Answer:
[tex]\boxed {\boxed {\sf 0.601 \ g \ As}}[/tex]
Explanation:
We want to convert atoms of arsenic to mass in grams. We have to complete 3 steps.
The first step is converting atoms to moles. We use Avogadro's Number for this. This number is 6.022*10²³ and it is the number of representative units (molecules, atoms, etc.) in 1 mole of a substance. In this problem, the particles are atoms of arsenic. So, 1 mole of arsenic contains 6.022*10²³ atoms of arsenic. Use this information to make a ratio.
[tex]\frac{1 \ mol \ As}{{6.022*10^{23} \ atoms \ As} }[/tex]
Multiply by the number of atoms provided in the problem: 4.83 × 10²¹
[tex]4.83 *10^{21} \ atoms \ As *\frac{1 \ mol \ As}{{6.022*10^{23} \ atoms \ As} }[/tex]
The units of atoms of arsenic (atoms As) cancel.
[tex]4.83 *10^{21} *\frac{1 \ mol \ As}{{6.022*10^{23}} }[/tex]
Condense into 1 fraction.
[tex]\frac{4.83 *10^{21} }{{6.022*10^{23}} } \ mol \ As[/tex]
[tex]0.008020591166 \ mol \ As[/tex]
The next step is converting moles to grams. We use the molar mass for this, which is provided. There are 74.92 grams of arsenic in 1 mole of arsenic, so we can make another ratio.
[tex]\frac {74.92 \ g\ As}{ 1 \ mol \ As}[/tex]
Multiply by the number of moles we calculated.
[tex]0.008020591166 \ mol \ As*\frac {74.92 \ g\ As}{ 1 \ mol \ As}[/tex]
The units of moles of arsenic (mol As) cancel.
[tex]0.008020591166 *\frac {74.92 \ g\ As}{ 1}[/tex]
[tex]0.6009026901 \ g \ As[/tex]
The original measurement of atoms (4.83 × 10²¹ ) has 3 significant figures, so our answer must have the same.
For the number we calculated, that is the thousandth place. The 9 in the ten-thousandth place (0.6009026901) tells us to round the 0 to a 1.
[tex]0.601 \ g \ As[/tex]
There are approximately 0.601 grams of arsenic.
