Silver has an atomic mass of 108 amu. How many silver atoms does it take to make 1.0 gram of Silver.
The Correct Answer and Explanation is:
Step-by-Step Solution
Given:
- Atomic mass of silver (Ag) = 108 amu
- Mass of silver sample = 1.0 gram
- Avogadro’s number = 6.022×10236.022 \times 10^{23}6.022×1023 atoms/mol
Step 1: Convert grams of silver to moles. Moles of Ag=1.0 g108 g/mol=0.00926 mol\text{Moles of Ag} = \frac{1.0\ \text{g}}{108\ \text{g/mol}} = 0.00926\ \text{mol}Moles of Ag=108 g/mol1.0 g=0.00926 mol
Step 2: Convert moles to atoms using Avogadro’s number. Atoms of Ag=0.00926 mol×6.022×1023 atoms/mol\text{Atoms of Ag} = 0.00926\ \text{mol} \times 6.022 \times 10^{23}\ \text{atoms/mol}Atoms of Ag=0.00926 mol×6.022×1023 atoms/mol Atoms of Ag≈5.58×1021 atoms\text{Atoms of Ag} \approx 5.58 \times 10^{21}\ \text{atoms}Atoms of Ag≈5.58×1021 atoms
Explanation
Silver is a metallic element with the symbol Ag and an atomic mass of approximately 108 atomic mass units (amu). The atomic mass tells how many grams one mole of silver atoms weighs. In this case, 1 mole of silver weighs 108 grams and contains 6.022×10236.022 \times 10^{23}6.022×1023 atoms, a constant known as Avogadro’s number.
To determine how many atoms are in a smaller sample, such as 1.0 gram of silver, begin by calculating the number of moles in the sample. This is done by dividing the sample mass by the molar mass (atomic mass in g/mol). For silver: Moles=1.0 g108 g/mol=0.00926 mol\text{Moles} = \frac{1.0\ \text{g}}{108\ \text{g/mol}} = 0.00926\ \text{mol}Moles=108 g/mol1.0 g=0.00926 mol
This means the 1.0 gram of silver contains about 0.00926 moles of silver atoms. To find how many individual atoms this represents, multiply the number of moles by Avogadro’s number: 0.00926 mol×6.022×1023 atoms/mol=5.58×1021 atoms0.00926\ \text{mol} \times 6.022 \times 10^{23}\ \text{atoms/mol} = 5.58 \times 10^{21}\ \text{atoms}0.00926 mol×6.022×1023 atoms/mol=5.58×1021 atoms
Therefore, 1.0 gram of silver contains approximately 5.58×10215.58 \times 10^{21}5.58×1021 silver atoms. This large number highlights the tiny mass and size of individual atoms. Even in a sample as small as 1.0 gram, the quantity of atoms present is astronomically large. This concept is central to understanding chemical reactions, where atoms interact in mole-based proportions to form new substances.
