Problem 57
Question
A If Avogadro number is \(6 \times 10^{23}\), then number of protons, neutrons and electrons is \(14 \mathrm{~g}\) of \({ }_{6} \mathrm{C}^{14}\) are respectively (a) \(36 \times 10^{23}, 48 \times 10^{23}, 36 \times 10^{23}\) (b) \(36 \times 10^{23}, 36 \times 10^{23}, 36 \times 10^{23}\) (c) \(48 \times 10^{23}, 36 \times 10^{23}, 48 \times 10^{23}\) (d) \(48 \times 10^{23}, 48 \times 10^{23}, 36 \times 10^{23}\) \(\mathrm{F}\)
Step-by-Step Solution
Verified Answer
The answer is (a): 36 × 10^{23}, 48 × 10^{23}, 36 × 10^{23}.
1Step 1: Understanding Mass and Moles
Given that the mass of the substance is 14 g and the substance in question is \(_{6} \mathrm{C}^{14}\), which means one mole of this isotope of Carbon weighs 14 g. Thus, 14 g corresponds to one mole.
2Step 2: Determine Total Atoms
One mole of any substance contains Avogadro's number of atoms. Therefore, there are \(6 \times 10^{23}\) atoms in 14 g of \(_{6} \mathrm{C}^{14}\).
3Step 3: Protons in the Sample
The atomic number for Carbon is 6, which means each atom has 6 protons. Therefore, the total number of protons in 14 g of \(_{6} \mathrm{C}^{14}\) is \(6 \times 6 \times 10^{23} = 36 \times 10^{23}\).
4Step 4: Neutrons in the Sample
The isotope notation \(_{6} \mathrm{C}^{14}\) suggests that each atom has 8 neutrons (since 14 - 6 = 8). Therefore, the total number of neutrons is \(8 \times 6 \times 10^{23} = 48 \times 10^{23}\) neutrons in the 14 g sample.
5Step 5: Electrons in the Sample
For a neutral carbon atom, the number of electrons equals the number of protons, which is 6. Therefore, the total number of electrons is \(6 \times 6 \times 10^{23} = 36 \times 10^{23}\).
Key Concepts
IsotopesMoles and Molar MassSubatomic Particles
Isotopes
Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons in their nuclei. This difference in neutron number leads to a difference in atomic mass but not chemical properties. For instance, carbon has several isotopes, such as \(_{6} \mathrm{C}^{12}\) and \(_{6} \mathrm{C}^{14}\). All carbon isotopes share the same atomic number, which is 6, due to having the same number of protons.
However, \(_{6} \mathrm{C}^{14}\) has two more neutrons than \(_{6} \mathrm{C}^{12}\), giving it a higher atomic mass of 14 instead of 12.
In essence:
However, \(_{6} \mathrm{C}^{14}\) has two more neutrons than \(_{6} \mathrm{C}^{12}\), giving it a higher atomic mass of 14 instead of 12.
In essence:
- The number of protons defines the element.
- The number of neutrons defines the isotope.
- Isotopes may be stable or radioactive.
Moles and Molar Mass
The concept of a mole is fundamental in chemistry as it expresses amounts of a chemical substance.
One mole is defined as exactly \(6.022 \times 10^{23}\) entities (usually atoms or molecules), known as Avogadro's number.
This helps in relating macroscopic quantities of substances to the atomic scale. Molar mass, on the other hand, is the mass of one mole of a substance, often expressed in grams per mole (g/mol).
For isotopes, such as \(_{6} \mathrm{C}^{14}\), the molar mass is equivalent to the sum of the masses of its protons, neutrons, and electrons, although the electron mass is usually negligible for calculations.
For \(_{6} \mathrm{C}^{14}\), its molar mass is 14 g/mol, reflecting the total mass of its subatomic components.
This relationship allows chemists to convert weight measurements into moles, and thus into numbers of atoms or molecules.
One mole is defined as exactly \(6.022 \times 10^{23}\) entities (usually atoms or molecules), known as Avogadro's number.
This helps in relating macroscopic quantities of substances to the atomic scale. Molar mass, on the other hand, is the mass of one mole of a substance, often expressed in grams per mole (g/mol).
For isotopes, such as \(_{6} \mathrm{C}^{14}\), the molar mass is equivalent to the sum of the masses of its protons, neutrons, and electrons, although the electron mass is usually negligible for calculations.
For \(_{6} \mathrm{C}^{14}\), its molar mass is 14 g/mol, reflecting the total mass of its subatomic components.
This relationship allows chemists to convert weight measurements into moles, and thus into numbers of atoms or molecules.
Subatomic Particles
Atoms are composed of subatomic particles, which include protons, neutrons, and electrons. Understanding their roles is crucial to chemistry:
- Protons: Positively charged particles located in the nucleus of an atom. The number of protons defines the element and is also known as the atomic number. For instance, carbon always has 6 protons.
- Neutrons: These are neutral particles that also reside in the nucleus. Neutrons contribute to the mass of an atom but do not affect the chemical properties. As seen in isotopes, they vary in number and influence the atomic mass.
- Electrons: Negatively charged particles that orbit the nucleus in electron clouds. Electrons determine the reactivity and bonding behavior of an atom. In a neutral atom, the number of electrons equals the number of protons.
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