How many atoms does 32 g of sulfur contain?
A. $32 \times\left(6.02 \times 10^{23}\right)$
B. $\frac{6.02 \times 10^{23}}{16}$
C. $6.02 \times 10^{23}$
D. $\frac{6.02 \times 10^{23}}{32}$
Answer (1)
Calculate the number of moles of sulfur: moles = 32 g/mol 32 g = 1 mol .
Multiply the number of moles by Avogadro's number to find the number of atoms: 1 mol × 6.02 × 1 0 23 atoms/mol .
The number of atoms in 32 g of sulfur is 6.02 × 1 0 23 .
Therefore, the correct answer is 6.02 × 1 0 23 .
Explanation
Problem Analysis We are asked to find the number of atoms in 32 g of sulfur. We know that the molar mass of sulfur is 32 g/mol, and Avogadro's number is approximately 6.022 × 1 0 23 atoms/mol. This means that one mole of sulfur weighs 32 grams and contains 6.022 × 1 0 23 atoms.
Calculating Moles of Sulfur First, we need to find the number of moles in 32 g of sulfur. We can use the formula: moles = molar mass given mass In this case, the given mass is 32 g and the molar mass of sulfur is 32 g/mol. So, moles of sulfur = 32 g/mol 32 g = 1 mol This means we have 1 mole of sulfur.
Calculating Number of Atoms Now, we need to find the number of atoms in 1 mole of sulfur. We know that 1 mole of any substance contains Avogadro's number of atoms, which is approximately 6.022 × 1 0 23 atoms/mol. Therefore, number of atoms = moles × Avogadro’s number number of atoms = 1 mol × 6.022 × 1 0 23 atoms/mol = 6.022 × 1 0 23 atoms So, 32 g of sulfur contains approximately 6.022 × 1 0 23 atoms.
Final Answer Comparing our result with the given options, we see that option C, 6.02 × 1 0 23 , is the closest to our calculated value. Therefore, the correct answer is C.
Conclusion Therefore, 32 g of sulfur contains 6.02 × 1 0 23 atoms.
Examples
Understanding the number of atoms in a given mass of a substance is crucial in various fields, such as chemistry and materials science. For example, if you're synthesizing a new material and need to combine sulfur with another element in a specific atomic ratio, you need to know how many atoms are present in a given mass of sulfur. This calculation ensures that you have the correct proportions of each element to achieve the desired properties of the new material. Imagine you are creating a compound where you need exactly one sulfur atom for every carbon atom. Knowing the atomic mass and using Avogadro's number, you can accurately measure the mass of sulfur needed to react with a known amount of carbon.
