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Answer :
To determine which statements about the atomic mass and molar mass are true, let's analyze each option:
Statement A:
"If one atom of [tex]\({ }^{12} C\)[/tex] has a mass of 12.0 amu, one mole of [tex]\({ }^{12} C\)[/tex] atoms has a mass of [tex]\(12\)[/tex] grams."
- An atom of [tex]\({ }^{12} C\)[/tex] has a mass of 12.0 atomic mass units (amu).
- By definition, one mole of any element in grams is numerically equal to its atomic mass in amu.
- Therefore, one mole of [tex]\({ }^{12} C\)[/tex] indeed has a mass of 12 grams.
This statement is true.
Statement B:
"If one mole of [tex]\({ }^{39} K\)[/tex] has a mass of 39.1 grams, the mass of one atom of [tex]\({ }^{39} K\)[/tex] is [tex]\(39.1 \times 10^{-23}\)[/tex] grams."
- One mole of [tex]\({ }^{39} K\)[/tex] (potassium) has a mass of 39.1 grams.
- To find the mass of a single atom, divide the molar mass by Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex]).
- The calculation should give the mass of one atom as approximately [tex]\(6.49 \times 10^{-23}\)[/tex] grams, not [tex]\(39.1 \times 10^{-23}\)[/tex] grams.
This statement is false.
Statement C:
"If one atom of [tex]\({ }^{223} Fr\)[/tex] has a mass of 223.0 amu, one mole of [tex]\({ }^{223} Fr\)[/tex] has a mass of [tex]\(223.0 \times 10^{23}\)[/tex] grams."
- An atom of [tex]\({ }^{223} Fr\)[/tex] has a mass of 223.0 amu.
- One mole of [tex]\({ }^{223} Fr\)[/tex] should have a mass of 223.0 grams, matching the atomic mass in amu.
- Multiplying by [tex]\(10^{23}\)[/tex] is incorrect here.
This statement is false.
Statement D:
"If one atom of [tex]\({ }^{127} I\)[/tex] has a mass of 126.9 amu, one mole of [tex]\({ }^{127} I\)[/tex] has a mass of 126.9 grams."
- An atom of [tex]\({ }^{127} I\)[/tex] has a mass of 126.9 amu.
- One mole of [tex]\({ }^{127} I\)[/tex] has a mass of 126.9 grams, consistent with the atomic mass in amu.
This statement is true.
So, the true statements are A and D.
Statement A:
"If one atom of [tex]\({ }^{12} C\)[/tex] has a mass of 12.0 amu, one mole of [tex]\({ }^{12} C\)[/tex] atoms has a mass of [tex]\(12\)[/tex] grams."
- An atom of [tex]\({ }^{12} C\)[/tex] has a mass of 12.0 atomic mass units (amu).
- By definition, one mole of any element in grams is numerically equal to its atomic mass in amu.
- Therefore, one mole of [tex]\({ }^{12} C\)[/tex] indeed has a mass of 12 grams.
This statement is true.
Statement B:
"If one mole of [tex]\({ }^{39} K\)[/tex] has a mass of 39.1 grams, the mass of one atom of [tex]\({ }^{39} K\)[/tex] is [tex]\(39.1 \times 10^{-23}\)[/tex] grams."
- One mole of [tex]\({ }^{39} K\)[/tex] (potassium) has a mass of 39.1 grams.
- To find the mass of a single atom, divide the molar mass by Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex]).
- The calculation should give the mass of one atom as approximately [tex]\(6.49 \times 10^{-23}\)[/tex] grams, not [tex]\(39.1 \times 10^{-23}\)[/tex] grams.
This statement is false.
Statement C:
"If one atom of [tex]\({ }^{223} Fr\)[/tex] has a mass of 223.0 amu, one mole of [tex]\({ }^{223} Fr\)[/tex] has a mass of [tex]\(223.0 \times 10^{23}\)[/tex] grams."
- An atom of [tex]\({ }^{223} Fr\)[/tex] has a mass of 223.0 amu.
- One mole of [tex]\({ }^{223} Fr\)[/tex] should have a mass of 223.0 grams, matching the atomic mass in amu.
- Multiplying by [tex]\(10^{23}\)[/tex] is incorrect here.
This statement is false.
Statement D:
"If one atom of [tex]\({ }^{127} I\)[/tex] has a mass of 126.9 amu, one mole of [tex]\({ }^{127} I\)[/tex] has a mass of 126.9 grams."
- An atom of [tex]\({ }^{127} I\)[/tex] has a mass of 126.9 amu.
- One mole of [tex]\({ }^{127} I\)[/tex] has a mass of 126.9 grams, consistent with the atomic mass in amu.
This statement is true.
So, the true statements are A and D.
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