Sure, let's break down the solution step-by-step:
(i) Definitions:
(a) Relative Atomic Mass (RAM):
RAM is the weighted average mass of the atoms in a naturally occurring sample of the element, compared to one-twelfth the mass of a carbon-12 atom. It takes into account the masses of all the isotopes of the element and their relative abundance.
(b) Isotopes:
Isotopes are atoms of the same element that have the same number of protons (and thus the same atomic number) but different numbers of neutrons, resulting in different mass numbers. This means that although they are chemically identical, they have different physical properties.
(ii) Calculation of RAM of element [tex]\(X\)[/tex]:
To calculate the Relative Atomic Mass (RAM) of element [tex]\(X\)[/tex], we need to use the given data for the isotopes and their natural abundances. The formula for RAM is:
[tex]\[ \text{RAM} = \left( \frac{\text{mass of isotope } 1 \times \text{%, abundance of isotope } 1}{100} \right) + \left( \frac{\text{mass of isotope } 2 \times \text{%, abundance of isotope } 2}{100} \right) \][/tex]
Given:
- Mass of [tex]\( ^{69}X \)[/tex] = 69
- Abundance of [tex]\( ^{69}X \)[/tex] = 60.4%
- Mass of [tex]\( ^{71}X \)[/tex] = 71
- Abundance of [tex]\( ^{71}X \)[/tex] = 39.6%
Plugging these values into the formula:
[tex]\[ \text{RAM} = \left( \frac{69 \times 60.4}{100} \right) + \left( \frac{71 \times 39.6}{100} \right) \][/tex]
Simplifying this expression:
[tex]\[ \text{RAM} = (69 \times 0.604) + (71 \times 0.396) \][/tex]
[tex]\[ \text{RAM} = 41.676 + 28.116 \][/tex]
[tex]\[ \text{RAM} = 69.792 \][/tex]
Rounded to one decimal place:
[tex]\[ \text{RAM} \approx 69.8 \][/tex]
Thus, the Relative Atomic Mass (RAM) of element [tex]\(X\)[/tex] is [tex]\(69.8\)[/tex].
(iii) Calculation of the mass of two moles of atoms of element [tex]\(X\)[/tex]:
To find the mass of two moles of atoms of element [tex]\(X\)[/tex], we use the relation that the mass of one mole of atoms of an element (in grams) is numerically equal to the RAM of the element in atomic mass units (amu).
So, if the RAM of element [tex]\(X\)[/tex] is [tex]\(69.8\)[/tex], then the mass of one mole of [tex]\(X\)[/tex] atoms is [tex]\(69.8 \text{ grams}\)[/tex].
Therefore, the mass of two moles of [tex]\(X\)[/tex] atoms would be:
[tex]\[ \text{Mass of two moles} = 2 \times 69.8 \text{ grams} \][/tex]
[tex]\[ \text{Mass of two moles} = 139.6 \text{ grams} \][/tex]
Thus, the mass of two moles of atoms of element [tex]\(X\)[/tex] is [tex]\(139.6\)[/tex] grams.
