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Sagot :
Answer:
[tex]\boxed {\boxed {\sf 1.57 \ g \ Pt}}[/tex]
Explanation:
We are asked to find the mass of 4.84 × 10²¹ platinum (Pt) atoms.
1. Atoms to Moles
First, we convert atoms to moles using Avogadro's Number of 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this case, the particles are platinum atoms. There are 6.022 × 10²³ platinum atoms in 1 mole of platinum.
We will convert using dimensional analysis, so we set up a ratio using the underlined information.
[tex]\frac {6.022 \times 10^{23} \ atoms \ Pt }{ 1 \ mol \ Pt}[/tex]
We are converting 4.84 × 10²¹ platinum atoms to moles, so we multiply the ratio by this value.
[tex]4.84 \times 10^{21} \ atoms \ Pt *\frac {6.022 \times 10^{23} \ atoms \ Pt }{ 1 \ mol \ Pt}[/tex]
Flip the ratio so the units of atoms of platinum cancel.
[tex]4.84 \times 10^{21} \ atoms \ Pt *\frac{ 1 \ mol \ Pt} {6.022 \times 10^{23} \ atoms \ Pt }[/tex]
[tex]4.84 \times 10^{21} *\frac{ 1 \ mol \ Pt} {6.022 \times 10^{23} }[/tex]
[tex]\frac{4.84 \times 10^{21} } {6.022 \times 10^{23} } \ mol \ Pt[/tex]
[tex]0.008037196945 \ mol \ Pt[/tex]
2. Moles to Grams
Next, we convert moles to grams using the molar mass. This is the mass of 1 mole of a substance. It is found on the Periodic Table because it is equal to the atomic mass, but the units are grams per mole instead of atomic mass units.
Look up the molar mass of platinum.
- Pt: 195.08 g/mol
Set up another ratio using the molar mass.
[tex]\frac {195.08 \ g \ Pt}{ 1 \ mol \ Pt}[/tex]
We multiply the ratio by the number of moles we calculated.
[tex]0.008037196945 \ mol \ Pt * \frac{195.08 \ g \ Pt}{ 1 \ mol \ Pt}[/tex]
The units of moles of platinum cancel.
[tex]0.008037196945 * \frac{195.08 \ g \ Pt}{ 1 }[/tex]
[tex]0.008037196945 * {195.08 \ g \ Pt}[/tex]
[tex]1.56789638 \ g \ Pt[/tex]
3. Round
The original value of atoms has 3 significant figures, so our answer must have the same. For the number we found, that is the hundredth place. The 7 in the thousandth place tells us to round the 6 up to a 7.
[tex]1.57 \ g \ Pt[/tex]
4.84 × 10²¹ platinum atoms have a mass of 1.57 grams.
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