Question

The measured enthalpy change for burning ketene$\left({\text{CH}}_2\text{CO}\right){\mathbf{\text{,CH}}}_{\mathbf{2}}\mathbf{\text{CO}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{\text{CO}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\text{O}}\mathbf{\left(}\mathit{g}\mathbf{\right)}$is $\mathbf{∆}{\mathit{H}}_{\mathbf{2}}\mathbf{=}\mathbf{}\mathbf{802}\mathbf{.}\mathbf{3}\mathit{k}\mathit{J}\mathbf{}\mathit{a}\mathit{t}\mathbf{}{\mathbf{25}}^{\mathbf{\circ }}\mathit{C}$ $\Delta H_1=-981.1\text{kJ}$at 25⁰C. The enthalpy change for burning methane

${\mathbf{\text{CH}}}_{\mathbf{4}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\to }{\mathbf{\text{CO}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\text{O}}\mathbf{\left(}\mathit{g}\mathbf{\right)}$is $\Delta H_2=802.3\text{kJ}$at 25⁰C. Calculate the enthalpy change at 25⁰Cfor the reaction

$2{\text{CH}}_4\left(g\right)+2{\text{O}}_2\left(g\right)\to {\text{CH}}_2\text{CO}\left(g\right)+3{\text{H}}_2\text{O}\left(g\right)$$\mathbf{2}{\mathbf{\text{CH}}}_{\mathbf{4}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\to }{\mathbf{\text{CH}}}_{\mathbf{2}}\mathbf{\text{CO}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\text{O}}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

Short answer

The heat change of the reaction,$\Delta H=-623.5\text{kJ}$

Step-by-step solution

Given data

The following reaction is given,

(a) ${\text{CH}}_2\text{CO}\left(g\right)+2{\text{O}}_2\left(g\right)\to 2{\text{CO}}_2\left(g\right)+{\text{H}}_2\text{O}\left(g\right),\Delta H_1=-981.1\text{kJ}$.

(b) ${\text{CH}}_4\left(g\right)+2{\text{O}}_2\left(g\right)\to {\text{CO}}_2\left(g\right)+2{\text{H}}_2\text{O}\left(g\right),\Delta H_2=-802.3\text{kJ}$.

Concept of the heat capacity

The ratio of heat absorbed by a substance to the temperature change is called heat capacity. In terms of the actual amount of material being considered, most frequently a mole, it is usually stated as calories per degree (the molecular weight in grams)

Simplify the reaction

To combine the two given reactions in a way that their sum is the needed reaction.

$$\begin{gathered} 1. {\text{CH}}_2\text{CO}\left(g\right)+2{\text{O}}_2\left(g\right)\to 2{\text{CO}}_2\left(g\right)+{\text{H}}_2\text{O}\left(g\right) \\ 2.{\text{CH}}_4\left(g\right)+2{\text{O}}_2\left(g\right)\to {\text{CO}}_2\left(g\right)+2{\text{H}}_2\text{O}\left(g\right) \end{gathered}$$

Start by multiplication of equation (1 ) reaction by (-1).

$$\begin{gathered} {\text{1. CH}}_2\text{CO}\left(g\right)+2{\text{O}}_2\left(g\right)\to 2{\text{CO}}_2\left(g\right)+{\text{H}}_{2}O\left(g\right)/\times (-1)a \\ 2.{\text{CH}}_4\left(g\right)+2{\text{O}}_2\left(g\right)\to {\text{CO}}_2\left(g\right)+2{\text{H}}_{2}O\left(g\right) \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ 1.2{\text{CO}}_2\left(g\right)+{\text{H}}_{2}O\left(g\right)\to {\text{CH}}_2\text{CO}\left(g\right)+2{\text{O}}_2\left(g\right) \\ 2.{\text{CH}}_4\left(g\right)+2O_2\left(g\right)\to {\text{CO}}_2\left(g\right)+2{\text{H}}_{2}O\left(g\right) \end{gathered}$$

Next, multiply the second reaction by 2:

$$\begin{gathered} 1.2{\text{CO}}_2\left(g\right)+{\text{H}}_{2}O\left(g\right)\to {\text{CH}}_2\text{CO}\left(g\right)+2{\text{O}}_2\left(g\right) \\ 2.{\text{CH}}_4\left(g\right)+2{\text{O}}_2\left(g\right)\to {\text{CO}}_2\left(g\right)+2{\text{H}}_2\text{O}\left(g\right)/\times 2 \\ 1.2{\text{CO}}_2\left(g\right)+{\text{H}}_2\left(g\right)\to {\text{CH}}_2\text{CO}\left(g\right)+2{\text{O}}_2\left(g\right) \\ 2.2{\text{CH}}_4\left(g\right)+4{\text{O}}_2\left(g\right)\to 2{\text{CO}}_2\left(g\right)+4{\text{H}}_2\left(g\right) \end{gathered}$$

Add equation 1 and 2

As it can be seen by sum up these reactions get the needed reaction:

1. $2{\text{CO}}_2\left(g\right)+{\text{H}}_2\text{O}\left(g\right)\to {\text{CH}}_2\text{CO}\left(g\right)+2{\text{O}}_2\left(g\right)+2.2{\text{CH}}_4\left(g\right)+4{\text{O}}_2\left(g\right)\to 2{\text{CO}}_2\left(g\right)+4{\text{H}}_{2}O\left(g\right)$
2. $2{\text{CH}}_4\left(g\right)+2{\text{O}}_2\left(g\right)\to {\text{CH}}_2\text{CO}\left(g\right)+3{\text{H}}_{2}O\left(g\right)$

Calculate change of heat

The enthalpy of this reaction is a combination of the 2 enthalpies.

The same combination is used to get the reaction.

Now, change of heat is determined with the help of formula $\Delta H=-\Delta H_1+2\times \Delta H_2$.

Put the value of given data in above equation.

$$\begin{gathered} \Delta H=-(-981.1)+2\times (-802.3) \\ \Delta H=-623.5\text{kJ} \end{gathered}$$