Chapter 12, Problem 46A

a.

Interpretation Introduction

Interpretation: To calculate the moles of each reactant.

Concept Introduction: A mole is $6.02\times {10}^{23}$ atoms/molecules. The SI unit for the amount of substance is a mole and it is represented by “mol”.

The coefficients are the numbers that are written in front of the chemical formula/symbol in order to balance a chemical reaction. The coefficients help in determining the conversion factors between the number of moles for two different substances in a chemical equation.

Answer to Problem 46A

The number of moles of carbon monoxide is $11.3$ moles.

The number of moles of hydrogen is $22.5$ moles.

Explanation of Solution

The given chemical reaction is depicted as follows:

  $\text{CO}\left(g\right)+2{\text{H}}_{\text{2}}\left(g\right)\to {\text{CH}}_3\text{OH}\left(g\right)$

When one mole of carbon monoxide reacts with two moles of hydrogen, it yields one mole of methanol.

The grams of methanol are given i.e., $3.60\times {10}^2\text{ g}$ .

The molar mass of methanol is $32.0{\text{ g mol}}^{-1}$ .

Therefore, the moles of carbon monoxide can be calculated as follows:

  $\text{3}\text{.60}\times {10}^2\cancel{{\text{g CH}}_3\text{OH}}\times \frac{1\cancel{{\text{mol CH}}_3\text{OH}}}{\text{32}\text{.0 }\cancel{{\text{g CH}}_3\text{OH}}}\times \frac{1\text{ mol CO}}{1\cancel{{\text{mol CH}}_3\text{OH}}}=11.3\text{ mol CO}$

Thus, the number of moles of carbon monoxide is $11.3$ moles.

The calculation for moles of hydrogen is as follows:

  $\text{3}\text{.60}\times {10}^2\cancel{{\text{g CH}}_3\text{OH}}\times \frac{1\cancel{{\text{mol CH}}_3\text{OH}}}{\text{32}\text{.0 }\cancel{{\text{g CH}}_3\text{OH}}}\times \frac{{\text{2 mol H}}_2}{1\cancel{{\text{mol CH}}_3\text{OH}}}=22.5{\text{ mol H}}_2$

Thus, the number of moles of hydrogen is $22.5$ moles.

b.

Interpretation Introduction

Interpretation: To calculate the number of grams of each reactant.

Concept Introduction: A mole is $6.02\times {10}^{23}$ atoms/molecules. The SI unit for the amount of substance is a mole and it is represented by “mol”.

The coefficients are the numbers that are written in front of the chemical formula/symbol in order to balance a chemical reaction. In a balanced chemical equation, the coefficients help in determining the conversion factors between the number of moles for two different substances in a chemical equation.

Answer to Problem 46A

The grams of carbon monoxide are $112$ grams.

The grams of hydrogen are $16$ grams.

Explanation of Solution

The given chemical reaction is depicted as follows:

  $\text{CO}\left(g\right)+2{\text{H}}_{\text{2}}\left(g\right)\to {\text{CH}}_3\text{OH}\left(g\right)$

When one mole of carbon monoxide reacts with two moles of hydrogen, it yields one mole of methanol.

The moles of methanol are given i.e., $4.00\text{ mol}$ .

The molar mass of carbon monoxide is $28.0{\text{ g mol}}^{-1}$ .

Therefore, the grams of carbon monoxide can be calculated as follows:

  $4.00\cancel{{\text{mol CH}}_3\text{OH}}\times \frac{1\cancel{\text{mol CO}}}{1\cancel{{\text{mol CH}}_3\text{OH}}}\times \frac{\text{28}\text{.0 g CO}}{1\cancel{\text{mol CO}}}=112\text{ g CO}$

Thus, the grams of carbon monoxide are $112$ grams.

The calculation for grams of hydrogen is as follows:

The molar mass of hydrogen is $2.0{\text{ g mol}}^{-1}$ .

  $4.00\cancel{{\text{mol CH}}_3\text{OH}}\times \frac{\text{2 }\cancel{{\text{mol H}}_2}}{1\cancel{{\text{mol CH}}_3\text{OH}}}\times \frac{\text{2}{\text{.0 g H}}_2}{1\cancel{{\text{mol H}}_2}}=16{\text{ g H}}_2$

Thus, the grams of hydrogen are $16$ grams.

c.

Interpretation Introduction

Interpretation: To calculate the grams of hydrogen needed to react.

Concept Introduction: A mole is $6.02\times {10}^{23}$ atoms/molecules. The SI unit for the amount of substance is a mole and it is represented by “mol”.

The coefficients are the numbers that are written in front of the chemical formula/symbol in order to balance a chemical reaction. In a balanced chemical equation, the coefficients help in determining the conversion factors between the number of moles for two different substances in a chemical equation.

Answer to Problem 46A

The grams of hydrogen are $11$ grams.

Explanation of Solution

The given chemical reaction is depicted as follows:

  $\text{CO}\left(g\right)+2{\text{H}}_{\text{2}}\left(g\right)\to {\text{CH}}_3\text{OH}\left(g\right)$

When one mole of carbon monoxide reacts with two moles of hydrogen, it yields one mole of methanol.

The moles of carbon monoxide is given, i.e., $2.85\text{ mol}$ .

The calculation for grams of hydrogen is as follows:

The molar mass of hydrogen is $2.0{\text{ g mol}}^{-1}$ .

  $2.85\cancel{\text{mol CO}}\times \frac{\text{2 }\cancel{{\text{mol H}}_2}}{1\cancel{\text{mol CO}}}\times \frac{\text{2}{\text{.0 g H}}_2}{1\cancel{{\text{mol H}}_2}}=11{\text{ g H}}_2$

Thus, the grams of hydrogen are $11$ grams.