Incandescent light bulbs produce light by heating a metal filament until it glows. The most common filament is tungsten, a grayish metal with atomic number 74 .
Incandescent light bulbs with tungsten filaments

A certain tungsten filament has a mass of $0.0176 \mathrm{~g}$.
How many tungsten atoms make up the filament?
Express your answer in scientific notation with two decimal places.
Show Avogadro's number
$\square$ atoms of tungsten

Question

Incandescent light bulbs produce light by heating a metal filament until it glows. The most common filament is tungsten, a grayish metal with atomic number 74 .
Incandescent light bulbs with tungsten filaments

A certain tungsten filament has a mass of $0.0176 \mathrm{~g}$.
How many tungsten atoms make up the filament?
Express your answer in scientific notation with two decimal places.
Show Avogadro's number
$\square$ atoms of tungsten

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Determine the molar mass of tungsten**: The atomic mass of tungsten (W) is approximately $183.84 \, \text{g/mol}$. ‖ ‖ 2 ⋮ **Calculate the number of moles of tungsten**: Use the formula $n = \frac{m}{M}$, where $n$ is the number of moles, $m$ is the mass of the tungsten filament, and $M$ is the molar mass of tungsten. $$ n = \frac{0.0176 \, \text{g}}{183.84 \, \text{g/mol}} \approx 9.57 \times 10^{-5} \, \text{mol} $$ ‖ ‖ 3 ⋮ **Use Avogadro's number to find the number of atoms**: Avogadro's number is $6.022 \times 10^{23} \, \text{atoms/mol}$. Multiply the number of moles by Avogadro's number to get the number of atoms. $$ \text{Number of atoms} = 9.57 \times 10^{-5} \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 5.76 \times 10^{19} \, \text{atoms} $$ ‖ ∻Answer∻ ⚹ $5.76 \times 10^{19}$ atoms of tungsten ⚹ ∻Key Concept∻ ⚹ Molar mass and Avogadro's number ⚹ ∻Explanation∻ ⚹ The molar mass of tungsten and Avogadro's number are used to convert the mass of the tungsten filament to the number of atoms. ⚹◊What is the atomic number of tungsten?⍭ Generate me a similar question◊

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