Chapter 9: Problem 30

Use the equation provided to answer the questions that follow. $$2 \mathrm{Na}+2 \mathrm{H}_{2} \mathrm{O} \longrightarrow 2 \mathrm{NaOH}+\mathrm{H}_{2}$$ \begin{equation}\begin{array}{l}{\text { a. How many molecules of } \mathrm{H}_{2} \text { could be }} \\ {\text { made from } 27.6 \mathrm{g} \mathrm{H}_{2} \mathrm{O} \text { ? }} \\ {\text { b. How many atoms of Na will completely }} \\ {\text { react with } 12.9 \mathrm{g} \mathrm{H}_{2} \mathrm{O} \text { ? }} \\ {\text { c. How many molecules of } \mathrm{H}_{2} \text { could form }} \\ {\text { when } 6.59 \times 10^{20} \text { atoms Na react? }}\end{array}\end{equation}

Short Answer

Expert verified

a. Approximately $9.2 \times 10^{23}$ H2 molecules. b. Approximately $4.31 \times 10^{23}$ Na atoms. c. Approximately $6.62 \times 10^{20}$ H2 molecules.

Step by step solution

Conversion of Grams to Moles for H2O in Part a

Firstly, convert the given mass of H2O to moles using the molar mass of H2O. The molar mass of H2O is approximately 18.02 g/mol. Therefore, $27.6 \, g \, H_2O \times \frac{1 \, mol \, H_2O}{18.02 \, g \, H_2O}$ gives approximately 1.53 moles of H2O.

Calculation of H2 molecules in Part a

Next, given the 1:1 molar ratio of H2O to H2, the moles of H2O directly gives the moles of H2 that can be produced. Therefore, 1.53 moles of H2 can be formed. To convert this to molecules, multiply by Avogadro's number ($6.022 \times 10^{23} \, molecules/mol$). So, $1.53 \, mol \, H_2 \times 6.022 \times 10^{23} \, molecules/mol$ gives approximately $9.2 \times 10^{23}$ molecules of H2.

Conversion of Grams to Moles for H2O in Part b

Similarly, convert the given mass of H2O to moles in Part b using its molar mass. Performing the calculation $12.9 \, g \, H_2O \times \frac{1 \, mol \, H_2O}{18.02 \, g \, H_2O}$ gives approximately 0.717 moles of H2O.

Calculation of Na atoms in Part b

Given the 1:1 molar ratio of Na to H2O, the moles of Na needed equals to the moles of H2O. Therefore, 0.717 moles of Na are needed. To convert this to atoms, multiply by Avogadro's number. Performing the calculation $0.717 \, mol \, Na \times 6.022 \times 10^{23} \, atoms/mol$ gives approximately $4.31 \times 10^{23}$ atoms of Na.

Conversion of Na atoms to Moles in Part c

Convert the given number of Na atoms to moles in Part c using Avogadro's number. Performing the calculation $6.59 \times 10^{20} \, atoms \, Na \times \frac{1 \, mol}{6.022 \times 10^{23} \, atoms}$ gives approximately $0.00110$ moles of Na.

Calculation of H2 molecules in Part c

Given the 1:1 molar ratio of Na to H2, the moles of Na equals to the moles of H2 that can be formed. Therefore, $0.00110$ moles of H2 can be formed. To convert this to molecules, multiply by Avogadro's number. Performing the calculation $0.00110 \, mol \, H_2 \times 6.022 \times 10^{23} \, molecules/mol$ gives approximately $6.62 \times 10^{20}$ molecules of H2.

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Short Answer

Step by step solution

Conversion of Grams to Moles for H2O in Part a

Calculation of H2 molecules in Part a

Conversion of Grams to Moles for H2O in Part b

Calculation of Na atoms in Part b

Conversion of Na atoms to Moles in Part c

Calculation of H2 molecules in Part c

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