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Answer :
Approximately 1.28 x 10²âµ molecules of sulfur trioxide (SO₃) are represented by 1.70 kg.
To determine how many molecules are represented by 1.70 kg of sulfur trioxide (SO₃), we will follow these steps:
Convert the mass from kilograms to grams:
Since there are 1000 grams in 1 kilogram, we can convert 1.70 kg to grams as follows:
[tex]1.70 \text{ kg} \times 1000 \frac{g}{kg} = 1700 \text{ g}[/tex]
Calculate the molar mass of sulfur trioxide (SO₃):
To find the molar mass of SO₃, we need to sum the atomic masses of its components: sulfur (S) and oxygen (O).
- The atomic mass of sulfur is approximately 32.07 g/mol.
- The atomic mass of oxygen is approximately 16.00 g/mol.
- Since there are three oxygen atoms in sulfur trioxide, we calculate:
[tex]\text{Molar mass of SO₃} = 32.07 \text{ g/mol} + (3 \times 16.00 \text{ g/mol}) = 32.07 \text{ g/mol} + 48.00 \text{ g/mol} = 80.07 \text{ g/mol}[/tex]
Calculate the number of moles in 1700 grams of SO₃:
We can find the number of moles by dividing the mass of the compound by its molar mass:
[tex]\text{Number of moles of SO₃} = \frac{1700 \text{ g}}{80.07 \text{ g/mol}} \approx 21.23 \text{ mol}[/tex]
Determine the number of molecules:
To find the number of molecules, we use Avogadro's number, which states that 1 mole of any substance contains approximately 6.022 x 10²³ entities (molecules, in this case). Thus, we can calculate the number of molecules as follows:
[tex]\text{Number of molecules} = 21.23 \text{ mol} \times 6.022 \times 10^{23} \frac{molecules}{mol} \approx 1.28 \times 10^{25} \text{ molecules}[/tex].
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