Chapter 7, Problem 43Q

Small quantities of hydrogen gas can be prepared in the lab by reacting metallic sodium with water, as shown in this equation.

$2\text{Na}(s)+2{\text{H}}_2\text{O}(l)\to {\text{H}}_2(g)+2\text{NaOH}(aq)$

1. a. Calculate the grams of sodium needed to produce 1.0 mol of hydrogen gas.
2. b. Calculate the grams of sodium needed to produce sufficient hydrogen to meet an American’s daily energy requirement of 1.1 × 10⁶ kJ.
3. c. If the price of sodium were $165/kg, what would be the cost of producing 1.0 mol of hydrogen? Assume the cost of water is negligible.

Interpretation Introduction

Interpretation:

How many grams of sodium needed to produce $1.0mol$ of hydrogen gas has to be calculated.

Concept introduction:

Oxidation: The gain of oxygen or the loss of hydrogen or the loss of an electron in a species during a redox reaction is called oxidation.

Reduction: The loss of oxygen or the gain of hydrogen or gain of an electron in a species during a redox reaction is called reduction.

Balanced equation: A balanced chemical equation is an equation which contains same elements in same number on both the sides (reactant and product side) of the chemical equation thereby obeying the law of conservation of mass.

The equation for a reaction, which has same number of atoms and charge of the ions in both reactants and product sides, is known as balanced equation.

Energy of Combustion: The energy released in the form of heat when given substance undergoes combustion reaction.

Explanation of Solution

Given decomposition reaction is,

A balanced equation will have same elements and same number of atoms of each side of the reaction.

$2Na(s)+2H_{2}O(l)\underset{}{\to }{H}_2(g)\uparrow +2NaOH(aq)$

Small quantities of hydrogen gas produced in the reacting metallic sodium with water.

Calculation of hydrogen gas formation:

Two moles of metallic sodium react with water to produced two moles of $NaOH$

$1.0mol{H}_2\times \frac{2molNa}{1molof{H}_2}\times \frac{23.0gNa}{1molNa}=46.0gNa$ 

Therefore, the $46.0gNa$ is needed to produced small quantities of hydrogen gas.

Interpretation Introduction

Interpretation:

How many grams of sodium needed to produce sufficient hydrogen to meet a given requirement energy has to be calculated. 

Concept introduction:

Oxidation: The gain of oxygen or the loss of hydrogen or the loss of an electron in a species during a redox reaction is called oxidation.

Reduction: The loss of oxygen or the gain of hydrogen or gain of an electron in a species during a redox reaction is called reduction.

Balanced equation: A balanced chemical equation is an equation which contains same elements in same number on both the sides (reactant and product side) of the chemical equation thereby obeying the law of conservation of mass.

The equation for a reaction, which has same number of atoms and charge of the ions in both reactants and product sides, is known as balanced equation.

Energy of Combustion: The energy released in the form of heat when given substance undergoes combustion reaction.

Explanation of Solution

Given decomposition reaction is,

A balanced equation will have same elements and same number of atoms of each side of the reaction.

$2Na(s)+2H_{2}O(l)\underset{}{\to }{H}_2(g)\uparrow +2NaOH(aq)$

Small quantities of hydrogen gas produced in the reacting metallic sodium with water.

Requirement energy calculation:

Two moles of metallic sodium react with water to produced two moles of $NaOH$

$1.1\times {10}^{6}kJ\times \frac{1mol{H}_2}{249kJ}\times \frac{2molNa}{1molof{H}_2}\times \frac{23.0gNa}{1molNa}=2.10\times {10}^{5}gNa$ 

Therefore, the $2.10\times {10}^{5}gNa$ of sodium needed to produce sufficient hydrogen to meet an daily requirement energy of $1.1\times {10}^{6}kJ$.

Interpretation Introduction

Interpretation:

From the give data and assumption, the cost of producing the given mole of hydrogen has to be found.

Concept introduction:

Oxidation: The gain of oxygen or the loss of hydrogen or the loss of an electron in a species during a redox reaction is called oxidation.

Reduction: The loss of oxygen or the gain of hydrogen or gain of an electron in a species during a redox reaction is called reduction.

Balanced equation: A balanced chemical equation is an equation which contains same elements in same number on both the sides (reactant and product side) of the chemical equation thereby obeying the law of conservation of mass.

The equation for a reaction, which has same number of atoms and charge of the ions in both reactants and product sides, is known as balanced equation.

Energy of Combustion: The energy released in the form of heat when given substance undergoes combustion reaction.

Explanation of Solution

Given hydrogen formation reaction is,

$2Na(s)+2H_{2}O(l)\underset{}{\to }{H}_2(g)\uparrow +2NaOH(aq)$

Small quantities of hydrogen gas produced in the reacting metallic sodium with water.

Using the result from calculation part (a):

The obtained grams of sodium is $46.0g$

The price of sodium per Kg =$\$165$

$46.0gNa\times \frac{1kgNa}{{10}^{3}gNa}\times \frac{\$165}{1kgNa}=\$7.59$ 

Therefore,

The $\$7.59$ cost must be required to be producing $1.0mol$ of hydrogen.