Q. 7.116 - An Introduction to General, Organic, and Biological Chemistry

Question

Liquid methanol ${\mathrm{CH}}_4\mathrm{O}$, which is used as a cooking fuel, burns with oxygen gas to produce the gases carbon dioxide and water. The reaction produces $363 \mathrm{kJ}$ of heat per mole of methanol.
a. Write a balanced equation for the reaction, including the heat of reaction.
b. Is the reaction endothermic or exothermic?
c. How many moles of ${\mathrm{O}}_2$ must react with $0.450$  mole of ${\mathrm{CH}}_4\mathrm{O}$
d. How many grams of ${\mathrm{CO}}_2$ are produced when $78.0 \mathrm{g}$ of ${\mathrm{CH}}_4\mathrm{O}$ reacts?

Step-by-Step Solution

Answer

Part(a) Balanced equation is ${\mathrm{CH}}_3\mathrm{OH}+\frac{3}{2}{\mathrm{O}}_2\to {\mathrm{CO}}_2+2{\mathrm{H}}_2\mathrm{O}$

Part(b) The reaction is exothermic.

Part(c) $0.675$ moles of $O_2$ must react with $0.45$ mole of $C{H}_{4}O$

Part(d) $107.25 \mathrm{g} {\mathrm{CO}}_2$ is produced when $78.0 \mathrm{g} {\mathrm{CH}}_4\mathrm{O}$ reacts.

Part(a) Step 1 : Given information

We are given that liquid methanol , which is used as a cooking fuel, burns with oxygen gas to produce the gases carbon dioxide and water. The reaction produces $363 \mathrm{kJ}$ of heat per mole of methanol.

Part(a) Step 2 : Simplify

As we know the reaction involved is ${\mathrm{CH}}_3\mathrm{OH}+{\mathrm{O}}_2\to {\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}$

Now we can see there are four hydrogen three oxygen and one carbon in left whereas one carbon three oxygen and two hydrogen at right. Therefore, Balanced equation will be ${\mathrm{CH}}_3\mathrm{OH}+\frac{3}{2}{\mathrm{O}}_2\to {\mathrm{CO}}_2+2{\mathrm{H}}_2\mathrm{O}$

Part(b) Step 1 : Given information

We are given that liquid methanol , which is used as a cooking fuel, burns with oxygen gas to produce the gases carbon dioxide and water. The reaction produces $363 \mathrm{kJ}$ of heat per mole of methanol.

Part(b) Step 2 : Simplify

The reaction is exothermic, As heat is released in the reaction according to question.

Part(c) Step 1 : Given information

We are given that liquid methanol , which is used as a cooking fuel, burns with oxygen gas to produce the gases carbon dioxide and water. The reaction produces $363 \mathrm{kJ}$ of heat per mole of methanol.

Part(c) Step 2 : Simplify

The reaction is ${\mathrm{CH}}_3\mathrm{OH}+\frac{3}{2}{\mathrm{O}}_2\to {\mathrm{CO}}_2+2{\mathrm{H}}_2\mathrm{O}$

Now, 

$$\begin{gathered} 1 \mathrm{mole} {\mathrm{CH}}_4\mathrm{O}=1.5 \mathrm{mole} {\mathrm{O}}_2 \\ 0.45 \mathrm{mole} {\mathrm{CH}}_4\mathrm{O}=0.675 \mathrm{mole} {\mathrm{O}}_2 \end{gathered}$$

Part(d) Step 1 : Given information

We are given that liquid methanol , which is used as a cooking fuel, burns with oxygen gas to produce the gases carbon dioxide and water. The reaction produces $363 \mathrm{kJ}$ of heat per mole of methanol.

Part(d) Step 2 : Simplify

The reaction is ${\mathrm{CH}}_3\mathrm{OH}+\frac{3}{2}{\mathrm{O}}_2\to {\mathrm{CO}}_2+2{\mathrm{H}}_2\mathrm{O}$

Now, according to question 

$1 \mathrm{mole} {\mathrm{CH}}_4\mathrm{O}=1 \mathrm{mole} {\mathrm{CO}}_2$

molar mass of methanol is $32 \mathrm{g}$

$$\begin{gathered} 32 \mathrm{g} {\mathrm{CH}}_4\mathrm{O}=44 \mathrm{g} {\mathrm{CO}}_2 \\ 78.0 \mathrm{g} {\mathrm{CH}}_4\mathrm{O}=107.25 \mathrm{g} {\mathrm{CO}}_2 \end{gathered}$$