How many molecules of SF6 are in [tex]$25.0 g SF _6$[/tex]?
([tex]$1 mol SF _6=146.06 g$[/tex])
([tex]$1 mol SF _6=6.02 \times 10^{23}$[/tex] molecules)
[?] [tex]$\times 10^{[?]}$[/tex] molecules [tex]$SF _6$[/tex]
Enter the coefficient and the exponent.
Answer (2)
Calculate the number of moles of S F 6 using the formula: moles = molar mass mass = 146.06 g/mol 25.0 g ≈ 0.17116 mol .
Determine the number of molecules using Avogadro's number: Number of molecules = moles × Avogadro’s number = 0.17116 mol × 6.02 × 1 0 23 mol molecules ≈ 1.03038 × 1 0 23 molecules .
Express the answer in scientific notation: 1.03 × 1 0 23 molecules.
The coefficient is 1.03 and the exponent is 23, so the final answer is 1.03 ; 23 .
Explanation
Problem Analysis We are given a mass of sulfur hexafluoride ( S F 6 ) and asked to find the number of molecules present in that mass. We are also given the molar mass of S F 6 and Avogadro's number, which relates moles to the number of molecules.
Calculating Moles of SF6 First, we need to find out how many moles of S F 6 are in 25.0 g. We can use the formula: moles = molar mass mass Plugging in the given values: moles of S F 6 = 146.06 g/mol 25.0 g The result of this division is approximately 0.17116 moles.
Calculating Number of Molecules Now that we know the number of moles, we can find the number of molecules using Avogadro's number, which states that 1 mole of any substance contains 6.02 × 1 0 23 molecules. Number of molecules = moles × Avogadro’s number Number of molecules of S F 6 = 0.17116 mol × 6.02 × 1 0 23 mol molecules Multiplying these values gives us approximately 1.03038 × 1 0 23 molecules.
Expressing the Answer in Scientific Notation Finally, we need to express the answer in the requested format: [ ?] × 1 0 [ ?] molecules S F 6 . Our calculated value is 1.03038 × 1 0 23 molecules. Therefore, the coefficient is approximately 1.03 and the exponent is 23.
Final Answer Therefore, there are approximately 1.03 × 1 0 23 molecules of S F 6 in 25.0 g of S F 6 .
Examples
Understanding how to convert between mass, moles, and the number of molecules is crucial in chemistry. For example, if you're conducting an experiment that requires a specific number of molecules of a reactant, you would use these calculations to determine the mass of the reactant you need to weigh out. This is essential in fields like pharmaceuticals, materials science, and environmental chemistry, where precise measurements are critical for successful outcomes. For instance, if a scientist needs to synthesize a new drug and the reaction requires 3.01 × 1 0 22 molecules of S F 6 , they would first calculate the required mass using the molar mass and Avogadro's number, ensuring the reaction proceeds as planned.
In 25.0 g of SF₆, there are approximately 1.03 × 1 0 23 molecules. We calculated this by determining the number of moles in the given mass and then using Avogadro's number to convert moles to molecules. The coefficient is 1.03 and the exponent is 23.
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