Select the correct answer. Thomas has [tex]$235$[/tex] grams of [tex]$K_2S$[/tex] in the chemistry lab. How many atoms of potassium (K) are in [tex]$235$[/tex] grams of the compound?
A. [tex]$2.13 \times 10^{23}$[/tex]
B. [tex]$4.26 \times 10^{23}$[/tex]
C. [tex]$2.57 \times 10^{24}$[/tex]
D. [tex]$3.37 \times 10^{24}$[/tex]
E. [tex]$7.08 \times 10^{24}$[/tex]
Answer (2)
Calculate the molar mass of K 2 S using the molar masses of K and S.
Determine the number of moles of K 2 S in 235 grams.
Calculate the number of moles of K atoms, which is twice the number of moles of K 2 S .
Find the number of K atoms by multiplying the moles of K by Avogadro's number, resulting in 2.57 × 1 0 24 .
Explanation
Calculate the molar mass of K2S First, we need to find the molar mass of K 2 S . The molar mass of potassium (K) is approximately 39.1 g/mol, and the molar mass of sulfur (S) is approximately 32.1 g/mol. Therefore, the molar mass of K 2 S is calculated as follows: M K 2 S = 2 × M K + M S = 2 × 39.1 + 32.1 = 78.2 + 32.1 = 110.3 g/mol (Note: The precise calculation using the tool gave 110.2616 g/mol, which we will use for higher accuracy.)
Calculate moles of K2S Next, we calculate the number of moles of K 2 S in 235 grams of the compound. We use the formula: moles = molar mass mass So, moles of K 2 S = 110.2616 g/mol 235 g = 2.131 mol (Note: The precise calculation using the tool gave 2.1312950292758313 mol, which we will use for higher accuracy.)
Calculate moles of K Since there are 2 atoms of potassium (K) in each molecule of K 2 S , the number of moles of K is twice the number of moles of K 2 S :
moles of K = 2 × moles of K 2 S = 2 × 2.131 = 4.262 mol (Note: The precise calculation using the tool gave 4.2625900585516625 mol, which we will use for higher accuracy.)
Calculate number of K atoms Now, we calculate the number of potassium atoms by multiplying the number of moles of K by Avogadro's number ( 6.022 × 1 0 23 atoms/mol): Number of K atoms = moles of K × Avogadro’s number = 4.262 × 6.022 × 1 0 23 = 2.566 × 1 0 24 atoms (Note: Using the more precise value 4.2625900585516625, we get 4.2625900585516625 × 6.022 × 1 0 23 = 2.5668 × 1 0 24 )
Select the correct answer Comparing our result with the given options, the closest answer is: C. 2.57 × 1 0 24
Examples
In chemistry, determining the number of atoms of a specific element in a compound is crucial for understanding reaction stoichiometry. For instance, if you're synthesizing a new material, knowing the exact atomic composition helps in predicting the material's properties and behavior. This calculation is also essential in quantitative analysis, where you might need to determine the amount of a specific element in a sample for quality control or environmental monitoring. By understanding the molar mass and Avogadro's number, we can accurately convert between mass and the number of atoms, enabling precise control over chemical processes and material design.
In 235 grams of potassium sulfide (K2S), there are approximately 2.57 x 10^24 potassium (K) atoms. This calculation involves determining the molar mass of K2S, calculating the moles of K2S present in the given mass, and then finding the number of K atoms based on the moles of K2S. The correct answer is C. 2.57 x 10^24.
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