Chapter 1: Problem 8

What is the number of carbon atoms in 0.5 nanomoles of carbon? One mole contains $6.02 \cdot 10^{23}$ atoms. a) $3.2 \cdot 10^{14}$ atoms d) $3.2 \cdot 10^{17}$ atoms b) $3.19 \cdot 10^{14}$ atoms e) $3.19 \cdot 10^{17}$ atoms c) $3 . \cdot 10^{14}$ atoms f) $3 . \cdot 10^{17}$ atoms

Short Answer

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a) $6.02 \cdot 10^{23}$ atoms b) $3.19 \cdot 10^{14}$ atoms c) $5.0 \cdot 10^{-10}$ atoms d) $2.50 \cdot 10^{9}$ atoms Answer: b) $3.19 \cdot 10^{14}$ atoms

Step by step solution

Convert nanomoles to moles

To convert the amount of carbon from nanomoles (nmol) to moles (mol), we need to remember the relationship between these units: 1 mole = $10^9$ nanomoles. So to convert 0.5 nmol of carbon to moles, simply divide by $10^9$: $$ 0.5 \ nmol \cdot \frac{1 \ mol}{10^9 \ nmol} = 0.5 \times 10^{-9} \ mol $$

Calculate the number of carbon atoms

Now that we have the amount of carbon in moles, we can use Avogadro's number ($6.02 \cdot 10^{23}$ atoms/mol) to calculate the number of carbon atoms. Multiply the amount in moles by Avogadro's number: $$ (0.5 \times 10^{-9} \ mol) \cdot (6.02 \cdot 10^{23} \ atoms/mol) = 3.01 \cdot 10^{14} \ atoms $$

Find the closest answer in the choices

Now that we have calculated the number of carbon atoms, we can look at the given options to find the closest answer. The closest answer to our calculated value ($3.01 \cdot 10^{14}$ atoms) is option b) $3.19 \cdot 10^{14}$ atoms.

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What is the number of carbon atoms in 0.5 nanomoles of carbon? One mole contains \(6.02 \cdot 10^{23}\) atoms. a) \(3.2 \cdot 10^{14}\) atoms d) \(3.2 \cdot 10^{17}\) atoms b) \(3.19 \cdot 10^{14}\) atoms e) \(3.19 \cdot 10^{17}\) atoms c) \(3 . \cdot 10^{14}\) atoms f) \(3 . \cdot 10^{17}\) atoms

Short Answer

Step by step solution

Convert nanomoles to moles

Calculate the number of carbon atoms

Find the closest answer in the choices

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