Question

The incorrect statement for \(14 \mathrm{~g}\) of \(\mathrm{CO}\) is (a) it occupies \(2.24\) litre at NTP (b) it corresponds to \(0.5 \mathrm{~mol}\) of \(\mathrm{CO}\) (c) it corresponds to same mol of \(\mathrm{CO}\) and \(\mathrm{N}_{2}\) (d) it corresponds to \(3.01 \times 10^{23}\) molecules of \(\mathrm{CO}\)

Short answer

Option (a) is incorrect: "it occupies \(2.24\) liters at NTP."

Step-by-step solution

Calculate Molar Mass

The first step is to determine the molar mass of carbon monoxide \(\text{CO}\). The atomic mass of carbon \(\text{C}\) is \(12\, \text{g/mol}\) and that of oxygen \(\text{O}\) is \(16\, \text{g/mol}\). Thus, \(\text{CO} = 12 + 16 = 28\, \text{g/mol}\).

Determine Moles of CO

Given that we have \(14\, \text{g}\) of \(\text{CO}\), calculate the number of moles using the molar mass: \[ \text{moles of CO} = \frac{14\, \text{g}}{28\, \text{g/mol}} = 0.5\, \text{mol}. \]

Calculate Volume at NTP

One mole of a gas occupies \(22.4\, \text{liters}\) at Normal Temperature and Pressure (NTP). Thus, \(0.5\, \text{mol}\) of \(\text{CO}\) will occupy: \[ 0.5 \times 22.4 = 11.2 \text{ liters}. \] Thus, option (a) is incorrect because it says \(2.24\) liters.

Compare Moles of CO and N2

Both \(\text{CO}\) and \(\text{N}_2\) will have \(0.5\, \text{mol}\) if you have \(14\, \text{g}\) of \(\text{CO}\), thus option (c) is correct since it states the same moles.

Calculate Number of Molecules

Avogadro's number states that one mole contains \(6.02 \times 10^{23}\) molecules. Therefore, \(0.5\, \text{mol}\) of \(\text{CO}\) will have: \[ 0.5 \times 6.02 \times 10^{23} = 3.01 \times 10^{23} \text{ molecules}. \] Thus, option (d) is correct.

Key concepts

Molar Mass

Molar mass is a fundamental concept in stoichiometry. It is the mass of one mole of a given substance, expressed in grams per mole (g/mol). It serves as the bridge to convert grams into moles or vice versa.
For example, the molar mass of carbon monoxide (CO) is determined by adding the atomic masses of its constituent elements. Carbon (C) has an atomic mass of 12 g/mol, while oxygen (O) has an atomic mass of 16 g/mol. Therefore, the molar mass of CO is calculated as follows:

\[ \text{Molar mass of CO} = 12 + 16 = 28 \text{ g/mol} \]
This value signifies that 28 grams of CO is equivalent to one mole. Understanding molar mass helps in learning how to calculate the number of moles in a given mass of a substance, which is essential for stoichiometry.

Avogadro's Number

Avogadro's number is a pivotal constant in chemistry, symbolized as \(6.02 \times 10^{23}\). It represents the number of atoms, ions, or molecules in one mole of a substance. Thus, it connects the microscopic world to the macroscopic measurements we use in laboratories.
When you have one mole of any substance, it contains \(6.02 \times 10^{23}\) fundamental entities. For example, if you have 0.5 moles of CO, then the number of molecules in that amount can be determined using Avogadro's number:

\[ 0.5 \times 6.02 \times 10^{23} = 3.01 \times 10^{23} \text{ molecules} \]
This large constant allows chemists to handle macroscopic quantities while working with reactions that occur at the atomic or molecular level. Knowing Avogadro's number is crucial for calculating the amount of substances in chemical reactions.

Mole Concept

The mole concept is central in chemistry and stoichiometry. It provides a method to quantify the amount of a substance. A mole is defined as the quantity of any chemical substance that contains the same number of particles as there are atoms in 12 grams of pure carbon-12.

This concept helps in translating between the mass of a substance and the number of molecules or atoms contained within it. In practical terms, it alleviates the difficulties of working with actual atoms or molecules, which are extremely tiny.
For instance, if you have 14 grams of CO, you can calculate the number of moles using its molar mass:

\[ \text{Moles of CO} = \frac{14 \text{ g}}{28 \text{ g/mol}} = 0.5 \text{ mol} \]
This tells us that 14 grams of CO is half a mole, providing a convenient way to relate mass with chemical equations and reactions. The mole concept simplifies computations in stoichiometry, making the complex nature of chemical reactions more understandable.