How many molecules of chlorine are in $0.500 mol Cl _2$ gas?
A. $1.20 \times 10^{23}$ molecules
B. $3.01 \times 10^{24}$ molecules
C. $1.20 \times 10^{24}$ molecules
D. $3.01 \times 10^{23}$ molecules
Answer (2)
We are given 0.500 mol of C l 2 gas.
We need to find the number of molecules of chlorine in the given amount.
We use Avogadro's number ( 6.022 × 1 0 23 molecules/mol) to convert moles to molecules.
Number of molecules = 0.500 × 6.022 × 1 0 23 = 3.011 × 1 0 23 . The final answer is 3.01 I m es 1 0 23 molecules.
Explanation
Problem Analysis We are asked to find the number of chlorine molecules ( C l 2 ) in 0.500 moles of C l 2 gas. To do this, we will use Avogadro's number, which is the number of molecules in one mole of any substance. Avogadro's number is approximately 6.022 I m es 1 0 23 molecules/mol.
Calculation Setup To find the number of molecules, we multiply the number of moles by Avogadro's number:
Number of molecules = (moles of C l 2 ) × (Avogadro's number)
Plugging in the values Now, we plug in the given values:
Number of molecules = 0.500 mol × 6.022 × 1 0 23 mol molecules
Calculating the Result Performing the calculation:
Number of molecules = 3.011 × 1 0 23 molecules
Final Answer Therefore, there are 3.011 × 1 0 23 molecules of chlorine in 0.500 mol of C l 2 gas. Among the given options, the closest one is 3.01 I m es 1 0 23 molecules.
Examples
Understanding how to convert moles to the number of molecules is crucial in many areas. For example, if you're working in a lab and need to prepare a solution with a specific concentration, you need to know how many molecules of a substance you're adding to the solution. Suppose you are synthesizing a new drug and need to know exactly how many molecules of a reactant are needed to react with another compound. If you know the number of moles, you can easily convert it to the number of molecules using Avogadro's number, ensuring the reaction proceeds as expected. This calculation ensures accuracy and efficiency in chemical reactions and experiments.
To find the number of molecules in 0.500 mol of C l 2 , we use Avogadro's number, which results in approximately 3.011 × 1 0 23 molecules. The answer closest to this calculation is D: 3.01 × 1 0 23 .
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