Answer:
[tex]\boxed {\boxed {\sf 0.070 \ g \ Si}}[/tex]
Explanation:
We are given a value of atoms and asked to find the mass. We can complete this in 2 steps.
1. Convert Atoms to Moles
First, we have to convert atoms to moles. We use Avogadro's Number or 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 silicon atoms. We can set up a proportion.
[tex]\frac { 6.022 \times 10^{23} \ atom \ Si }{1 \ mol \ Si}[/tex]
Multiply by the value of atoms given.
[tex]1.5 \times 10^{21} \ atom \ Si *\frac { 6.022 \times 10^{23} \ atom \ Si }{1 \ mol \ Si}[/tex]
Flip the ratio. This allows the atoms of silicon units to cancel and leave the moles of silicon.
[tex]1.5 \times 10^{21} \ atom \ Si *\frac {1 \ mol \ Si } {6.022 \times 10^{23} \ atom \ Si}[/tex]
[tex]1.5 \times 10^{21}*\frac {1 \ mol \ Si } {6.022 \times 10^{23} }[/tex]
[tex]\frac {1.5 \times 10^{21} \ mol \ Si } {6.022 \times 10^{23} }[/tex]
[tex]0.002490866822 \ mol \ Si[/tex]
2. Convert Moles to Grams
Next, we convert the moles to grams. We use the molar mass, which is found on the Periodic Table. This value is the number of grams in 1 mole of a substance. Look for silicon (Si).
Use this value as a ratio.
[tex]\frac {28.085 \ g \ Si}{1 \ mol \ Si}[/tex]
Multiply by the number of moles we calculated.
[tex]0.002490866822 \ mol \ Si *\frac {28.085 \ g \ Si}{1 \ mol \ Si}[/tex]
The moles of silicon units cancel, so we are left with grams.
[tex]0.002490866822 *\frac {28.085 \ g \ Si}{1}[/tex]
[tex]0.002490866822 *{28.085 \ g \ Si}[/tex]
[tex]0.06995599469 \ g \ Si[/tex]
3. Round
Finally we must round our answer. The original value has 2 significant figures, so our answer must have the same. For the number we calculated, that is the thousandth place.
[tex]0.069\underline95599469 \ g Si[/tex]
The 9 tells us to round the other 9 to a 0, then the 6 to a 7.
[tex]0.070 \ g \ Si[/tex]
The mass of 1.5 × 10²¹ silicon atoms is 0.070 grams of silicon.
