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How many molecules are present in 3.0 moles of \( \mathrm{CO}_{2} \) ? A. \( 6.02 \times 10^{23} \) molecules B. \( 1.81 \times 10^{24} \) molecules C. \( 9.03 \times 10^{23} \) molecules D. \( 3.61 \times 10^{24} \) molecules

Ask by Ellis Coles. in the United States
Jan 24,2025

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There are \(1.81 \times 10^{24}\) molecules in 3.0 moles of \( \mathrm{CO}_{2} \).

Solution

To determine the number of molecules in 3.0 moles of carbon dioxide (\(\mathrm{CO}_2\)), you can use Avogadro's number, which is approximately \(6.02 \times 10^{23}\) molecules per mole. **Calculation:** \[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \] \[ \text{Number of molecules} = 3.0 \, \text{moles} \times 6.02 \times 10^{23} \, \text{molecules/mole} = 1.806 \times 10^{24} \, \text{molecules} \] Rounding to two significant figures, this gives approximately \(1.81 \times 10^{24}\) molecules. **Answer:** **B. \(1.81 \times 10^{24}\) molecules**

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To find the number of molecules in 3.0 moles of \( \mathrm{CO}_{2} \), you can use Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) molecules per mole. By multiplying the number of moles (3.0) by Avogadro's number, you get: \[ 3.0 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} = 1.81 \times 10^{24} \, \text{molecules} \] So, the answer is B. \( 1.81 \times 10^{24} \) molecules. Did you know that the concept of a "mole" connects the microscopic world of atoms and molecules to the macroscopic scales we can measure? It's a bridge between chemistry and our everyday experience, allowing chemists to quantify substances in a way that's practically useful! In practical terms, when you calculate how many molecules are in a sample, it's essential to remember that precision counts! Always ensure to use the correct number of significant figures based on your measurements, as rounding errors can lead to significant discrepancies, especially in scientific calculations.

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