Jessica has 12.7 moles of a compound for an experiment. How many particles of the compound does she have?
A. $2.11 \times 10^{23}$
B. $4.74 \times 10^{23}$
C. $7.65 \times 10^{23}$
D. $4.74 \times 10^{24}$
E. $7.65 \times 10^{24}$
Answer (2)
Multiply the number of moles by Avogadro's number.
Perform the calculation: 12.7 × 6.022 × 1 0 23 = 7.64794 × 1 0 24 .
Round the result to two decimal places: 7.65 × 1 0 24 .
The final answer is 7.65 × 1 0 24 .
Explanation
Problem Analysis Jessica has 12.7 moles of a compound, and we need to find the number of particles in this amount. We know that 1 mole of any substance contains Avogadro's number of particles, which is approximately 6.022 × 1 0 23 . To find the total number of particles, we need to multiply the number of moles by Avogadro's number.
Solution Plan We will multiply the number of moles (12.7) by Avogadro's number ( 6.022 × 1 0 23 ) to find the total number of particles.
Calculations Number of particles = Number of moles × Avogadro's number Number of particles = 12.7 × 6.022 × 1 0 23
Result 12.7 × 6.022 × 1 0 23 = 7.64794 × 1 0 24
Final Answer The number of particles is approximately 7.65 × 1 0 24 . Therefore, the correct answer is E.
Examples
Understanding the number of particles in a given amount of substance is crucial in chemistry. For instance, if you're conducting an experiment that requires a specific number of molecules to react, you need to convert the number of moles into the number of particles to accurately measure the reactants. This calculation is also essential in fields like materials science, where the properties of materials are often determined by the arrangement and number of atoms or molecules.
Jessica has approximately 7.65 × 1 0 24 particles in 12.7 moles of the compound, calculated by multiplying the number of moles by Avogadro's number. Therefore, the correct answer is E: 7.65 × 1 0 24 .
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