Ideal Gas Law, given by PV=nRT, is particularly helpful for calculations involving gases.
For conditions at Standard Temperature and Pressure (STP), which is 0 degrees Celsius and 1 atmosphere, 1 mole of gas occupies 22.4 liters.
This direct relationship makes it easy to convert volumes of gases to moles under these conditions.
For example, in our solution, we use the fact that 22.4 liters of \(\text{N}_2\) corresponds to 1 mole.
Thus, for volumes less than 22.4 liters, like 11.2 cc (which is 0.0112 liters), we can calculate the number of moles by simply dividing by 22.4 liters per mole.
This approach simplifies comparison between different gas samples.
Stoichiometry
Stoichiometry involves using balanced chemical equations to calculate the quantities of reactants and products.
It's about the proportions of atoms and molecules in chemical reactions.
In the context of our problem, knowing the number of each type of atom in a molecule helps with these calculations.
For example, 1 mole of hydrogen peroxide (H₂O₂) contains 2 moles of hydrogen atoms and 2 moles of oxygen atoms.
Similarly, 1 mole of dinitrogen tetroxide (N₂O₄) consists of 2 moles of nitrogen atoms and 4 moles of oxygen atoms.
Understanding this helps us determine the total number of atoms in each molecule and compare different samples accurately.
Stoichiometry ensures that we understand how to balance these quantities correctly when comparing or combining substances.
It's about the proportions of atoms and molecules in chemical reactions.
In the context of our problem, knowing the number of each type of atom in a molecule helps with these calculations.
For example, 1 mole of hydrogen peroxide (H₂O₂) contains 2 moles of hydrogen atoms and 2 moles of oxygen atoms.
Similarly, 1 mole of dinitrogen tetroxide (N₂O₄) consists of 2 moles of nitrogen atoms and 4 moles of oxygen atoms.
Understanding this helps us determine the total number of atoms in each molecule and compare different samples accurately.
Stoichiometry ensures that we understand how to balance these quantities correctly when comparing or combining substances.
